Merged branch 'dev_native' into lm_sla_supports_auto

Added igl library files

src/igl/copyleft/README.md

@@ -0,0 +1,14 @@
+## IGL copyleft subdirectory
+
+Functions in the `include/igl/copyleft/` subdirectory are in the
+`igl::copyleft::` namespace to indicate that they are under a more aggressive
+[copyleft](https://en.wikipedia.org/wiki/Copyleft) than
+[MPL2](https://en.wikipedia.org/wiki/Mozilla_Public_License) used for the main
+`include/igl` directory and `igl::` namespace. Most notably, this subdirectory
+includes code that is under
+[GPL](https://en.wikipedia.org/wiki/GNU_General_Public_License).
+
+Typically a company planning on developing software without releasing its
+source code will avoid or purchase licenses for such dependencies. If you do
+obtain such a license for the dependencies employed here, you are free to use
+the libigl functions here as per their MPL2 license.

src/igl/copyleft/cgal/BinaryWindingNumberOperations.h

@@ -0,0 +1,167 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+//
+#ifndef IGL_COPYLEFT_CGAL_BINARY_WINDING_NUMBER_OPERATIONS_H
+#define IGL_COPYLEFT_CGAL_BINARY_WINDING_NUMBER_OPERATIONS_H
+
+#include <stdexcept>
+#include "../../igl_inline.h"
+#include "../../MeshBooleanType.h"
+#include <Eigen/Core>
+
+// TODO: This is not written according to libigl style. These should be
+// function handles.
+//
+// Why is this templated on DerivedW
+//
+// These are all generalized to n-ary operations
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      template <igl::MeshBooleanType Op>
+      class BinaryWindingNumberOperations {
+        public:
+          template<typename DerivedW>
+            typename DerivedW::Scalar operator()(
+                const Eigen::PlainObjectBase<DerivedW>& /*win_nums*/) const {
+              throw (std::runtime_error("not implemented!"));
+            }
+      };
+
+      // A ∪ B ∪ ... ∪ Z
+      template <>
+      class BinaryWindingNumberOperations<MESH_BOOLEAN_TYPE_UNION> {
+        public:
+          template<typename DerivedW>
+          typename DerivedW::Scalar operator()(
+              const Eigen::PlainObjectBase<DerivedW>& win_nums) const 
+          {
+            for(int i = 0;i<win_nums.size();i++)
+            {
+              if(win_nums(i) > 0) return true;
+            }
+            return false;
+          }
+      };
+
+      // A ∩ B ∩ ... ∩ Z
+      template <>
+      class BinaryWindingNumberOperations<MESH_BOOLEAN_TYPE_INTERSECT> {
+        public:
+          template<typename DerivedW>
+          typename DerivedW::Scalar operator()(
+              const Eigen::PlainObjectBase<DerivedW>& win_nums) const 
+          {
+            for(int i = 0;i<win_nums.size();i++)
+            {
+              if(win_nums(i)<=0) return false;
+            }
+            return true;
+          }
+      };
+
+      // A \ B \ ... \ Z = A \ (B ∪ ... ∪ Z)
+      template <>
+      class BinaryWindingNumberOperations<MESH_BOOLEAN_TYPE_MINUS> {
+        public:
+          template<typename DerivedW>
+          typename DerivedW::Scalar operator()(
+              const Eigen::PlainObjectBase<DerivedW>& win_nums) const 
+          {
+            assert(win_nums.size()>1);
+            // Union of objects 1 through n-1
+            bool union_rest = false;
+            for(int i = 1;i<win_nums.size();i++)
+            {
+              union_rest = union_rest || win_nums(i) > 0;
+              if(union_rest) break;
+            }
+            // Must be in object 0 and not in union of objects 1 through n-1
+            return win_nums(0) > 0 && !union_rest;
+          }
+      };
+
+      // A ∆ B ∆ ... ∆ Z  (equivalent to set inside odd number of objects)
+      template <>
+      class BinaryWindingNumberOperations<MESH_BOOLEAN_TYPE_XOR> {
+        public:
+          template<typename DerivedW>
+          typename DerivedW::Scalar operator()(
+              const Eigen::PlainObjectBase<DerivedW>& win_nums) const 
+          {
+            // If inside an odd number of objects
+            int count = 0;
+            for(int i = 0;i<win_nums.size();i++)
+            {
+              if(win_nums(i) > 0) count++;
+            }
+            return count % 2 == 1;
+          }
+      };
+
+      template <>
+      class BinaryWindingNumberOperations<MESH_BOOLEAN_TYPE_RESOLVE> {
+        public:
+          template<typename DerivedW>
+            typename DerivedW::Scalar operator()(
+                const Eigen::PlainObjectBase<DerivedW>& /*win_nums*/) const {
+              return true;
+            }
+      };
+
+      typedef BinaryWindingNumberOperations<MESH_BOOLEAN_TYPE_UNION> BinaryUnion;
+      typedef BinaryWindingNumberOperations<MESH_BOOLEAN_TYPE_INTERSECT> BinaryIntersect;
+      typedef BinaryWindingNumberOperations<MESH_BOOLEAN_TYPE_MINUS> BinaryMinus;
+      typedef BinaryWindingNumberOperations<MESH_BOOLEAN_TYPE_XOR> BinaryXor;
+      typedef BinaryWindingNumberOperations<MESH_BOOLEAN_TYPE_RESOLVE> BinaryResolve;
+
+      enum KeeperType {
+        KEEP_INSIDE,
+        KEEP_ALL
+      };
+
+      template<KeeperType T>
+      class WindingNumberFilter {
+        public:
+          template<typename DerivedW>
+            short operator()(
+                const Eigen::PlainObjectBase<DerivedW>& /*win_nums*/) const {
+              throw std::runtime_error("Not implemented");
+            }
+      };
+
+      template<>
+      class WindingNumberFilter<KEEP_INSIDE> {
+        public:
+          template<typename T>
+          short operator()(T out_w, T in_w) const {
+            if (in_w > 0 && out_w <= 0) return 1;
+            else if (in_w <= 0 && out_w > 0) return -1;
+            else return 0;
+          }
+      };
+
+      template<>
+      class WindingNumberFilter<KEEP_ALL> {
+        public:
+          template<typename T>
+            short operator()(T /*out_w*/, T /*in_w*/) const {
+              return 1;
+            }
+      };
+
+      typedef WindingNumberFilter<KEEP_INSIDE> KeepInside;
+      typedef WindingNumberFilter<KEEP_ALL> KeepAll;
+    }
+  }
+}
+
+#endif

src/igl/copyleft/cgal/CGAL_includes.hpp

@@ -0,0 +1,50 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_CGAL_INCLUDES_H
+#define IGL_CGAL_INCLUDES_H
+
+// This causes unknown bugs during intersection meshing:
+//// http://www.alecjacobson.com/weblog/?p=4291
+//#define CGAL_INTERSECTION_VERSION 1
+// Use this instead to mute errors resulting from bad CGAL assertions
+#define CGAL_KERNEL_NO_ASSERTIONS
+// Triangle triangle intersection
+#include <CGAL/intersections.h>
+// THIS CANNOT BE INCLUDED IN THE SAME FILE AS <CGAL/intersections.h>
+// #include <CGAL/Boolean_set_operations_2.h>
+
+// Constrained Delaunay Triangulation types
+#include <CGAL/Constrained_Delaunay_triangulation_2.h>
+#include <CGAL/Constrained_triangulation_plus_2.h>
+
+// Axis-align boxes for all-pairs self-intersection detection
+#include <CGAL/point_generators_3.h>
+#include <CGAL/Bbox_3.h>
+#include <CGAL/box_intersection_d.h>
+#include <CGAL/function_objects.h>
+#include <CGAL/Join_input_iterator.h>
+#include <CGAL/algorithm.h>
+#include <vector>
+
+// Axis-aligned bounding box tree for tet tri intersection
+#include <CGAL/AABB_tree.h>
+#include <CGAL/AABB_traits.h>
+#include <CGAL/AABB_triangle_primitive.h>
+
+// Boolean operations
+#include <CGAL/Polyhedron_3.h>
+// Is this actually used?
+//#include <CGAL/Nef_polyhedron_3.h>
+
+// Delaunay Triangulation in 3D
+#include <CGAL/Delaunay_triangulation_3.h>
+
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+
+#endif

src/igl/copyleft/cgal/CSGTree.h

@@ -0,0 +1,189 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_CSG_TREE_H
+#define IGL_COPYLEFT_CGAL_CSG_TREE_H
+
+#include "../../MeshBooleanType.h"
+#include "string_to_mesh_boolean_type.h"
+#include "mesh_boolean.h"
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/number_utils.h>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Class for defining and computing a constructive solid geometry result
+      // out of a tree of boolean operations on "solid" triangle meshes.
+      //
+      //template <typename DerivedF>
+      class CSGTree
+      {
+        public:
+          typedef CGAL::Epeck::FT ExactScalar;
+          //typedef Eigen::PlainObjectBase<DerivedF> POBF;
+          typedef Eigen::MatrixXi POBF;
+          typedef POBF::Index FIndex;
+          typedef Eigen::Matrix<ExactScalar,Eigen::Dynamic,3> MatrixX3E;
+          typedef Eigen::Matrix<FIndex,Eigen::Dynamic,1> VectorJ;
+        private:
+          // Resulting mesh
+          MatrixX3E m_V;
+          POBF m_F;
+          VectorJ m_J;
+          // Number of birth faces in A + those in B. I.e. sum of original "leaf"
+          // faces involved in result.
+          size_t m_number_of_birth_faces;
+        public:
+          CSGTree()
+          {
+          }
+          //typedef Eigen::MatrixXd MatrixX3E;
+          //typedef Eigen::MatrixXi POBF;
+          // http://stackoverflow.com/a/3279550/148668
+          CSGTree(const CSGTree & other)
+            :
+            // copy things
+            m_V(other.m_V),
+            // This is an issue if m_F is templated
+            // https://forum.kde.org/viewtopic.php?f=74&t=128414
+            m_F(other.m_F),
+            m_J(other.m_J),
+            m_number_of_birth_faces(other.m_number_of_birth_faces)
+          {
+          }
+          // copy-swap idiom
+          friend void swap(CSGTree& first, CSGTree& second)
+          {
+            using std::swap;
+            // swap things
+            swap(first.m_V,second.m_V);
+            // This is an issue if m_F is templated, similar to
+            // https://forum.kde.org/viewtopic.php?f=74&t=128414
+            swap(first.m_F,second.m_F);
+            swap(first.m_J,second.m_J);
+            swap(first.m_number_of_birth_faces,second.m_number_of_birth_faces);
+          }
+          // Pass-by-value (aka copy)
+          CSGTree& operator=(CSGTree other)
+          {
+            swap(*this,other);
+            return *this;
+          }
+          CSGTree(CSGTree&& other):
+            // initialize via default constructor
+            CSGTree() 
+          {
+            swap(*this,other);
+          }
+          // Construct and compute a boolean operation on existing CSGTree nodes.
+          //
+          // Inputs:
+          //   A  Solid result of previous CSG operation (or identity, see below)
+          //   B  Solid result of previous CSG operation (or identity, see below)
+          //   type  type of mesh boolean to compute 
+          CSGTree(
+            const CSGTree & A,
+            const CSGTree & B,
+            const MeshBooleanType & type)
+          {
+            // conduct boolean operation
+            mesh_boolean(A.V(),A.F(),B.V(),B.F(),type,m_V,m_F,m_J);
+            // reindex m_J
+            std::for_each(m_J.data(),m_J.data()+m_J.size(),
+              [&](typename VectorJ::Scalar & j) -> void
+              {
+                if(j < A.F().rows())
+                {
+                  j = A.J()(j);
+                }else
+                {
+                  assert(j<(A.F().rows()+B.F().rows()));
+                  j = A.number_of_birth_faces()+(B.J()(j-A.F().rows()));
+                }
+              });
+            m_number_of_birth_faces = 
+              A.number_of_birth_faces() + B.number_of_birth_faces();
+          }
+          // Overload using string for type
+          CSGTree(
+            const CSGTree & A,
+            const CSGTree & B,
+            const std::string & s):
+            CSGTree(A,B,string_to_mesh_boolean_type(s))
+          {
+            // do nothing (all done in constructor).
+          }
+          // "Leaf" node with identity operation on assumed "solid" mesh (V,F)
+          //
+          // Inputs:
+          //   V  #V by 3 list of mesh vertices (in any precision, will be
+          //     converted to exact)
+          //   F  #F by 3 list of mesh face indices into V
+          template <typename DerivedV>
+          CSGTree(const Eigen::PlainObjectBase<DerivedV> & V, const POBF & F)//:
+          // Possible Eigen bug:
+          // https://forum.kde.org/viewtopic.php?f=74&t=128414
+            //m_V(V.template cast<ExactScalar>()),m_F(F)
+          {
+            m_V = V.template cast<ExactScalar>();
+            m_F = F;
+            // number of faces
+            m_number_of_birth_faces = m_F.rows();
+            // identity birth index
+            m_J = VectorJ::LinSpaced(
+              m_number_of_birth_faces,0,m_number_of_birth_faces-1);
+          }
+          // Returns reference to resulting mesh vertices m_V in exact scalar
+          // representation
+          const MatrixX3E & V() const
+          {
+            return m_V;
+          }
+          // Returns mesh vertices in the desired output type, casting when
+          // appropriate to floating precision.
+          template <typename DerivedV>
+          DerivedV cast_V() const
+          {
+            DerivedV dV;
+            dV.resize(m_V.rows(),m_V.cols());
+            for(int i = 0;i<m_V.rows();i++)
+            {
+              for(int j = 0;j<m_V.cols();j++)
+              {
+                dV(i,j) = CGAL::to_double(m_V(i,j));
+              }
+            }
+            return dV;
+          }
+          // Returns reference to resulting mesh faces m_F
+          const POBF & F() const
+          {
+            return m_F;
+          }
+          // Returns reference to "birth parents" indices into [F1;F2;...;Fn]
+          // where F1, ... , Fn are the face lists of the leaf ("original") input
+          // meshes.
+          const VectorJ & J() const
+          {
+            return m_J;
+          }
+          // The number of leaf faces = #F1 + #F2 + ... + #Fn
+          const size_t & number_of_birth_faces() const
+          {
+            return m_number_of_birth_faces;
+          }
+      };
+    }
+  }
+}
+
+
+#endif

src/igl/copyleft/cgal/RemeshSelfIntersectionsParam.h

@@ -0,0 +1,36 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_REMESH_SELF_INTERSECTIONS_PARAM_H
+#define IGL_COPYLEFT_CGAL_REMESH_SELF_INTERSECTIONS_PARAM_H
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Optional Parameters
+      //   DetectOnly  Only compute IF, leave VV and FF alone
+      struct RemeshSelfIntersectionsParam
+      {
+        bool detect_only;
+        bool first_only;
+        bool stitch_all;
+        inline RemeshSelfIntersectionsParam(
+          bool _detect_only=false, 
+          bool _first_only=false,
+          bool _stitch_all=false):
+          detect_only(_detect_only),
+          first_only(_first_only),
+          stitch_all(_stitch_all){};
+      };
+    }
+  }
+}
+
+#endif

src/igl/copyleft/cgal/SelfIntersectMesh.h

@@ -0,0 +1,939 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_SELFINTERSECTMESH_H
+#define IGL_COPYLEFT_CGAL_SELFINTERSECTMESH_H
+
+#include "CGAL_includes.hpp"
+#include "RemeshSelfIntersectionsParam.h"
+#include "../../unique.h"
+
+#include <Eigen/Dense>
+#include <list>
+#include <map>
+#include <vector>
+#include <thread>
+#include <mutex>
+
+//#define IGL_SELFINTERSECTMESH_DEBUG
+#ifndef IGL_FIRST_HIT_EXCEPTION
+#define IGL_FIRST_HIT_EXCEPTION 10
+#endif
+
+// The easiest way to keep track of everything is to use a class
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Kernel is a CGAL kernel like:
+      //     CGAL::Exact_predicates_inexact_constructions_kernel
+      // or 
+      //     CGAL::Exact_predicates_exact_constructions_kernel
+    
+      template <
+        typename Kernel,
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedVV,
+        typename DerivedFF,
+        typename DerivedIF,
+        typename DerivedJ,
+        typename DerivedIM>
+      class SelfIntersectMesh
+      {
+        typedef 
+          SelfIntersectMesh<
+          Kernel,
+          DerivedV,
+          DerivedF,
+          DerivedVV,
+          DerivedFF,
+          DerivedIF,
+          DerivedJ,
+          DerivedIM> Self;
+        public:
+          // 3D Primitives
+          typedef CGAL::Point_3<Kernel>    Point_3;
+          typedef CGAL::Segment_3<Kernel>  Segment_3; 
+          typedef CGAL::Triangle_3<Kernel> Triangle_3; 
+          typedef CGAL::Plane_3<Kernel>    Plane_3;
+          typedef CGAL::Tetrahedron_3<Kernel> Tetrahedron_3; 
+          // 2D Primitives
+          typedef CGAL::Point_2<Kernel>    Point_2;
+          typedef CGAL::Segment_2<Kernel>  Segment_2; 
+          typedef CGAL::Triangle_2<Kernel> Triangle_2; 
+          // 2D Constrained Delaunay Triangulation types
+          typedef CGAL::Exact_intersections_tag Itag;
+          // Axis-align boxes for all-pairs self-intersection detection
+          typedef std::vector<Triangle_3> Triangles;
+          typedef typename Triangles::iterator TrianglesIterator;
+          typedef typename Triangles::const_iterator TrianglesConstIterator;
+          typedef 
+            CGAL::Box_intersection_d::Box_with_handle_d<double,3,TrianglesIterator> 
+            Box;
+    
+          // Input mesh
+          const Eigen::MatrixBase<DerivedV> & V;
+          const Eigen::MatrixBase<DerivedF> & F;
+          // Number of self-intersecting triangle pairs
+          typedef typename DerivedF::Index Index;
+          Index count;
+          typedef std::vector<std::pair<Index, CGAL::Object>> ObjectList;
+          // Using a vector here makes this **not** output sensitive
+          Triangles T;
+          typedef std::vector<Index> IndexList;
+          IndexList lIF;
+          // #F-long list of faces with intersections mapping to the order in
+          // which they were first found
+          std::map<Index,ObjectList> offending;
+          // Make a short name for the edge map's key
+          typedef std::pair<Index,Index> EMK;
+          // Make a short name for the type stored at each edge, the edge map's
+          // value
+          typedef std::vector<Index> EMV;
+          // Make a short name for the edge map
+          typedef std::map<EMK,EMV> EdgeMap;
+          // Maps edges of offending faces to all incident offending faces
+          std::vector<std::pair<TrianglesIterator, TrianglesIterator> >
+              candidate_triangle_pairs;
+
+        public:
+          RemeshSelfIntersectionsParam params;
+        public:
+          // Constructs (VV,FF) a new mesh with self-intersections of (V,F)
+          // subdivided
+          //
+          // See also: remesh_self_intersections.h
+          inline SelfIntersectMesh(
+              const Eigen::MatrixBase<DerivedV> & V,
+              const Eigen::MatrixBase<DerivedF> & F,
+              const RemeshSelfIntersectionsParam & params,
+              Eigen::PlainObjectBase<DerivedVV> & VV,
+              Eigen::PlainObjectBase<DerivedFF> & FF,
+              Eigen::PlainObjectBase<DerivedIF> & IF,
+              Eigen::PlainObjectBase<DerivedJ> & J,
+              Eigen::PlainObjectBase<DerivedIM> & IM);
+        private:
+          // Helper function to mark a face as offensive
+          //
+          // Inputs:
+          //   f  index of face in F
+          inline void mark_offensive(const Index f);
+          // Helper function to count intersections between faces
+          //
+          // Input:
+          //   fa  index of face A in F
+          //   fb  index of face B in F
+          inline void count_intersection( const Index fa, const Index fb);
+          // Helper function for box_intersect. Intersect two triangles A and B,
+          // append the intersection object (point,segment,triangle) to a running
+          // list for A and B
+          //
+          // Inputs:
+          //   A  triangle in 3D
+          //   B  triangle in 3D
+          //   fa  index of A in F (and key into offending)
+          //   fb  index of B in F (and key into offending)
+          // Returns true only if A intersects B
+          //
+          inline bool intersect(
+              const Triangle_3 & A, 
+              const Triangle_3 & B, 
+              const Index fa,
+              const Index fb);
+          // Helper function for box_intersect. In the case where A and B have
+          // already been identified to share a vertex, then we only want to
+          // add possible segment intersections. Assumes truly duplicate
+          // triangles are not given as input
+          //
+          // Inputs:
+          //   A  triangle in 3D
+          //   B  triangle in 3D
+          //   fa  index of A in F (and key into offending)
+          //   fb  index of B in F (and key into offending)
+          //   va  index of shared vertex in A (and key into offending)
+          //   vb  index of shared vertex in B (and key into offending)
+          //   Returns true if intersection (besides shared point)
+          //
+          inline bool single_shared_vertex(
+              const Triangle_3 & A,
+              const Triangle_3 & B,
+              const Index fa,
+              const Index fb,
+              const Index va,
+              const Index vb);
+          // Helper handling one direction
+          inline bool single_shared_vertex(
+              const Triangle_3 & A,
+              const Triangle_3 & B,
+              const Index fa,
+              const Index fb,
+              const Index va);
+          // Helper function for box_intersect. In the case where A and B have
+          // already been identified to share two vertices, then we only want
+          // to add a possible coplanar (Triangle) intersection. Assumes truly
+          // degenerate facets are not givin as input.
+          inline bool double_shared_vertex(
+              const Triangle_3 & A,
+              const Triangle_3 & B,
+              const Index fa,
+              const Index fb,
+              const std::vector<std::pair<Index,Index> > shared);
+    
+        public:
+          // Callback function called during box self intersections test. Means
+          // boxes a and b intersect. This method then checks if the triangles
+          // in each box intersect and if so, then processes the intersections
+          //
+          // Inputs:
+          //   a  box containing a triangle
+          //   b  box containing a triangle
+          inline void box_intersect(const Box& a, const Box& b);
+          inline void process_intersecting_boxes();
+        public:
+          // Getters:
+          //const IndexList& get_lIF() const{ return lIF;}
+          static inline void box_intersect_static(
+            SelfIntersectMesh * SIM, 
+            const Box &a, 
+            const Box &b);
+        private:
+          std::mutex m_offending_lock;
+      };
+    }
+  }
+}
+
+// Implementation
+
+#include "mesh_to_cgal_triangle_list.h"
+#include "remesh_intersections.h"
+
+#include "../../REDRUM.h"
+#include "../../get_seconds.h"
+#include "../../C_STR.h"
+
+
+#include <functional>
+#include <algorithm>
+#include <exception>
+#include <cassert>
+#include <iostream>
+
+// References:
+// http://minregret.googlecode.com/svn/trunk/skyline/src/extern/CGAL-3.3.1/examples/Polyhedron/polyhedron_self_intersection.cpp
+// http://www.cgal.org/Manual/3.9/examples/Boolean_set_operations_2/do_intersect.cpp
+
+// Q: Should we be using CGAL::Polyhedron_3?
+// A: No! Input is just a list of unoriented triangles. Polyhedron_3 requires
+// a 2-manifold.
+// A: But! It seems we could use CGAL::Triangulation_3. Though it won't be easy
+// to take advantage of functions like insert_in_facet because we want to
+// constrain segments. Hmmm. Actually Triangulation_3 doesn't look right...
+
+// CGAL's box_self_intersection_d uses C-style function callbacks without
+// userdata. This is a leapfrog method for calling a member function. It should
+// be bound as if the prototype was:
+//   static void box_intersect(const Box &a, const Box &b)
+// using boost:
+//  boost::function<void(const Box &a,const Box &b)> cb
+//    = boost::bind(&::box_intersect, this, _1,_2);
+//   
+template <
+  typename Kernel,
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedVV,
+  typename DerivedFF,
+  typename DerivedIF,
+  typename DerivedJ,
+  typename DerivedIM>
+inline void igl::copyleft::cgal::SelfIntersectMesh<
+  Kernel,
+  DerivedV,
+  DerivedF,
+  DerivedVV,
+  DerivedFF,
+  DerivedIF,
+  DerivedJ,
+  DerivedIM>::box_intersect_static(
+  Self * SIM, 
+  const typename Self::Box &a, 
+  const typename Self::Box &b)
+{
+  SIM->box_intersect(a,b);
+}
+
+template <
+  typename Kernel,
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedVV,
+  typename DerivedFF,
+  typename DerivedIF,
+  typename DerivedJ,
+  typename DerivedIM>
+inline igl::copyleft::cgal::SelfIntersectMesh<
+  Kernel,
+  DerivedV,
+  DerivedF,
+  DerivedVV,
+  DerivedFF,
+  DerivedIF,
+  DerivedJ,
+  DerivedIM>::SelfIntersectMesh(
+  const Eigen::MatrixBase<DerivedV> & V,
+  const Eigen::MatrixBase<DerivedF> & F,
+  const RemeshSelfIntersectionsParam & params,
+  Eigen::PlainObjectBase<DerivedVV> & VV,
+  Eigen::PlainObjectBase<DerivedFF> & FF,
+  Eigen::PlainObjectBase<DerivedIF> & IF,
+  Eigen::PlainObjectBase<DerivedJ> & J,
+  Eigen::PlainObjectBase<DerivedIM> & IM):
+  V(V),
+  F(F),
+  count(0),
+  T(),
+  lIF(),
+  offending(),
+  params(params)
+{
+  using namespace std;
+  using namespace Eigen;
+
+#ifdef IGL_SELFINTERSECTMESH_DEBUG
+  const auto & tictoc = []() -> double
+  {
+    static double t_start = igl::get_seconds();
+    double diff = igl::get_seconds()-t_start;
+    t_start += diff;
+    return diff;
+  };
+  const auto log_time = [&](const std::string& label) -> void{
+    std::cout << "SelfIntersectMesh." << label << ": "
+      << tictoc() << std::endl;
+  };
+  tictoc();
+#endif
+
+  // Compute and process self intersections
+  mesh_to_cgal_triangle_list(V,F,T);
+#ifdef IGL_SELFINTERSECTMESH_DEBUG
+  log_time("convert_to_triangle_list");
+#endif
+  // http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Box_intersection_d/Chapter_main.html#Section_63.5 
+  // Create the corresponding vector of bounding boxes
+  std::vector<Box> boxes;
+  boxes.reserve(T.size());
+  for ( 
+    TrianglesIterator tit = T.begin(); 
+    tit != T.end(); 
+    ++tit)
+  {
+    if (!tit->is_degenerate())
+    {
+      boxes.push_back(Box(tit->bbox(), tit));
+    }
+  }
+  // Leapfrog callback
+  std::function<void(const Box &a,const Box &b)> cb = 
+    std::bind(&box_intersect_static, this, 
+      // Explicitly use std namespace to avoid confusion with boost (who puts
+      // _1 etc. in global namespace)
+      std::placeholders::_1,
+      std::placeholders::_2);
+#ifdef IGL_SELFINTERSECTMESH_DEBUG
+  log_time("box_and_bind");
+#endif
+  // Run the self intersection algorithm with all defaults
+  CGAL::box_self_intersection_d(boxes.begin(), boxes.end(),cb);
+#ifdef IGL_SELFINTERSECTMESH_DEBUG
+  log_time("box_intersection_d");
+#endif
+  try{
+    process_intersecting_boxes();
+  }catch(int e)
+  {
+    // Rethrow if not IGL_FIRST_HIT_EXCEPTION
+    if(e != IGL_FIRST_HIT_EXCEPTION)
+    {
+      throw e;
+    }
+    // Otherwise just fall through
+  }
+#ifdef IGL_SELFINTERSECTMESH_DEBUG
+  log_time("resolve_intersection");
+#endif
+
+  // Convert lIF to Eigen matrix
+  assert(lIF.size()%2 == 0);
+  IF.resize(lIF.size()/2,2);
+  {
+    Index i=0;
+    for(
+      typename IndexList::const_iterator ifit = lIF.begin();
+      ifit!=lIF.end();
+      )
+    {
+      IF(i,0) = (*ifit);
+      ifit++; 
+      IF(i,1) = (*ifit);
+      ifit++;
+      i++;
+    }
+  }
+#ifdef IGL_SELFINTERSECTMESH_DEBUG
+  log_time("store_intersecting_face_pairs");
+#endif
+
+  if(params.detect_only)
+  {
+    return;
+  }
+
+  remesh_intersections(
+    V,F,T,offending,params.stitch_all,VV,FF,J,IM);
+
+#ifdef IGL_SELFINTERSECTMESH_DEBUG
+  log_time("remesh_intersection");
+#endif
+}
+
+
+template <
+  typename Kernel,
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedVV,
+  typename DerivedFF,
+  typename DerivedIF,
+  typename DerivedJ,
+  typename DerivedIM>
+inline void igl::copyleft::cgal::SelfIntersectMesh<
+  Kernel,
+  DerivedV,
+  DerivedF,
+  DerivedVV,
+  DerivedFF,
+  DerivedIF,
+  DerivedJ,
+  DerivedIM>::mark_offensive(const Index f)
+{
+  using namespace std;
+  lIF.push_back(f);
+  if(offending.count(f) == 0)
+  {
+    // first time marking, initialize with new id and empty list
+    offending[f] = {};
+  }
+}
+
+template <
+  typename Kernel,
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedVV,
+  typename DerivedFF,
+  typename DerivedIF,
+  typename DerivedJ,
+  typename DerivedIM>
+inline void igl::copyleft::cgal::SelfIntersectMesh<
+  Kernel,
+  DerivedV,
+  DerivedF,
+  DerivedVV,
+  DerivedFF,
+  DerivedIF,
+  DerivedJ,
+  DerivedIM>::count_intersection(
+  const Index fa,
+  const Index fb)
+{
+  std::lock_guard<std::mutex> guard(m_offending_lock);
+  mark_offensive(fa);
+  mark_offensive(fb);
+  this->count++;
+  // We found the first intersection
+  if(params.first_only && this->count >= 1)
+  {
+    throw IGL_FIRST_HIT_EXCEPTION;
+  }
+
+}
+
+template <
+  typename Kernel,
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedVV,
+  typename DerivedFF,
+  typename DerivedIF,
+  typename DerivedJ,
+  typename DerivedIM>
+inline bool igl::copyleft::cgal::SelfIntersectMesh<
+  Kernel,
+  DerivedV,
+  DerivedF,
+  DerivedVV,
+  DerivedFF,
+  DerivedIF,
+  DerivedJ,
+  DerivedIM>::intersect(
+  const Triangle_3 & A, 
+  const Triangle_3 & B, 
+  const Index fa,
+  const Index fb)
+{
+  // Determine whether there is an intersection
+  if(!CGAL::do_intersect(A,B))
+  {
+    return false;
+  }
+  count_intersection(fa,fb);
+  if(!params.detect_only)
+  {
+    // Construct intersection
+    CGAL::Object result = CGAL::intersection(A,B);
+    std::lock_guard<std::mutex> guard(m_offending_lock);
+    offending[fa].push_back({fb, result});
+    offending[fb].push_back({fa, result});
+  }
+  return true;
+}
+
+template <
+  typename Kernel,
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedVV,
+  typename DerivedFF,
+  typename DerivedIF,
+  typename DerivedJ,
+  typename DerivedIM>
+inline bool igl::copyleft::cgal::SelfIntersectMesh<
+  Kernel,
+  DerivedV,
+  DerivedF,
+  DerivedVV,
+  DerivedFF,
+  DerivedIF,
+  DerivedJ,
+  DerivedIM>::single_shared_vertex(
+  const Triangle_3 & A,
+  const Triangle_3 & B,
+  const Index fa,
+  const Index fb,
+  const Index va,
+  const Index vb)
+{
+  if(single_shared_vertex(A,B,fa,fb,va))
+  {
+    return true;
+  }
+  return single_shared_vertex(B,A,fb,fa,vb);
+}
+
+template <
+  typename Kernel,
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedVV,
+  typename DerivedFF,
+  typename DerivedIF,
+  typename DerivedJ,
+  typename DerivedIM>
+inline bool igl::copyleft::cgal::SelfIntersectMesh<
+  Kernel,
+  DerivedV,
+  DerivedF,
+  DerivedVV,
+  DerivedFF,
+  DerivedIF,
+  DerivedJ,
+  DerivedIM>::single_shared_vertex(
+  const Triangle_3 & A,
+  const Triangle_3 & B,
+  const Index fa,
+  const Index fb,
+  const Index va)
+{
+  // This was not a good idea. It will not handle coplanar triangles well.
+  using namespace std;
+  Segment_3 sa(
+    A.vertex((va+1)%3),
+    A.vertex((va+2)%3));
+
+  if(CGAL::do_intersect(sa,B))
+  {
+    // can't put count_intersection(fa,fb) here since we use intersect below
+    // and then it will be counted twice.
+    if(params.detect_only)
+    {
+      count_intersection(fa,fb);
+      return true;
+    }
+    CGAL::Object result = CGAL::intersection(sa,B);
+    if(const Point_3 * p = CGAL::object_cast<Point_3 >(&result))
+    {
+      // Single intersection --> segment from shared point to intersection
+      CGAL::Object seg = CGAL::make_object(Segment_3(
+        A.vertex(va),
+        *p));
+      count_intersection(fa,fb);
+      std::lock_guard<std::mutex> guard(m_offending_lock);
+      offending[fa].push_back({fb, seg});
+      offending[fb].push_back({fa, seg});
+      return true;
+    }else if(CGAL::object_cast<Segment_3 >(&result))
+    {
+      // Need to do full test. Intersection could be a general poly.
+      bool test = intersect(A,B,fa,fb);
+      ((void)test);
+      assert(test && "intersect should agree with do_intersect");
+      return true;
+    }else
+    {
+      cerr<<REDRUM("Segment ∩ triangle neither point nor segment?")<<endl;
+      assert(false);
+    }
+  }
+
+  return false;
+}
+
+
+template <
+  typename Kernel,
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedVV,
+  typename DerivedFF,
+  typename DerivedIF,
+  typename DerivedJ,
+  typename DerivedIM>
+inline bool igl::copyleft::cgal::SelfIntersectMesh<
+  Kernel,
+  DerivedV,
+  DerivedF,
+  DerivedVV,
+  DerivedFF,
+  DerivedIF,
+  DerivedJ,
+  DerivedIM>::double_shared_vertex(
+  const Triangle_3 & A,
+  const Triangle_3 & B,
+  const Index fa,
+  const Index fb,
+  const std::vector<std::pair<Index,Index> > shared)
+{
+  using namespace std;
+
+  // must be co-planar
+  if(
+    A.supporting_plane() != B.supporting_plane() &&
+    A.supporting_plane() != B.supporting_plane().opposite())
+  {
+    return false;
+  }
+  // Since A and B are non-degenerate the intersection must be a polygon
+  // (triangle). Either
+  //   - the vertex of A (B) opposite the shared edge of lies on B (A), or
+  //   - an edge of A intersects and edge of B without sharing a vertex
+  //
+  // Determine if the vertex opposite edge (a0,a1) in triangle A lies in
+  // (intersects) triangle B
+  const auto & opposite_point_inside = [](
+    const Triangle_3 & A, const Index a0, const Index a1, const Triangle_3 & B) 
+    -> bool
+  {
+    // get opposite index
+    Index a2 = -1;
+    for(int c = 0;c<3;c++)
+    {
+      if(c != a0 && c != a1)
+      {
+        a2 = c;
+        break;
+      }
+    }
+    assert(a2 != -1);
+    bool ret = CGAL::do_intersect(A.vertex(a2),B);
+    return ret;
+  };
+
+  // Determine if edge opposite vertex va in triangle A intersects edge
+  // opposite vertex vb in triangle B.
+  const auto & opposite_edges_intersect = [](
+    const Triangle_3 & A, const Index va,
+    const Triangle_3 & B, const Index vb) -> bool
+  {
+    Segment_3 sa( A.vertex((va+1)%3), A.vertex((va+2)%3));
+    Segment_3 sb( B.vertex((vb+1)%3), B.vertex((vb+2)%3));
+    bool ret = CGAL::do_intersect(sa,sb);
+    return ret;
+  };
+
+  if( 
+    !opposite_point_inside(A,shared[0].first,shared[1].first,B) &&
+    !opposite_point_inside(B,shared[0].second,shared[1].second,A) &&
+    !opposite_edges_intersect(A,shared[0].first,B,shared[1].second) && 
+    !opposite_edges_intersect(A,shared[1].first,B,shared[0].second))
+  {
+    return false;
+  }
+
+  // there is an intersection indeed
+  count_intersection(fa,fb);
+  if(params.detect_only)
+  {
+    return true;
+  }
+  // Construct intersection
+  try
+  {
+    // This can fail for Epick but not Epeck
+    CGAL::Object result = CGAL::intersection(A,B);
+    if(!result.empty())
+    {
+      if(CGAL::object_cast<Segment_3 >(&result))
+      {
+        // not coplanar
+        assert(false && 
+          "Co-planar non-degenerate triangles should intersect over triangle");
+        return false;
+      } else if(CGAL::object_cast<Point_3 >(&result))
+      {
+        // this "shouldn't" happen but does for inexact
+        assert(false && 
+          "Co-planar non-degenerate triangles should intersect over triangle");
+        return false;
+      } else
+      {
+        // Triangle object
+        std::lock_guard<std::mutex> guard(m_offending_lock);
+        offending[fa].push_back({fb, result});
+        offending[fb].push_back({fa, result});
+        return true;
+      }
+    }else
+    {
+      // CGAL::intersection is disagreeing with do_intersect
+      assert(false && "CGAL::intersection should agree with predicate tests");
+      return false;
+    }
+  }catch(...)
+  {
+    // This catches some cgal assertion:
+    //     CGAL error: assertion violation!
+    //     Expression : is_finite(d)
+    //     File       : /opt/local/include/CGAL/GMP/Gmpq_type.h
+    //     Line       : 132
+    //     Explanation: 
+    // But only if NDEBUG is not defined, otherwise there's an uncaught
+    // "Floating point exception: 8" SIGFPE
+    return false;
+  }
+  // No intersection.
+  return false;
+}
+
+template <
+  typename Kernel,
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedVV,
+  typename DerivedFF,
+  typename DerivedIF,
+  typename DerivedJ,
+  typename DerivedIM>
+inline void igl::copyleft::cgal::SelfIntersectMesh<
+  Kernel,
+  DerivedV,
+  DerivedF,
+  DerivedVV,
+  DerivedFF,
+  DerivedIF,
+  DerivedJ,
+  DerivedIM>::box_intersect(
+  const Box& a, 
+  const Box& b)
+{
+  candidate_triangle_pairs.push_back({a.handle(), b.handle()});
+}
+
+template <
+  typename Kernel,
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedVV,
+  typename DerivedFF,
+  typename DerivedIF,
+  typename DerivedJ,
+  typename DerivedIM>
+inline void igl::copyleft::cgal::SelfIntersectMesh<
+  Kernel,
+  DerivedV,
+  DerivedF,
+  DerivedVV,
+  DerivedFF,
+  DerivedIF,
+  DerivedJ,
+  DerivedIM>::process_intersecting_boxes()
+{
+  std::vector<std::mutex> triangle_locks(T.size());
+  std::vector<std::mutex> vertex_locks(V.rows());
+  std::mutex index_lock;
+  std::mutex exception_mutex;
+  bool exception_fired = false;
+  int exception = -1;
+  auto process_chunk = 
+    [&](
+      const size_t first, 
+      const size_t last) -> void
+  {
+    try
+    {
+      assert(last >= first);
+
+      for (size_t i=first; i<last; i++) 
+      {
+        if(exception_fired) return;
+        Index fa=T.size(), fb=T.size();
+        {
+          // Before knowing which triangles are involved, we need to lock
+          // everything to prevent race condition in updating reference
+          // counters.
+          std::lock_guard<std::mutex> guard(index_lock);
+          const auto& tri_pair = candidate_triangle_pairs[i];
+          fa = tri_pair.first - T.begin();
+          fb = tri_pair.second - T.begin();
+        }
+        assert(fa < T.size());
+        assert(fb < T.size());
+
+        // Lock triangles
+        std::lock_guard<std::mutex> guard_A(triangle_locks[fa]);
+        std::lock_guard<std::mutex> guard_B(triangle_locks[fb]);
+
+        // Lock vertices
+        std::list<std::lock_guard<std::mutex> > guard_vertices;
+        {
+          std::vector<typename DerivedF::Scalar> unique_vertices;
+          std::vector<size_t> tmp1, tmp2;
+          igl::unique({F(fa,0), F(fa,1), F(fa,2), F(fb,0), F(fb,1), F(fb,2)},
+              unique_vertices, tmp1, tmp2);
+          std::for_each(unique_vertices.begin(), unique_vertices.end(),
+              [&](const typename DerivedF::Scalar& vi) {
+              guard_vertices.emplace_back(vertex_locks[vi]);
+              });
+        }
+        if(exception_fired) return;
+
+        const Triangle_3& A = T[fa];
+        const Triangle_3& B = T[fb];
+
+        // Number of combinatorially shared vertices
+        Index comb_shared_vertices = 0;
+        // Number of geometrically shared vertices (*not* including
+        // combinatorially shared)
+        Index geo_shared_vertices = 0;
+        // Keep track of shared vertex indices
+        std::vector<std::pair<Index,Index> > shared;
+        Index ea,eb;
+        for(ea=0;ea<3;ea++)
+        {
+          for(eb=0;eb<3;eb++)
+          {
+            if(F(fa,ea) == F(fb,eb))
+            {
+              comb_shared_vertices++;
+              shared.emplace_back(ea,eb);
+            }else if(A.vertex(ea) == B.vertex(eb))
+            {
+              geo_shared_vertices++;
+              shared.emplace_back(ea,eb);
+            }
+          }
+        }
+        const Index total_shared_vertices = 
+          comb_shared_vertices + geo_shared_vertices;
+        if(exception_fired) return;
+
+        if(comb_shared_vertices== 3)
+        {
+          assert(shared.size() == 3);
+          // Combinatorially duplicate face, these should be removed by
+          // preprocessing
+          continue;
+        }
+        if(total_shared_vertices== 3)
+        {
+          assert(shared.size() == 3);
+          // Geometrically duplicate face, these should be removed by
+          // preprocessing
+          continue;
+        }
+        if(total_shared_vertices == 2)
+        {
+          assert(shared.size() == 2);
+          // Q: What about coplanar?
+          //
+          // o    o
+          // |\  /|
+          // | \/ |
+          // | /\ |
+          // |/  \|
+          // o----o
+          double_shared_vertex(A,B,fa,fb,shared);
+          continue;
+        }
+        assert(total_shared_vertices<=1);
+        if(total_shared_vertices==1)
+        {
+          single_shared_vertex(A,B,fa,fb,shared[0].first,shared[0].second);
+        }else
+        {
+          intersect(A,B,fa,fb);
+        }
+      }
+    }catch(int e)
+    {
+      std::lock_guard<std::mutex> exception_lock(exception_mutex);
+      exception_fired = true;
+      exception = e;
+    }
+  };
+  size_t num_threads=0;
+  const size_t hardware_limit = std::thread::hardware_concurrency();
+  if (const char* igl_num_threads = std::getenv("LIBIGL_NUM_THREADS")) {
+    num_threads = atoi(igl_num_threads);
+  }
+  if (num_threads == 0 || num_threads > hardware_limit) {
+    num_threads = hardware_limit;
+  }
+  assert(num_threads > 0);
+  const size_t num_pairs = candidate_triangle_pairs.size();
+  const size_t chunk_size = num_pairs / num_threads;
+  std::vector<std::thread> threads;
+  for (size_t i=0; i<num_threads-1; i++) 
+  {
+    threads.emplace_back(process_chunk, i*chunk_size, (i+1)*chunk_size);
+  }
+  // Do some work in the master thread.
+  process_chunk((num_threads-1)*chunk_size, num_pairs);
+  for (auto& t : threads) 
+  {
+    if (t.joinable()) t.join();
+  }
+  if(exception_fired) throw exception;
+  //process_chunk(0, candidate_triangle_pairs.size());
+}
+
+#endif

src/igl/copyleft/cgal/assign.cpp

@@ -0,0 +1,80 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "assign.h"
+#include "assign_scalar.h"
+
+template <typename DerivedC, typename DerivedD>
+IGL_INLINE void igl::copyleft::cgal::assign(
+  const Eigen::MatrixBase<DerivedC> & C,
+  Eigen::PlainObjectBase<DerivedD> & D)
+{
+  D.resizeLike(C);
+  for(int i = 0;i<C.rows();i++)
+  {
+    for(int j = 0;j<C.cols();j++)
+    {
+      assign_scalar(C(i,j),D(i,j));
+    }
+  }
+}
+
+template <typename ReturnScalar, typename DerivedC>
+IGL_INLINE 
+Eigen::Matrix<
+  ReturnScalar,
+  DerivedC::RowsAtCompileTime, 
+  DerivedC::ColsAtCompileTime, 
+  1,
+  DerivedC::MaxRowsAtCompileTime, 
+  DerivedC::MaxColsAtCompileTime>
+igl::copyleft::cgal::assign(
+  const Eigen::MatrixBase<DerivedC> & C)
+{
+  Eigen::Matrix<
+    ReturnScalar,
+    DerivedC::RowsAtCompileTime, 
+    DerivedC::ColsAtCompileTime, 
+    1,
+    DerivedC::MaxRowsAtCompileTime, 
+    DerivedC::MaxColsAtCompileTime> D;
+  assign(C,D);
+  return D;
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::assign<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<double, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::assign<Eigen::Matrix<double, -1, 3, 1, -1, 3>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 1, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::assign<Eigen::Matrix<float, -1, 3, 1, -1, 3>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::assign<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>,  Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&,   Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::assign<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::assign<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::assign<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::assign<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<float, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<float, -1, 3, 0, -1, 3> >&);
+template void igl::copyleft::cgal::assign<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> >&);
+template void igl::copyleft::cgal::assign<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> >&);
+template void igl::copyleft::cgal::assign<Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+template void igl::copyleft::cgal::assign<Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> >&);
+template void igl::copyleft::cgal::assign<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+template void igl::copyleft::cgal::assign<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> >&);
+template void igl::copyleft::cgal::assign<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<double, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> >&);
+template void igl::copyleft::cgal::assign<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> >&);
+template void igl::copyleft::cgal::assign<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+template void igl::copyleft::cgal::assign<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> >&);
+template void igl::copyleft::cgal::assign<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<double, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> >&);
+template void igl::copyleft::cgal::assign<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3> >&);
+template void igl::copyleft::cgal::assign<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3>, Eigen::Matrix<double, 8, 3, 0, 8, 3> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, 8, 3, 0, 8, 3> >&);
+#endif

src/igl/copyleft/cgal/assign.h

@@ -0,0 +1,42 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_ASSIGN_H
+#define IGL_COPYLEFT_CGAL_ASSIGN_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      template <typename DerivedC, typename DerivedD>
+      IGL_INLINE void assign(
+        const Eigen::MatrixBase<DerivedC> & C,
+        Eigen::PlainObjectBase<DerivedD> & D);
+      template <typename ReturnScalar, typename DerivedC>
+      IGL_INLINE 
+      Eigen::Matrix<
+        ReturnScalar,
+        DerivedC::RowsAtCompileTime, 
+        DerivedC::ColsAtCompileTime, 
+        1,
+        DerivedC::MaxRowsAtCompileTime, 
+        DerivedC::MaxColsAtCompileTime> 
+      assign(
+        const Eigen::MatrixBase<DerivedC> & C);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "assign.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/assign_scalar.cpp

@@ -0,0 +1,136 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "assign_scalar.h"
+
+IGL_INLINE void igl::copyleft::cgal::assign_scalar(
+  const CGAL::Epeck::FT & cgal,
+  CGAL::Epeck::FT & d)
+{
+  d = cgal;
+}
+
+IGL_INLINE void igl::copyleft::cgal::assign_scalar(
+  const CGAL::Epeck::FT & _cgal,
+  double & d)
+{
+  // FORCE evaluation of the exact type otherwise interval might be huge.
+  const CGAL::Epeck::FT cgal = _cgal.exact();
+  const auto interval = CGAL::to_interval(cgal);
+  d = interval.first;
+  do {
+      const double next = nextafter(d, interval.second);
+      if (CGAL::abs(cgal-d) < CGAL::abs(cgal-next)) break;
+      d = next;
+  } while (d < interval.second);
+}
+
+IGL_INLINE void igl::copyleft::cgal::assign_scalar(
+  const CGAL::Epeck::FT & _cgal,
+  float& d)
+{
+  // FORCE evaluation of the exact type otherwise interval might be huge.
+  const CGAL::Epeck::FT cgal = _cgal.exact();
+  const auto interval = CGAL::to_interval(cgal);
+  d = interval.first;
+  do {
+      const float next = nextafter(d, float(interval.second));
+      if (CGAL::abs(cgal-d) < CGAL::abs(cgal-next)) break;
+      d = next;
+  } while (d < float(interval.second));
+}
+
+IGL_INLINE void igl::copyleft::cgal::assign_scalar(
+  const double & c,
+  double & d)
+{
+  d = c;
+}
+
+IGL_INLINE void igl::copyleft::cgal::assign_scalar(
+  const float& c,
+  float& d)
+{
+  d = c;
+}
+
+IGL_INLINE void igl::copyleft::cgal::assign_scalar(
+  const float& c,
+  double& d)
+{
+  d = c;
+}
+
+IGL_INLINE void igl::copyleft::cgal::assign_scalar(
+  const CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt::FT & cgal,
+  CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt::FT & d)
+{
+  d = cgal;
+}
+
+IGL_INLINE void igl::copyleft::cgal::assign_scalar(
+  const CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt::FT & cgal,
+  double & d)
+{
+  const auto interval = CGAL::to_interval(cgal);
+  d = interval.first;
+  do {
+      const double next = nextafter(d, interval.second);
+      if (CGAL::abs(cgal-d) < CGAL::abs(cgal-next)) break;
+      d = next;
+  } while (d < interval.second);
+}
+
+IGL_INLINE void igl::copyleft::cgal::assign_scalar(
+  const CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt::FT & cgal,
+  float& d)
+{
+  const auto interval = CGAL::to_interval(cgal);
+  d = interval.first;
+  do {
+      const float next = nextafter(d, float(interval.second));
+      if (CGAL::abs(cgal-d) < CGAL::abs(cgal-next)) break;
+      d = next;
+  } while (d < float(interval.second));
+}
+
+#ifndef WIN32
+
+IGL_INLINE void igl::copyleft::cgal::assign_scalar(
+  const CGAL::Simple_cartesian<mpq_class>::FT & cgal,
+  CGAL::Simple_cartesian<mpq_class>::FT & d)
+{
+  d = cgal;
+}
+
+IGL_INLINE void igl::copyleft::cgal::assign_scalar(
+  const CGAL::Simple_cartesian<mpq_class>::FT & cgal,
+  double & d)
+{
+  const auto interval = CGAL::to_interval(cgal);
+  d = interval.first;
+  do {
+      const double next = nextafter(d, interval.second);
+      if (CGAL::abs(cgal-d) < CGAL::abs(cgal-next)) break;
+      d = next;
+  } while (d < interval.second);
+}
+
+IGL_INLINE void igl::copyleft::cgal::assign_scalar(
+  const CGAL::Simple_cartesian<mpq_class>::FT & cgal,
+  float& d)
+{
+  const auto interval = CGAL::to_interval(cgal);
+  d = interval.first;
+  do {
+      const float next = nextafter(d, float(interval.second));
+      if (CGAL::abs(cgal-d) < CGAL::abs(cgal-next)) break;
+      d = next;
+  } while (d < float(interval.second));
+}
+
+#endif // WIN32

src/igl/copyleft/cgal/assign_scalar.h

@@ -0,0 +1,74 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_ASSIGN_SCALAR_H
+#define IGL_COPYLEFT_CGAL_ASSIGN_SCALAR_H
+#include "../../igl_inline.h"
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_exact_constructions_kernel_with_sqrt.h>
+#ifndef WIN32
+#include <CGAL/gmpxx.h>
+#endif
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Inputs:
+      //   cgal  cgal scalar
+      // Outputs:
+      //   d  output scalar
+      IGL_INLINE void assign_scalar(
+        const CGAL::Epeck::FT & cgal,
+        CGAL::Epeck::FT & d);
+      IGL_INLINE void assign_scalar(
+        const CGAL::Epeck::FT & cgal,
+        double & d);
+      IGL_INLINE void assign_scalar(
+        const CGAL::Epeck::FT & cgal,
+        float& d);
+      IGL_INLINE void assign_scalar(
+        const double & c,
+        double & d);
+      IGL_INLINE void assign_scalar(
+        const float& c,
+        float & d);
+      IGL_INLINE void assign_scalar(
+        const float& c,
+        double& d);
+
+      IGL_INLINE void assign_scalar(
+        const CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt::FT & cgal,
+        CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt::FT & d);
+      IGL_INLINE void assign_scalar(
+        const CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt::FT & cgal,
+        double & d);
+      IGL_INLINE void assign_scalar(
+        const CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt::FT & cgal,
+        float& d);
+
+#ifndef WIN32
+      IGL_INLINE void assign_scalar(
+        const CGAL::Simple_cartesian<mpq_class>::FT & cgal,
+        CGAL::Simple_cartesian<mpq_class>::FT & d);
+      IGL_INLINE void assign_scalar(
+        const CGAL::Simple_cartesian<mpq_class>::FT & cgal,
+        double & d);
+      IGL_INLINE void assign_scalar(
+        const CGAL::Simple_cartesian<mpq_class>::FT & cgal,
+        float& d);
+#endif // WIN32
+
+    }
+  }
+}
+#ifndef IGL_STATIC_LIBRARY
+#  include "assign_scalar.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/barycenter.cpp

@@ -0,0 +1,15 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2017 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "../../barycenter.h"
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#ifdef IGL_STATIC_LIBRARY
+#undef IGL_STATIC_LIBRARY
+#include "../../barycenter.cpp"
+template void igl::barycenter<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> >&);
+#endif

src/igl/copyleft/cgal/cell_adjacency.cpp

@@ -0,0 +1,34 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+//
+
+#include "cell_adjacency.h"
+
+template <typename DerivedC>
+IGL_INLINE void igl::copyleft::cgal::cell_adjacency(
+    const Eigen::PlainObjectBase<DerivedC>& per_patch_cells,
+    const size_t num_cells,
+    std::vector<std::set<std::tuple<typename DerivedC::Scalar, bool, size_t> > >&
+    adjacency_list) {
+
+  const size_t num_patches = per_patch_cells.rows();
+  adjacency_list.resize(num_cells);
+  for (size_t i=0; i<num_patches; i++) {
+    const int positive_cell = per_patch_cells(i,0);
+    const int negative_cell = per_patch_cells(i,1);
+    adjacency_list[positive_cell].emplace(negative_cell, false, i);
+    adjacency_list[negative_cell].emplace(positive_cell, true, i);
+  }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+template void igl::copyleft::cgal::cell_adjacency<Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, unsigned long, std::vector<std::set<std::tuple<Eigen::Matrix<int, -1, -1, 0, -1, -1>::Scalar, bool, unsigned long>, std::less<std::tuple<Eigen::Matrix<int, -1, -1, 0, -1, -1>::Scalar, bool, unsigned long> >, std::allocator<std::tuple<Eigen::Matrix<int, -1, -1, 0, -1, -1>::Scalar, bool, unsigned long> > >, std::allocator<std::set<std::tuple<Eigen::Matrix<int, -1, -1, 0, -1, -1>::Scalar, bool, unsigned long>, std::less<std::tuple<Eigen::Matrix<int, -1, -1, 0, -1, -1>::Scalar, bool, unsigned long> >, std::allocator<std::tuple<Eigen::Matrix<int, -1, -1, 0, -1, -1>::Scalar, bool, unsigned long> > > > >&);
+#ifdef WIN32
+template void igl::copyleft::cgal::cell_adjacency<class Eigen::Matrix<int, -1, -1, 0, -1, -1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, unsigned __int64, class std::vector<class std::set<class std::tuple<int, bool, unsigned __int64>, struct std::less<class std::tuple<int, bool, unsigned __int64>>, class std::allocator<class std::tuple<int, bool, unsigned __int64>>>, class std::allocator<class std::set<class std::tuple<int, bool, unsigned __int64>, struct std::less<class std::tuple<int, bool, unsigned __int64>>, class std::allocator<class std::tuple<int, bool, unsigned __int64>>>>> &);
+#endif
+#endif

src/igl/copyleft/cgal/cell_adjacency.h

@@ -0,0 +1,50 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+//
+#ifndef IGL_COPYLEFT_CGAL_CELL_ADJACENCY_H
+#define IGL_COPYLEFT_CGAL_CELL_ADJACENCY_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <set>
+#include <tuple>
+#include <vector>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Inputs:
+      //   per_patch_cells  #P by 2 list of cell labels on each side of each
+      //                    patch.  Cell labels are assumed to be continuous
+      //                    from 0 to #C.
+      //   num_cells        number of cells.
+      //
+      // Outputs:
+      //   adjacency_list  #C array of list of adjcent cell information.  If
+      //                   cell i and cell j are adjacent via patch x, where i
+      //                   is on the positive side of x, and j is on the
+      //                   negative side.  Then,
+      //                   adjacency_list[i] will contain the entry {j, false, x}
+      //                   and
+      //                   adjacency_list[j] will contain the entry {i, true, x}
+      template < typename DerivedC >
+      IGL_INLINE void cell_adjacency(
+          const Eigen::PlainObjectBase<DerivedC>& per_patch_cells,
+          const size_t num_cells,
+          std::vector<std::set<std::tuple<typename DerivedC::Scalar, bool, size_t> > >&
+          adjacency_list);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "cell_adjacency.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/closest_facet.cpp

@@ -0,0 +1,504 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+//
+#include "closest_facet.h"
+
+#include <vector>
+#include <stdexcept>
+#include <unordered_map>
+
+#include "order_facets_around_edge.h"
+#include "submesh_aabb_tree.h"
+#include "../../vertex_triangle_adjacency.h"
+#include "../../LinSpaced.h"
+//#include "../../writePLY.h"
+
+template<
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedI,
+  typename DerivedP,
+  typename uE2EType,
+  typename DerivedEMAP,
+  typename DerivedR,
+  typename DerivedS >
+IGL_INLINE void igl::copyleft::cgal::closest_facet(
+    const Eigen::PlainObjectBase<DerivedV>& V,
+    const Eigen::PlainObjectBase<DerivedF>& F,
+    const Eigen::PlainObjectBase<DerivedI>& I,
+    const Eigen::PlainObjectBase<DerivedP>& P,
+    const std::vector<std::vector<uE2EType> >& uE2E,
+    const Eigen::PlainObjectBase<DerivedEMAP>& EMAP,
+    Eigen::PlainObjectBase<DerivedR>& R,
+    Eigen::PlainObjectBase<DerivedS>& S)
+{
+
+  typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
+  typedef Kernel::Point_3 Point_3;
+  typedef Kernel::Plane_3 Plane_3;
+  typedef Kernel::Segment_3 Segment_3;
+  typedef Kernel::Triangle_3 Triangle;
+  typedef std::vector<Triangle>::iterator Iterator;
+  typedef CGAL::AABB_triangle_primitive<Kernel, Iterator> Primitive;
+  typedef CGAL::AABB_traits<Kernel, Primitive> AABB_triangle_traits;
+  typedef CGAL::AABB_tree<AABB_triangle_traits> Tree;
+
+  if (F.rows() <= 0 || I.rows() <= 0) {
+    throw std::runtime_error(
+        "Closest facet cannot be computed on empty mesh.");
+  }
+
+  std::vector<std::vector<size_t> > VF, VFi;
+  igl::vertex_triangle_adjacency(V.rows(), F, VF, VFi);
+  std::vector<bool> in_I;
+  std::vector<Triangle> triangles;
+  Tree tree;
+  submesh_aabb_tree(V,F,I,tree,triangles,in_I);
+
+  return closest_facet(
+    V,F,I,P,uE2E,EMAP,VF,VFi,tree,triangles,in_I,R,S);
+}
+
+template<
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedI,
+  typename DerivedP,
+  typename uE2EType,
+  typename DerivedEMAP,
+  typename Kernel,
+  typename DerivedR,
+  typename DerivedS >
+IGL_INLINE void igl::copyleft::cgal::closest_facet(
+    const Eigen::PlainObjectBase<DerivedV>& V,
+    const Eigen::PlainObjectBase<DerivedF>& F,
+    const Eigen::PlainObjectBase<DerivedI>& I,
+    const Eigen::PlainObjectBase<DerivedP>& P,
+    const std::vector<std::vector<uE2EType> >& uE2E,
+    const Eigen::PlainObjectBase<DerivedEMAP>& EMAP,
+    const std::vector<std::vector<size_t> > & VF,
+    const std::vector<std::vector<size_t> > & VFi,
+    const CGAL::AABB_tree<
+      CGAL::AABB_traits<
+        Kernel, 
+        CGAL::AABB_triangle_primitive<
+          Kernel, typename std::vector<
+            typename Kernel::Triangle_3 >::iterator > > > & tree,
+    const std::vector<typename Kernel::Triangle_3 > & triangles,
+    const std::vector<bool> & in_I,
+    Eigen::PlainObjectBase<DerivedR>& R,
+    Eigen::PlainObjectBase<DerivedS>& S)
+{
+  typedef typename Kernel::Point_3 Point_3;
+  typedef typename Kernel::Plane_3 Plane_3;
+  typedef typename Kernel::Segment_3 Segment_3;
+  typedef typename Kernel::Triangle_3 Triangle;
+  typedef typename std::vector<Triangle>::iterator Iterator;
+  typedef typename CGAL::AABB_triangle_primitive<Kernel, Iterator> Primitive;
+  typedef typename CGAL::AABB_traits<Kernel, Primitive> AABB_triangle_traits;
+  typedef typename CGAL::AABB_tree<AABB_triangle_traits> Tree;
+
+  const size_t num_faces = I.rows();
+  if (F.rows() <= 0 || I.rows() <= 0) {
+    throw std::runtime_error(
+        "Closest facet cannot be computed on empty mesh.");
+  }
+
+  auto on_the_positive_side = [&](size_t fid, const Point_3& p) -> bool
+  {
+    const auto& f = F.row(fid).eval();
+    Point_3 v0(V(f[0], 0), V(f[0], 1), V(f[0], 2));
+    Point_3 v1(V(f[1], 0), V(f[1], 1), V(f[1], 2));
+    Point_3 v2(V(f[2], 0), V(f[2], 1), V(f[2], 2));
+    auto ori = CGAL::orientation(v0, v1, v2, p);
+    switch (ori) {
+      case CGAL::POSITIVE:
+        return true;
+      case CGAL::NEGATIVE:
+        return false;
+      case CGAL::COPLANAR:
+        // Warning:
+        // This can only happen if fid contains a boundary edge.
+        // Categorized this ambiguous case as negative side.
+        return false;
+      default:
+        throw std::runtime_error("Unknown CGAL state.");
+    }
+    return false;
+  };
+
+  auto get_orientation = [&](size_t fid, size_t s, size_t d) -> bool 
+  {
+    const auto& f = F.row(fid);
+    if      ((size_t)f[0] == s && (size_t)f[1] == d) return false;
+    else if ((size_t)f[1] == s && (size_t)f[2] == d) return false;
+    else if ((size_t)f[2] == s && (size_t)f[0] == d) return false;
+    else if ((size_t)f[0] == d && (size_t)f[1] == s) return true;
+    else if ((size_t)f[1] == d && (size_t)f[2] == s) return true;
+    else if ((size_t)f[2] == d && (size_t)f[0] == s) return true;
+    else {
+      throw std::runtime_error(
+          "Cannot compute orientation due to incorrect connectivity");
+      return false;
+    }
+  };
+  auto index_to_signed_index = [&](size_t index, bool ori) -> int{
+    return (index+1) * (ori? 1:-1);
+  };
+  //auto signed_index_to_index = [&](int signed_index) -> size_t {
+  //    return abs(signed_index) - 1;
+  //};
+
+  enum ElementType { VERTEX, EDGE, FACE };
+  auto determine_element_type = [&](const Point_3& p, const size_t fid,
+      size_t& element_index) -> ElementType {
+    const auto& tri = triangles[fid];
+    const Point_3 p0 = tri[0];
+    const Point_3 p1 = tri[1];
+    const Point_3 p2 = tri[2];
+
+    if (p == p0) { element_index = 0; return VERTEX; }
+    if (p == p1) { element_index = 1; return VERTEX; }
+    if (p == p2) { element_index = 2; return VERTEX; }
+    if (CGAL::collinear(p0, p1, p)) { element_index = 2; return EDGE; }
+    if (CGAL::collinear(p1, p2, p)) { element_index = 0; return EDGE; }
+    if (CGAL::collinear(p2, p0, p)) { element_index = 1; return EDGE; }
+
+    element_index = 0;
+    return FACE;
+  };
+
+  auto process_edge_case = [&](
+      size_t query_idx,
+      const size_t s, const size_t d,
+      size_t preferred_facet,
+      bool& orientation) -> size_t 
+  {
+    Point_3 query_point(
+      P(query_idx, 0),
+      P(query_idx, 1),
+      P(query_idx, 2));
+
+    size_t corner_idx = std::numeric_limits<size_t>::max();
+    if ((s == F(preferred_facet, 0) && d == F(preferred_facet, 1)) ||
+        (s == F(preferred_facet, 1) && d == F(preferred_facet, 0))) 
+    {
+      corner_idx = 2;
+    } else if ((s == F(preferred_facet, 0) && d == F(preferred_facet, 2)) ||
+        (s == F(preferred_facet, 2) && d == F(preferred_facet, 0))) 
+    {
+      corner_idx = 1;
+    } else if ((s == F(preferred_facet, 1) && d == F(preferred_facet, 2)) ||
+        (s == F(preferred_facet, 2) && d == F(preferred_facet, 1))) 
+    {
+      corner_idx = 0;
+    } else 
+    {
+      std::cerr << "s: " << s << "\t d:" << d << std::endl;
+      std::cerr << F.row(preferred_facet) << std::endl;
+      throw std::runtime_error(
+          "Invalid connectivity, edge does not belong to facet");
+    }
+
+    auto ueid = EMAP(preferred_facet + corner_idx * F.rows());
+    auto eids = uE2E[ueid];
+    std::vector<size_t> intersected_face_indices;
+    for (auto eid : eids) 
+    {
+      const size_t fid = eid % F.rows();
+      if (in_I[fid]) 
+      {
+        intersected_face_indices.push_back(fid);
+      }
+    }
+
+    const size_t num_intersected_faces = intersected_face_indices.size();
+    std::vector<int> intersected_face_signed_indices(num_intersected_faces);
+    std::transform(
+        intersected_face_indices.begin(),
+        intersected_face_indices.end(),
+        intersected_face_signed_indices.begin(),
+        [&](size_t index) {
+        return index_to_signed_index(
+          index, get_orientation(index, s,d));
+        });
+
+    assert(num_intersected_faces >= 1);
+    if (num_intersected_faces == 1) 
+    {
+      // The edge must be a boundary edge.  Thus, the orientation can be
+      // simply determined by checking if the query point is on the
+      // positive side of the facet.
+      const size_t fid = intersected_face_indices[0];
+      orientation = on_the_positive_side(fid, query_point);
+      return fid;
+    }
+
+    Eigen::VectorXi order;
+    DerivedP pivot = P.row(query_idx).eval();
+    igl::copyleft::cgal::order_facets_around_edge(V, F, s, d,
+      intersected_face_signed_indices,
+      pivot, order);
+
+    // Although first and last are equivalent, make the choice based on
+    // preferred_facet.
+    const size_t first = order[0];
+    const size_t last = order[num_intersected_faces-1];
+    if (intersected_face_indices[first] == preferred_facet) {
+      orientation = intersected_face_signed_indices[first] < 0;
+      return intersected_face_indices[first];
+    } else if (intersected_face_indices[last] == preferred_facet) {
+      orientation = intersected_face_signed_indices[last] > 0;
+      return intersected_face_indices[last];
+    } else {
+      orientation = intersected_face_signed_indices[order[0]] < 0;
+      return intersected_face_indices[order[0]];
+    }
+  };
+
+  auto process_face_case = [&](
+      const size_t query_idx, const Point_3& closest_point,
+      const size_t fid, bool& orientation) -> size_t {
+    const auto& f = F.row(I(fid, 0));
+    return process_edge_case(query_idx, f[0], f[1], I(fid, 0), orientation);
+  };
+
+  // Given that the closest point to query point P(query_idx,:) on (V,F(I,:))
+  // is the vertex at V(s,:) which is incident at least on triangle
+  // F(preferred_facet,:), determine a facet incident on V(s,:) that is
+  // _exposed_ to the query point and determine whether that facet is facing
+  // _toward_ or _away_ from the query point.
+  //
+  // Inputs:
+  //   query_idx  index into P of query point
+  //   s  index into V of closest point at vertex
+  //   preferred_facet  facet incident on s
+  // Outputs:
+  //   orientation  whether returned face is facing toward or away from
+  //     query (parity unclear)
+  // Returns face guaranteed to be "exposed" to P(query_idx,:)
+  auto process_vertex_case = [&](
+    const size_t query_idx, 
+    size_t s,
+    size_t preferred_facet, 
+    bool& orientation) -> size_t
+  {
+    const Point_3 query_point(
+        P(query_idx, 0), P(query_idx, 1), P(query_idx, 2));
+    const Point_3 closest_point(V(s, 0), V(s, 1), V(s, 2));
+    std::vector<size_t> adj_faces;
+    std::vector<size_t> adj_face_corners;
+    {
+      // Gather adj faces to s within I.
+      const auto& all_adj_faces = VF[s];
+      const auto& all_adj_face_corners = VFi[s];
+      const size_t num_all_adj_faces = all_adj_faces.size();
+      for (size_t i=0; i<num_all_adj_faces; i++) 
+      {
+        const size_t fid = all_adj_faces[i];
+        // Shouldn't this always be true if I is a full connected component?
+        if (in_I[fid]) 
+        {
+          adj_faces.push_back(fid);
+          adj_face_corners.push_back(all_adj_face_corners[i]);
+        }
+      }
+    }
+    const size_t num_adj_faces = adj_faces.size();
+    assert(num_adj_faces > 0);
+
+    std::set<size_t> adj_vertices_set;
+    std::unordered_multimap<size_t, size_t> v2f;
+    for (size_t i=0; i<num_adj_faces; i++) 
+    {
+      const size_t fid = adj_faces[i];
+      const size_t cid = adj_face_corners[i];
+      const auto& f = F.row(adj_faces[i]);
+      const size_t next = f[(cid+1)%3];
+      const size_t prev = f[(cid+2)%3];
+      adj_vertices_set.insert(next);
+      adj_vertices_set.insert(prev);
+      v2f.insert({{next, fid}, {prev, fid}});
+    }
+    const size_t num_adj_vertices = adj_vertices_set.size();
+    std::vector<size_t> adj_vertices(num_adj_vertices);
+    std::copy(adj_vertices_set.begin(), adj_vertices_set.end(),
+        adj_vertices.begin());
+
+    std::vector<Point_3> adj_points;
+    for (size_t vid : adj_vertices) 
+    {
+      adj_points.emplace_back(V(vid,0), V(vid,1), V(vid,2));
+    }
+
+    // A plane is on the exterior if all adj_points lies on or to
+    // one side of the plane.
+    auto is_on_exterior = [&](const Plane_3& separator) -> bool{
+      size_t positive=0;
+      size_t negative=0;
+      size_t coplanar=0;
+      for (const auto& point : adj_points) {
+        switch(separator.oriented_side(point)) {
+          case CGAL::ON_POSITIVE_SIDE:
+            positive++;
+            break;
+          case CGAL::ON_NEGATIVE_SIDE:
+            negative++;
+            break;
+          case CGAL::ON_ORIENTED_BOUNDARY:
+            coplanar++;
+            break;
+          default:
+            throw "Unknown plane-point orientation";
+        }
+      }
+      auto query_orientation = separator.oriented_side(query_point);
+      if (query_orientation == CGAL::ON_ORIENTED_BOUNDARY &&
+          (positive == 0 && negative == 0)) {
+        // All adj vertices and query point are coplanar.
+        // In this case, all separators are equally valid.
+        return true;
+      } else {
+        bool r = (positive == 0 && query_orientation == CGAL::POSITIVE)
+          || (negative == 0 && query_orientation == CGAL::NEGATIVE);
+        return r;
+      }
+    };
+
+    size_t d = std::numeric_limits<size_t>::max();
+    for (size_t i=0; i<num_adj_vertices; i++) {
+      const size_t vi = adj_vertices[i];
+      for (size_t j=i+1; j<num_adj_vertices; j++) {
+        Plane_3 separator(closest_point, adj_points[i], adj_points[j]);
+        if (separator.is_degenerate()) {
+          continue;
+        }
+        if (is_on_exterior(separator)) {
+          if (!CGAL::collinear(
+                query_point, adj_points[i], closest_point)) {
+            d = vi;
+            break;
+          } else {
+            d = adj_vertices[j];
+            assert(!CGAL::collinear(
+                  query_point, adj_points[j], closest_point));
+            break;
+          }
+        }
+      }
+    }
+    if (d == std::numeric_limits<size_t>::max()) {
+      Eigen::MatrixXd tmp_vertices(V.rows(), V.cols());
+      for (size_t i=0; i<V.rows(); i++) {
+        for (size_t j=0; j<V.cols(); j++) {
+          tmp_vertices(i,j) = CGAL::to_double(V(i,j));
+        }
+      }
+      Eigen::MatrixXi tmp_faces(adj_faces.size(), 3);
+      for (size_t i=0; i<adj_faces.size(); i++) {
+        tmp_faces.row(i) = F.row(adj_faces[i]);
+      }
+      //igl::writePLY("debug.ply", tmp_vertices, tmp_faces, false);
+      throw std::runtime_error("Invalid vertex neighborhood");
+    }
+    const auto itr = v2f.equal_range(d);
+    assert(itr.first != itr.second);
+
+    return process_edge_case(query_idx, s, d, itr.first->second, orientation);
+  };
+
+  const size_t num_queries = P.rows();
+  R.resize(num_queries, 1);
+  S.resize(num_queries, 1);
+  for (size_t i=0; i<num_queries; i++) {
+    const Point_3 query(P(i,0), P(i,1), P(i,2));
+    auto projection = tree.closest_point_and_primitive(query);
+    const Point_3 closest_point = projection.first;
+    size_t fid = projection.second - triangles.begin();
+    bool fid_ori = false;
+
+    // Gether all facets sharing the closest point.
+    typename std::vector<typename Tree::Primitive_id> intersected_faces;
+    tree.all_intersected_primitives(Segment_3(closest_point, query),
+        std::back_inserter(intersected_faces));
+    const size_t num_intersected_faces = intersected_faces.size();
+    std::vector<size_t> intersected_face_indices(num_intersected_faces);
+    std::transform(intersected_faces.begin(),
+        intersected_faces.end(),
+        intersected_face_indices.begin(),
+        [&](const typename Tree::Primitive_id& itr) -> size_t
+        { return I(itr-triangles.begin(), 0); });
+
+    size_t element_index;
+    auto element_type = determine_element_type(closest_point, fid,
+        element_index);
+    switch(element_type) {
+      case VERTEX:
+        {
+          const auto& f = F.row(I(fid, 0));
+          const size_t s = f[element_index];
+          fid = process_vertex_case(i, s, I(fid, 0), fid_ori);
+        }
+        break;
+      case EDGE:
+        {
+          const auto& f = F.row(I(fid, 0));
+          const size_t s = f[(element_index+1)%3];
+          const size_t d = f[(element_index+2)%3];
+          fid = process_edge_case(i, s, d, I(fid, 0), fid_ori);
+        }
+        break;
+      case FACE:
+        {
+          fid = process_face_case(i, closest_point, fid, fid_ori);
+        }
+        break;
+      default:
+        throw std::runtime_error("Unknown element type.");
+    }
+
+
+    R(i,0) = fid;
+    S(i,0) = fid_ori;
+  }
+}
+
+template<
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedP,
+  typename uE2EType,
+  typename DerivedEMAP,
+  typename DerivedR,
+  typename DerivedS >
+IGL_INLINE void igl::copyleft::cgal::closest_facet(
+    const Eigen::PlainObjectBase<DerivedV>& V,
+    const Eigen::PlainObjectBase<DerivedF>& F,
+    const Eigen::PlainObjectBase<DerivedP>& P,
+    const std::vector<std::vector<uE2EType> >& uE2E,
+    const Eigen::PlainObjectBase<DerivedEMAP>& EMAP,
+    Eigen::PlainObjectBase<DerivedR>& R,
+    Eigen::PlainObjectBase<DerivedS>& S) {
+  const size_t num_faces = F.rows();
+  Eigen::VectorXi I = igl::LinSpaced<Eigen::VectorXi>(num_faces, 0, num_faces-1);
+  igl::copyleft::cgal::closest_facet(V, F, I, P, uE2E, EMAP, R, S);
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::closest_facet<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, unsigned long, Eigen::Matrix<int, -1, 1, 0, -1, 1>, CGAL::Epeck, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, std::vector<std::vector<unsigned long, std::allocator<unsigned long> >, std::allocator<std::vector<unsigned long, std::allocator<unsigned long> > > > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, std::vector<std::vector<unsigned long, std::allocator<unsigned long> >, std::allocator<std::vector<unsigned long, std::allocator<unsigned long> > > > const&, std::vector<std::vector<unsigned long, std::allocator<unsigned long> >, std::allocator<std::vector<unsigned long, std::allocator<unsigned long> > > > const&, CGAL::AABB_tree<CGAL::AABB_traits<CGAL::Epeck, CGAL::AABB_triangle_primitive<CGAL::Epeck, std::vector<CGAL::Epeck::Triangle_3, std::allocator<CGAL::Epeck::Triangle_3> >::iterator, CGAL::Boolean_tag<false> > > > const&, std::vector<CGAL::Epeck::Triangle_3, std::allocator<CGAL::Epeck::Triangle_3> > const&, std::vector<bool, std::allocator<bool> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::closest_facet<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, unsigned long, Eigen::Matrix<int, -1, 1, 0, -1, 1>, CGAL::Epeck, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, std::vector<std::vector<unsigned long, std::allocator<unsigned long> >, std::allocator<std::vector<unsigned long, std::allocator<unsigned long> > > > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, std::vector<std::vector<unsigned long, std::allocator<unsigned long> >, std::allocator<std::vector<unsigned long, std::allocator<unsigned long> > > > const&, std::vector<std::vector<unsigned long, std::allocator<unsigned long> >, std::allocator<std::vector<unsigned long, std::allocator<unsigned long> > > > const&, CGAL::AABB_tree<CGAL::AABB_traits<CGAL::Epeck, CGAL::AABB_triangle_primitive<CGAL::Epeck, std::vector<CGAL::Epeck::Triangle_3, std::allocator<CGAL::Epeck::Triangle_3> >::iterator, CGAL::Boolean_tag<false> > > > const&, std::vector<CGAL::Epeck::Triangle_3, std::allocator<CGAL::Epeck::Triangle_3> > const&, std::vector<bool, std::allocator<bool> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::closest_facet<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, unsigned long, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, std::vector<std::vector<unsigned long, std::allocator<unsigned long> >, std::allocator<std::vector<unsigned long, std::allocator<unsigned long> > > > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+#ifdef WIN32
+template void igl::copyleft::cgal::closest_facet<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>, unsigned __int64, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class CGAL::Epeck, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>> const &, class std::vector<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>, class std::allocator<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, class std::vector<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>, class std::allocator<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>>> const &, class std::vector<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>, class std::allocator<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>>> const &, class CGAL::AABB_tree<class CGAL::AABB_traits<class CGAL::Epeck, class CGAL::AABB_triangle_primitive<class CGAL::Epeck, class std::_Vector_iterator<class std::_Vector_val<struct std::_Simple_types<class CGAL::Triangle_3<class CGAL::Epeck>>>>, struct CGAL::Boolean_tag<0>>>> const &, class std::vector<class CGAL::Triangle_3<class CGAL::Epeck>, class std::allocator<class CGAL::Triangle_3<class CGAL::Epeck>>> const &, class std::vector<bool, class std::allocator<bool>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> &);
+template void igl::copyleft::cgal::closest_facet<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, unsigned __int64, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class CGAL::Epeck, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class std::vector<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>, class std::allocator<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, class std::vector<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>, class std::allocator<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>>> const &, class std::vector<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>, class std::allocator<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>>> const &, class CGAL::AABB_tree<class CGAL::AABB_traits<class CGAL::Epeck, class CGAL::AABB_triangle_primitive<class CGAL::Epeck, class std::_Vector_iterator<class std::_Vector_val<struct std::_Simple_types<class CGAL::Triangle_3<class CGAL::Epeck>>>>, struct CGAL::Boolean_tag<0>>>> const &, class std::vector<class CGAL::Triangle_3<class CGAL::Epeck>, class std::allocator<class CGAL::Triangle_3<class CGAL::Epeck>>> const &, class std::vector<bool, class std::allocator<bool>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> &);
+template void igl::copyleft::cgal::closest_facet<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, 3, 1, -1, 3>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, unsigned __int64, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class CGAL::Epeck, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 3, 1, -1, 3>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class std::vector<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>, class std::allocator<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, class std::vector<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>, class std::allocator<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>>> const &, class std::vector<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>, class std::allocator<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>>> const &, class CGAL::AABB_tree<class CGAL::AABB_traits<class CGAL::Epeck, class CGAL::AABB_triangle_primitive<class CGAL::Epeck, class std::_Vector_iterator<class std::_Vector_val<struct std::_Simple_types<class CGAL::Triangle_3<class CGAL::Epeck>>>>, struct CGAL::Boolean_tag<0>>>> const &, class std::vector<class CGAL::Triangle_3<class CGAL::Epeck>, class std::allocator<class CGAL::Triangle_3<class CGAL::Epeck>>> const &, class std::vector<bool, class std::allocator<bool>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> &);
+#endif
+#endif

src/igl/copyleft/cgal/closest_facet.h

@@ -0,0 +1,110 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+//
+#ifndef IGL_COPYLET_CGAL_CLOSEST_FACET_H
+#define IGL_COPYLET_CGAL_CLOSEST_FACET_H
+
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <vector>
+
+#include <CGAL/AABB_tree.h>
+#include <CGAL/AABB_traits.h>
+#include <CGAL/AABB_triangle_primitive.h>
+#include <CGAL/intersections.h>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Determine the closest facet for each of the input points.
+      //
+      // Inputs:
+      //   V  #V by 3 array of vertices.
+      //   F  #F by 3 array of faces.
+      //   I  #I list of triangle indices to consider.
+      //   P  #P by 3 array of query points.
+      //
+      // Outputs:
+      //   R  #P list of closest facet indices.
+      //   S  #P list of bools indicating on which side of the closest facet
+      //      each query point lies.
+      template<
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedI,
+        typename DerivedP,
+        typename uE2EType,
+        typename DerivedEMAP,
+        typename DerivedR,
+        typename DerivedS >
+      IGL_INLINE void closest_facet(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        const Eigen::PlainObjectBase<DerivedI>& I,
+        const Eigen::PlainObjectBase<DerivedP>& P,
+        const std::vector<std::vector<uE2EType> >& uE2E,
+        const Eigen::PlainObjectBase<DerivedEMAP>& EMAP,
+              Eigen::PlainObjectBase<DerivedR>& R,
+              Eigen::PlainObjectBase<DerivedS>& S);
+      template<
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedP,
+        typename uE2EType,
+        typename DerivedEMAP,
+        typename DerivedR,
+        typename DerivedS >
+      IGL_INLINE void closest_facet(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        const Eigen::PlainObjectBase<DerivedP>& P,
+        const std::vector<std::vector<uE2EType> >& uE2E,
+        const Eigen::PlainObjectBase<DerivedEMAP>& EMAP,
+        Eigen::PlainObjectBase<DerivedR>& R,
+        Eigen::PlainObjectBase<DerivedS>& S);
+      template<
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedI,
+        typename DerivedP,
+        typename uE2EType,
+        typename DerivedEMAP,
+        typename Kernel,
+        typename DerivedR,
+        typename DerivedS >
+      IGL_INLINE void closest_facet(
+          const Eigen::PlainObjectBase<DerivedV>& V,
+          const Eigen::PlainObjectBase<DerivedF>& F,
+          const Eigen::PlainObjectBase<DerivedI>& I,
+          const Eigen::PlainObjectBase<DerivedP>& P,
+          const std::vector<std::vector<uE2EType> >& uE2E,
+          const Eigen::PlainObjectBase<DerivedEMAP>& EMAP,
+          const std::vector<std::vector<size_t> > & VF,
+          const std::vector<std::vector<size_t> > & VFi,
+          const CGAL::AABB_tree<
+            CGAL::AABB_traits<
+              Kernel, 
+              CGAL::AABB_triangle_primitive<
+                Kernel, typename std::vector<
+                  typename Kernel::Triangle_3 >::iterator > > > & tree,
+          const std::vector<typename Kernel::Triangle_3 > & triangles,
+          const std::vector<bool> & in_I,
+          Eigen::PlainObjectBase<DerivedR>& R,
+          Eigen::PlainObjectBase<DerivedS>& S);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#include "closest_facet.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/complex_to_mesh.cpp

@@ -0,0 +1,152 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "complex_to_mesh.h"
+
+#include "../../centroid.h"
+#include "../../remove_unreferenced.h"
+
+#include <CGAL/Surface_mesh_default_triangulation_3.h>
+#include <CGAL/Delaunay_triangulation_cell_base_with_circumcenter_3.h>
+#include <set>
+#include <stack>
+
+template <typename Tr, typename DerivedV, typename DerivedF>
+IGL_INLINE bool igl::copyleft::cgal::complex_to_mesh(
+  const CGAL::Complex_2_in_triangulation_3<Tr> & c2t3,
+  Eigen::PlainObjectBase<DerivedV> & V, 
+  Eigen::PlainObjectBase<DerivedF> & F)
+{
+  using namespace Eigen;
+  // CGAL/IO/Complex_2_in_triangulation_3_file_writer.h
+  using CGAL::Surface_mesher::number_of_facets_on_surface;
+
+  typedef typename CGAL::Complex_2_in_triangulation_3<Tr> C2t3;
+  typedef typename Tr::Finite_facets_iterator Finite_facets_iterator;
+  typedef typename Tr::Finite_vertices_iterator Finite_vertices_iterator;
+  typedef typename Tr::Facet Facet;
+  typedef typename Tr::Edge Edge;
+  typedef typename Tr::Vertex_handle Vertex_handle;
+
+  // Header.
+  const Tr& tr = c2t3.triangulation();
+
+  bool success = true;
+
+  const int n = tr.number_of_vertices();
+  const int m = c2t3.number_of_facets();
+
+  assert(m == number_of_facets_on_surface(tr));
+  
+  // Finite vertices coordinates.
+  std::map<Vertex_handle, int> v2i;
+  V.resize(n,3);
+  {
+    int v = 0;
+    for(Finite_vertices_iterator vit = tr.finite_vertices_begin();
+        vit != tr.finite_vertices_end();
+        ++vit)
+    {
+      V(v,0) = vit->point().x(); 
+      V(v,1) = vit->point().y(); 
+      V(v,2) = vit->point().z(); 
+      v2i[vit] = v++;
+    }
+  }
+
+  {
+    Finite_facets_iterator fit = tr.finite_facets_begin();
+    std::set<Facet> oriented_set;
+    std::stack<Facet> stack;
+
+    while ((int)oriented_set.size() != m) 
+    {
+      while ( fit->first->is_facet_on_surface(fit->second) == false ||
+        oriented_set.find(*fit) != oriented_set.end() ||
+        oriented_set.find(c2t3.opposite_facet(*fit)) !=
+        oriented_set.end() ) 
+      {
+        ++fit;
+      }
+      oriented_set.insert(*fit);
+      stack.push(*fit);
+      while(! stack.empty() )
+      {
+        Facet f = stack.top();
+        stack.pop();
+        for(int ih = 0 ; ih < 3 ; ++ih)
+        {
+          const int i1  = tr.vertex_triple_index(f.second, tr. cw(ih));
+          const int i2  = tr.vertex_triple_index(f.second, tr.ccw(ih));
+
+          const typename C2t3::Face_status face_status
+            = c2t3.face_status(Edge(f.first, i1, i2));
+          if(face_status == C2t3::REGULAR) 
+          {
+            Facet fn = c2t3.neighbor(f, ih);
+            if (oriented_set.find(fn) == oriented_set.end())
+            {
+              if(oriented_set.find(c2t3.opposite_facet(fn)) == oriented_set.end())
+              {
+                oriented_set.insert(fn);
+                stack.push(fn);
+              }else {
+                success = false; // non-orientable
+              }
+            }
+          }else if(face_status != C2t3::BOUNDARY)
+          {
+            success = false; // non manifold, thus non-orientable
+          }
+        } // end "for each neighbor of f"
+      } // end "stack non empty"
+    } // end "oriented_set not full"
+
+    F.resize(m,3);
+    int f = 0;
+    for(typename std::set<Facet>::const_iterator fit = 
+        oriented_set.begin();
+        fit != oriented_set.end();
+        ++fit)
+    {
+      const typename Tr::Cell_handle cell = fit->first;
+      const int& index = fit->second;
+      const int index1 = v2i[cell->vertex(tr.vertex_triple_index(index, 0))];
+      const int index2 = v2i[cell->vertex(tr.vertex_triple_index(index, 1))];
+      const int index3 = v2i[cell->vertex(tr.vertex_triple_index(index, 2))];
+      // This order is flipped
+      F(f,0) = index1;
+      F(f,1) = index2;
+      F(f,2) = index3;
+      f++;
+    }
+    assert(f == m);
+  } // end if(facets must be oriented)
+
+  // This CGAL code seems to randomly assign the global orientation
+  // Flip based on the signed volume.
+  Eigen::Vector3d cen;
+  double vol;
+  igl::centroid(V,F,cen,vol);
+  if(vol < 0)
+  {
+    // Flip
+    F = F.rowwise().reverse().eval();
+  }
+
+  // CGAL code somehow can end up with unreferenced vertices
+  {
+    VectorXi _1;
+    remove_unreferenced( MatrixXd(V), MatrixXi(F), V,F,_1);
+  }
+
+  return success;
+}
+
+#ifdef IGL_STATIC_LIBRARY
+template bool igl::copyleft::cgal::complex_to_mesh<CGAL::Delaunay_triangulation_3<CGAL::Robust_circumcenter_traits_3<CGAL::Epick>, CGAL::Triangulation_data_structure_3<CGAL::Surface_mesh_vertex_base_3<CGAL::Robust_circumcenter_traits_3<CGAL::Epick>, CGAL::Triangulation_vertex_base_3<CGAL::Robust_circumcenter_traits_3<CGAL::Epick>, CGAL::Triangulation_ds_vertex_base_3<void> > >, CGAL::Delaunay_triangulation_cell_base_with_circumcenter_3<CGAL::Robust_circumcenter_traits_3<CGAL::Epick>, CGAL::Surface_mesh_cell_base_3<CGAL::Robust_circumcenter_traits_3<CGAL::Epick>, CGAL::Triangulation_cell_base_3<CGAL::Robust_circumcenter_traits_3<CGAL::Epick>, CGAL::Triangulation_ds_cell_base_3<void> > > >, CGAL::Sequential_tag>, CGAL::Default, CGAL::Default>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(CGAL::Complex_2_in_triangulation_3<CGAL::Delaunay_triangulation_3<CGAL::Robust_circumcenter_traits_3<CGAL::Epick>, CGAL::Triangulation_data_structure_3<CGAL::Surface_mesh_vertex_base_3<CGAL::Robust_circumcenter_traits_3<CGAL::Epick>, CGAL::Triangulation_vertex_base_3<CGAL::Robust_circumcenter_traits_3<CGAL::Epick>, CGAL::Triangulation_ds_vertex_base_3<void> > >, CGAL::Delaunay_triangulation_cell_base_with_circumcenter_3<CGAL::Robust_circumcenter_traits_3<CGAL::Epick>, CGAL::Surface_mesh_cell_base_3<CGAL::Robust_circumcenter_traits_3<CGAL::Epick>, CGAL::Triangulation_cell_base_3<CGAL::Robust_circumcenter_traits_3<CGAL::Epick>, CGAL::Triangulation_ds_cell_base_3<void> > > >, CGAL::Sequential_tag>, CGAL::Default, CGAL::Default>, void> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+#endif

src/igl/copyleft/cgal/complex_to_mesh.h

@@ -0,0 +1,47 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_COMPLEX_TO_MESH_H
+#define IGL_COPYLEFT_CGAL_COMPLEX_TO_MESH_H
+#include "../../igl_inline.h"
+
+#include <Eigen/Dense>
+#include <CGAL/Complex_2_in_triangulation_3.h>
+
+namespace igl 
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Templates:
+      //   Tr  CGAL triangulation type, e.g.
+      //     CGAL::Surface_mesh_default_triangulation_3
+      // Inputs
+      //   c2t3  2-complex (surface) living in a 3d triangulation (e.g. result of
+      //     CGAL::make_surface_mesh)
+      // Outputs:
+      //   V  #V by 3 list of vertex positions
+      //   F  #F by 3 list of triangle indices
+      // Returns true iff conversion was successful, failure can ok if CGAL code
+      // can't figure out ordering.
+      //
+      template <typename Tr, typename DerivedV, typename DerivedF>
+      IGL_INLINE bool complex_to_mesh(
+        const CGAL::Complex_2_in_triangulation_3<Tr> & c2t3,
+        Eigen::PlainObjectBase<DerivedV> & V, 
+        Eigen::PlainObjectBase<DerivedF> & F);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "complex_to_mesh.cpp"
+#endif
+
+#endif
+

src/igl/copyleft/cgal/component_inside_component.cpp

@@ -0,0 +1,83 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "component_inside_component.h"
+
+#include "order_facets_around_edge.h"
+#include "../../LinSpaced.h"
+#include "points_inside_component.h"
+
+#include <CGAL/AABB_tree.h>
+#include <CGAL/AABB_traits.h>
+#include <CGAL/AABB_triangle_primitive.h>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+
+#include <cassert>
+#include <list>
+#include <limits>
+#include <vector>
+
+template <typename DerivedV, typename DerivedF, typename DerivedI>
+IGL_INLINE bool igl::copyleft::cgal::component_inside_component(
+        const Eigen::PlainObjectBase<DerivedV>& V1,
+        const Eigen::PlainObjectBase<DerivedF>& F1,
+        const Eigen::PlainObjectBase<DerivedI>& I1,
+        const Eigen::PlainObjectBase<DerivedV>& V2,
+        const Eigen::PlainObjectBase<DerivedF>& F2,
+        const Eigen::PlainObjectBase<DerivedI>& I2) {
+    if (F1.rows() <= 0 || I1.rows() <= 0 || F2.rows() <= 0 || I2.rows() <= 0) {
+        throw "Component inside test cannot be done on empty component!";
+    }
+
+    const Eigen::Vector3i& f = F1.row(I1(0, 0));
+    const Eigen::Matrix<typename DerivedV::Scalar, 1, 3> query(
+            (V1(f[0],0) + V1(f[1],0) + V1(f[2],0))/3.0,
+            (V1(f[0],1) + V1(f[1],1) + V1(f[2],1))/3.0,
+            (V1(f[0],2) + V1(f[1],2) + V1(f[2],2))/3.0);
+    Eigen::VectorXi inside;
+    igl::copyleft::cgal::points_inside_component(V2, F2, I2, query, inside);
+    assert(inside.size() == 1);
+    return inside[0];
+}
+
+template<typename DerivedV, typename DerivedF>
+IGL_INLINE bool igl::copyleft::cgal::component_inside_component(
+        const Eigen::PlainObjectBase<DerivedV>& V1,
+        const Eigen::PlainObjectBase<DerivedF>& F1,
+        const Eigen::PlainObjectBase<DerivedV>& V2,
+        const Eigen::PlainObjectBase<DerivedF>& F2) {
+    if (F1.rows() <= 0 || F2.rows() <= 0) {
+        throw "Component inside test cannot be done on empty component!";
+    }
+    Eigen::VectorXi I1(F1.rows()), I2(F2.rows());
+    I1 = igl::LinSpaced<Eigen::VectorXi>(F1.rows(), 0, F1.rows()-1);
+    I2 = igl::LinSpaced<Eigen::VectorXi>(F2.rows(), 0, F2.rows()-1);
+    return igl::copyleft::cgal::component_inside_component(V1, F1, I1, V2, F2, I2);
+}
+
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template bool igl::copyleft::cgal::component_inside_component<
+Eigen::Matrix<double, -1, -1, 0, -1, -1>,
+Eigen::Matrix<   int, -1, -1, 0, -1, -1>,
+Eigen::Matrix<   int, -1, -1, 0, -1, -1> > (
+Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&,
+Eigen::PlainObjectBase<Eigen::Matrix<   int, -1, -1, 0, -1, -1> > const&,
+Eigen::PlainObjectBase<Eigen::Matrix<   int, -1, -1, 0, -1, -1> > const&,
+Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&,
+Eigen::PlainObjectBase<Eigen::Matrix<   int, -1, -1, 0, -1, -1> > const&,
+Eigen::PlainObjectBase<Eigen::Matrix<   int, -1, -1, 0, -1, -1> > const&);
+
+template bool igl::copyleft::cgal::component_inside_component<
+Eigen::Matrix<double, -1, -1, 0, -1, -1>,
+Eigen::Matrix<   int, -1, -1, 0, -1, -1> > (
+Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&,
+Eigen::PlainObjectBase<Eigen::Matrix<   int, -1, -1, 0, -1, -1> > const&,
+Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&,
+Eigen::PlainObjectBase<Eigen::Matrix<   int, -1, -1, 0, -1, -1> > const&);
+#endif

src/igl/copyleft/cgal/component_inside_component.h

@@ -0,0 +1,75 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_COMONENT_INSIDE_COMPONENT
+#define IGL_COPYLEFT_CGAL_COMONENT_INSIDE_COMPONENT
+
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <vector>
+
+namespace igl {
+  namespace copyleft
+  {
+    namespace cgal {
+
+        // Determine if connected facet component (V1, F1, I1) is inside of
+        // connected facet component (V2, F2, I2).
+        //
+        // Precondition:
+        // Both components must represent closed, self-intersection free,
+        // non-degenerated surfaces that are the boundary of 3D volumes. In
+        // addition, (V1, F1, I1) must not intersect with (V2, F2, I2).
+        //
+        // Inputs:
+        //   V1  #V1 by 3 list of vertex position of mesh 1
+        //   F1  #F1 by 3 list of triangles indices into V1
+        //   I1  #I1 list of indices into F1, indicate the facets of component
+        //   V2  #V2 by 3 list of vertex position of mesh 2
+        //   F2  #F2 by 3 list of triangles indices into V2
+        //   I2  #I2 list of indices into F2, indicate the facets of component
+        //
+        // Outputs:
+        //   return true iff (V1, F1, I1) is entirely inside of (V2, F2, I2).
+        template<typename DerivedV, typename DerivedF, typename DerivedI>
+            IGL_INLINE bool component_inside_component(
+                    const Eigen::PlainObjectBase<DerivedV>& V1,
+                    const Eigen::PlainObjectBase<DerivedF>& F1,
+                    const Eigen::PlainObjectBase<DerivedI>& I1,
+                    const Eigen::PlainObjectBase<DerivedV>& V2,
+                    const Eigen::PlainObjectBase<DerivedF>& F2,
+                    const Eigen::PlainObjectBase<DerivedI>& I2);
+
+        // Determine if mesh (V1, F1) is inside of mesh (V2, F2).
+        //
+        // Precondition:
+        // Both meshes must be closed, self-intersection free, non-degenerated
+        // surfaces that are the boundary of 3D volumes.  They should not
+        // intersect each other.
+        //
+        // Inputs:
+        //   V1  #V1 by 3 list of vertex position of mesh 1
+        //   F1  #F1 by 3 list of triangles indices into V1
+        //   V2  #V2 by 3 list of vertex position of mesh 2
+        //   F2  #F2 by 3 list of triangles indices into V2
+        //
+        // Outputs:
+        //   return true iff (V1, F1) is entirely inside of (V2, F2).
+        template<typename DerivedV, typename DerivedF>
+            IGL_INLINE bool component_inside_component(
+                    const Eigen::PlainObjectBase<DerivedV>& V1,
+                    const Eigen::PlainObjectBase<DerivedF>& F1,
+                    const Eigen::PlainObjectBase<DerivedV>& V2,
+                    const Eigen::PlainObjectBase<DerivedF>& F2);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#include "component_inside_component.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/convex_hull.cpp

@@ -0,0 +1,72 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2017 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "convex_hull.h"
+#include "../../ismember.h"
+#include "polyhedron_to_mesh.h"
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Polyhedron_3.h>
+#include <CGAL/Surface_mesh.h>
+#include <CGAL/convex_hull_3.h>
+#include <vector>
+
+template <
+  typename DerivedV,
+  typename DerivedW,
+  typename DerivedG>
+IGL_INLINE void igl::copyleft::cgal::convex_hull(
+  const Eigen::MatrixBase<DerivedV> & V,
+  Eigen::PlainObjectBase<DerivedW> & W,
+  Eigen::PlainObjectBase<DerivedG> & G)
+{
+  typedef CGAL::Exact_predicates_inexact_constructions_kernel      K;
+  typedef K::Point_3                                              Point_3;
+  //typedef CGAL::Delaunay_triangulation_3<K>                       Delaunay;
+  //typedef Delaunay::Vertex_handle                                 Vertex_handle;
+  //typedef CGAL::Surface_mesh<Point_3>                             Surface_mesh;
+  typedef CGAL::Polyhedron_3<K>                             Polyhedron_3;
+  std::vector<Point_3> points(V.rows());
+  for(int i = 0;i<V.rows();i++)
+  {
+    points[i] = Point_3(V(i,0),V(i,1),V(i,2));
+  }
+  Polyhedron_3 poly;
+  CGAL::convex_hull_3(points.begin(),points.end(),poly);
+  assert(poly.is_pure_triangle() && "Assuming CGAL outputs a triangle mesh");
+  polyhedron_to_mesh(poly,W,G);
+}
+
+template <
+  typename DerivedV,
+  typename DerivedF>
+IGL_INLINE void igl::copyleft::cgal::convex_hull(
+  const Eigen::MatrixBase<DerivedV> & V,
+  Eigen::PlainObjectBase<DerivedF> & F)
+{
+  Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, Eigen::Dynamic> W;
+  Eigen::Matrix<typename DerivedF::Scalar, Eigen::Dynamic, Eigen::Dynamic> G;
+  convex_hull(V,W,G);
+  // This is a lazy way to reindex into the original mesh
+  Eigen::Matrix<bool,Eigen::Dynamic,1> I;
+  Eigen::VectorXi J;
+  igl::ismember_rows(W,V,I,J);
+  assert(I.all() && "Should find all W in V");
+  F.resizeLike(G);
+  for(int f = 0;f<G.rows();f++)
+  {
+    for(int c = 0;c<3;c++)
+    {
+      F(f,c) = J(G(f,c));
+    }
+  }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::convex_hull<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+#endif

src/igl/copyleft/cgal/convex_hull.h

@@ -0,0 +1,56 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2017 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_CONVEX_HULL_H
+#define IGL_COPYLEFT_CGAL_CONVEX_HULL_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Given a set of points (V), compute the convex hull as a triangle mesh (W,G)
+      // 
+      // Inputs:
+      //   V  #V by 3 list of input points
+      // Outputs:
+      //   W  #W by 3 list of convex hull points
+      //   G  #G by 3 list of triangle indices into W
+      template <
+        typename DerivedV,
+        typename DerivedW,
+        typename DerivedG>
+      IGL_INLINE void convex_hull(
+        const Eigen::MatrixBase<DerivedV> & V,
+        Eigen::PlainObjectBase<DerivedW> & W,
+        Eigen::PlainObjectBase<DerivedG> & G);
+      // Given a set of points (V), compute the convex hull as a triangle mesh (F)
+      // over input vertex set (V)
+      // 
+      // Inputs:
+      //   V  #V by 3 list of input points
+      // Outputs:
+      //   F  #F by 3 list of triangle indices into V
+      //
+      template <
+        typename DerivedV,
+        typename DerivedF>
+      IGL_INLINE void convex_hull(
+        const Eigen::MatrixBase<DerivedV> & V,
+        Eigen::PlainObjectBase<DerivedF> & F);
+    }
+  }
+}
+  
+#ifndef IGL_STATIC_LIBRARY
+#  include "convex_hull.cpp"
+#endif
+
+#endif 

src/igl/copyleft/cgal/delaunay_triangulation.cpp

@@ -0,0 +1,62 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2018 Alec Jacobson
+// Copyright (C) 2016 Qingnan Zhou <qnzhou@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "delaunay_triangulation.h"
+#include "../../delaunay_triangulation.h"
+#include "orient2D.h"
+#include "incircle.h"
+
+template<
+  typename DerivedV,
+  typename DerivedF>
+IGL_INLINE void igl::copyleft::cgal::delaunay_triangulation(
+    const Eigen::PlainObjectBase<DerivedV>& V,
+    Eigen::PlainObjectBase<DerivedF>& F)
+{
+  typedef typename DerivedV::Scalar Scalar;
+  igl::delaunay_triangulation(V, orient2D<Scalar>, incircle<Scalar>, F);
+  // This function really exists to test our igl::delaunay_triangulation
+  // 
+  // It's currently much faster to call cgal's native Delaunay routine
+  //
+//#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+//#include <CGAL/Delaunay_triangulation_2.h>
+//#include <CGAL/Triangulation_vertex_base_with_info_2.h>
+//#include <vector>
+//  const auto delaunay = 
+//    [&](const Eigen::MatrixXd & V,Eigen::MatrixXi & F)
+//  {
+//    typedef CGAL::Exact_predicates_inexact_constructions_kernel            Kernel;
+//    typedef CGAL::Triangulation_vertex_base_with_info_2<unsigned int, Kernel> Vb;
+//    typedef CGAL::Triangulation_data_structure_2<Vb>                       Tds;
+//    typedef CGAL::Delaunay_triangulation_2<Kernel, Tds>                    Delaunay;
+//    typedef Kernel::Point_2                                                Point;
+//    std::vector< std::pair<Point,unsigned> > points(V.rows());
+//    for(int i = 0;i<V.rows();i++)
+//    {
+//      points[i] = std::make_pair(Point(V(i,0),V(i,1)),i);
+//    }
+//    Delaunay triangulation;
+//    triangulation.insert(points.begin(),points.end());
+//    F.resize(triangulation.number_of_faces(),3);
+//    {
+//      int j = 0;
+//      for(Delaunay::Finite_faces_iterator fit = triangulation.finite_faces_begin();
+//          fit != triangulation.finite_faces_end(); ++fit) 
+//      {
+//        Delaunay::Face_handle face = fit;
+//        F(j,0) = face->vertex(0)->info();
+//        F(j,1) = face->vertex(1)->info();
+//        F(j,2) = face->vertex(2)->info();
+//        j++;
+//      }
+//    }
+//  };
+}
+

src/igl/copyleft/cgal/delaunay_triangulation.h

@@ -0,0 +1,47 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Qingan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef IGL_COPYLEFT_CGAL_DELAUNAY_TRIANGULATION_H
+#define IGL_COPYLEFT_CGAL_DELAUNAY_TRIANGULATION_H
+
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+
+      // Given a set of points in 2D, return a Delaunay triangulation of these
+      // points.
+      //
+      // Inputs:
+      //   V  #V by 2 list of vertex positions
+      //
+      // Outputs:
+      //   F  #F by 3 of faces in Delaunay triangulation.
+      template<
+        typename DerivedV,
+        typename DerivedF
+        >
+      IGL_INLINE void delaunay_triangulation(
+          const Eigen::PlainObjectBase<DerivedV>& V,
+          Eigen::PlainObjectBase<DerivedF>& F);
+    }
+  }
+}
+
+
+
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "delaunay_triangulation.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/extract_cells.cpp

@@ -0,0 +1,547 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+//
+#include "extract_cells.h"
+#include "closest_facet.h"
+#include "order_facets_around_edge.h"
+#include "outer_facet.h"
+#include "submesh_aabb_tree.h"
+#include "../../extract_manifold_patches.h"
+#include "../../facet_components.h"
+#include "../../get_seconds.h"
+#include "../../triangle_triangle_adjacency.h"
+#include "../../unique_edge_map.h"
+#include "../../vertex_triangle_adjacency.h"
+
+#include <CGAL/AABB_tree.h>
+#include <CGAL/AABB_traits.h>
+#include <CGAL/AABB_triangle_primitive.h>
+#include <CGAL/intersections.h>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+
+#include <iostream>
+#include <vector>
+#include <queue>
+#include <map>
+#include <set>
+
+//#define EXTRACT_CELLS_DEBUG
+
+template<
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedC >
+IGL_INLINE size_t igl::copyleft::cgal::extract_cells(
+  const Eigen::PlainObjectBase<DerivedV>& V,
+  const Eigen::PlainObjectBase<DerivedF>& F,
+  Eigen::PlainObjectBase<DerivedC>& cells)
+{
+  const size_t num_faces = F.rows();
+  // Construct edge adjacency
+  Eigen::MatrixXi E, uE;
+  Eigen::VectorXi EMAP;
+  std::vector<std::vector<size_t> > uE2E;
+  igl::unique_edge_map(F, E, uE, EMAP, uE2E);
+  // Cluster into manifold patches
+  Eigen::VectorXi P;
+  igl::extract_manifold_patches(F, EMAP, uE2E, P);
+  // Extract cells
+  DerivedC per_patch_cells;
+  const size_t num_cells =
+    igl::copyleft::cgal::extract_cells(V,F,P,E,uE,uE2E,EMAP,per_patch_cells);
+  // Distribute per-patch cell information to each face
+  cells.resize(num_faces, 2);
+  for (size_t i=0; i<num_faces; i++) 
+  {
+    cells.row(i) = per_patch_cells.row(P[i]);
+  }
+  return num_cells;
+}
+
+
+template<
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedP,
+  typename DerivedE,
+  typename DeriveduE,
+  typename uE2EType,
+  typename DerivedEMAP,
+  typename DerivedC >
+IGL_INLINE size_t igl::copyleft::cgal::extract_cells(
+  const Eigen::PlainObjectBase<DerivedV>& V,
+  const Eigen::PlainObjectBase<DerivedF>& F,
+  const Eigen::PlainObjectBase<DerivedP>& P,
+  const Eigen::PlainObjectBase<DerivedE>& E,
+  const Eigen::PlainObjectBase<DeriveduE>& uE,
+  const std::vector<std::vector<uE2EType> >& uE2E,
+  const Eigen::PlainObjectBase<DerivedEMAP>& EMAP,
+  Eigen::PlainObjectBase<DerivedC>& cells) 
+{
+  // Trivial base case
+  if(P.size() == 0)
+  {
+    assert(F.size() == 0);
+    cells.resize(0,2);
+    return 0;
+  }
+
+  typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
+  typedef Kernel::Point_3 Point_3;
+  typedef Kernel::Plane_3 Plane_3;
+  typedef Kernel::Segment_3 Segment_3;
+  typedef Kernel::Triangle_3 Triangle;
+  typedef std::vector<Triangle>::iterator Iterator;
+  typedef CGAL::AABB_triangle_primitive<Kernel, Iterator> Primitive;
+  typedef CGAL::AABB_traits<Kernel, Primitive> AABB_triangle_traits;
+  typedef CGAL::AABB_tree<AABB_triangle_traits> Tree;
+
+#ifdef EXTRACT_CELLS_DEBUG
+  const auto & tictoc = []() -> double
+  {
+    static double t_start = igl::get_seconds();
+    double diff = igl::get_seconds()-t_start;
+    t_start += diff;
+    return diff;
+  };
+  const auto log_time = [&](const std::string& label) -> void {
+    std::cout << "extract_cells." << label << ": "
+      << tictoc() << std::endl;
+  };
+  tictoc();
+#else
+  // no-op
+  const auto log_time = [](const std::string){};
+#endif
+  const size_t num_faces = F.rows();
+  typedef typename DerivedF::Scalar Index;
+  assert(P.size() > 0);
+  const size_t num_patches = P.maxCoeff()+1;
+
+  // Extract all cells...
+  DerivedC raw_cells;
+  const size_t num_raw_cells =
+    extract_cells_single_component(V,F,P,uE,uE2E,EMAP,raw_cells);
+  log_time("extract_single_component_cells");
+
+  // Compute triangle-triangle adjacency data-structure
+  std::vector<std::vector<std::vector<Index > > > TT,_1;
+  igl::triangle_triangle_adjacency(E, EMAP, uE2E, false, TT, _1);
+  log_time("compute_face_adjacency");
+
+  // Compute connected components of the mesh
+  Eigen::VectorXi C, counts;
+  igl::facet_components(TT, C, counts);
+  log_time("form_components");
+
+  const size_t num_components = counts.size();
+  // components[c] --> list of face indices into F of faces in component c
+  std::vector<std::vector<size_t> > components(num_components);
+  // Loop over all faces
+  for (size_t i=0; i<num_faces; i++) 
+  {
+    components[C[i]].push_back(i);
+  }
+  // Convert vector lists to Eigen lists...
+  // and precompute data-structures for each component
+  std::vector<std::vector<size_t> > VF,VFi;
+  igl::vertex_triangle_adjacency(V.rows(), F, VF, VFi);
+  std::vector<Eigen::VectorXi> Is(num_components);
+  std::vector<
+    CGAL::AABB_tree<
+      CGAL::AABB_traits<
+        Kernel, 
+        CGAL::AABB_triangle_primitive<
+          Kernel, std::vector<
+            Kernel::Triangle_3 >::iterator > > > > trees(num_components);
+  std::vector< std::vector<Kernel::Triangle_3 > > 
+    triangle_lists(num_components);
+  std::vector<std::vector<bool> > in_Is(num_components);
+
+  // Find outer facets, their orientations and cells for each component
+  Eigen::VectorXi outer_facets(num_components);
+  Eigen::VectorXi outer_facet_orientation(num_components);
+  Eigen::VectorXi outer_cells(num_components);
+  for (size_t i=0; i<num_components; i++)
+  {
+    Is[i].resize(components[i].size());
+    std::copy(components[i].begin(), components[i].end(),Is[i].data());
+    bool flipped;
+    igl::copyleft::cgal::outer_facet(V, F, Is[i], outer_facets[i], flipped);
+    outer_facet_orientation[i] = flipped?1:0;
+    outer_cells[i] = raw_cells(P[outer_facets[i]], outer_facet_orientation[i]);
+  }
+#ifdef EXTRACT_CELLS_DEBUG
+  log_time("outer_facet_per_component");
+#endif
+
+  // Compute barycenter of a triangle in mesh (V,F)
+  //
+  // Inputs:
+  //   fid  index into F
+  // Returns row-vector of barycenter coordinates
+  const auto get_triangle_center = [&V,&F](const size_t fid) 
+  {
+    return ((V.row(F(fid,0))+V.row(F(fid,1))+V.row(F(fid,2)))/3.0).eval();
+  };
+  std::vector<std::vector<size_t> > nested_cells(num_raw_cells);
+  std::vector<std::vector<size_t> > ambient_cells(num_raw_cells);
+  std::vector<std::vector<size_t> > ambient_comps(num_components);
+  // Only bother if there's more than one component
+  if(num_components > 1) 
+  {
+    // construct bounding boxes for each component
+    DerivedV bbox_min(num_components, 3);
+    DerivedV bbox_max(num_components, 3);
+    // Assuming our mesh (in exact numbers) fits in the range of double.
+    bbox_min.setConstant(std::numeric_limits<double>::max());
+    bbox_max.setConstant(std::numeric_limits<double>::min());
+    // Loop over faces
+    for (size_t i=0; i<num_faces; i++)
+    {
+      // component of this face
+      const auto comp_id = C[i];
+      const auto& f = F.row(i);
+      for (size_t j=0; j<3; j++) 
+      {
+        for(size_t d=0;d<3;d++)
+        {
+          bbox_min(comp_id,d) = std::min(bbox_min(comp_id,d), V(f[j],d));
+          bbox_max(comp_id,d) = std::max(bbox_max(comp_id,d), V(f[j],d));
+        }
+      }
+    }
+    // Return true if box of component ci intersects that of cj
+    const auto bbox_intersects = [&bbox_max,&bbox_min](size_t ci, size_t cj)
+    {
+      return !(
+        bbox_max(ci,0) < bbox_min(cj,0) ||
+        bbox_max(ci,1) < bbox_min(cj,1) ||
+        bbox_max(ci,2) < bbox_min(cj,2) ||
+        bbox_max(cj,0) < bbox_min(ci,0) ||
+        bbox_max(cj,1) < bbox_min(ci,1) ||
+        bbox_max(cj,2) < bbox_min(ci,2));
+    };
+    
+    // Loop over components. This section is O(m²)
+    for (size_t i=0; i<num_components; i++)
+    {
+      // List of components that could overlap with component i
+      std::vector<size_t> candidate_comps;
+      candidate_comps.reserve(num_components);
+      // Loop over components
+      for (size_t j=0; j<num_components; j++) 
+      {
+        if (i == j) continue;
+        if (bbox_intersects(i,j)) candidate_comps.push_back(j);
+      }
+
+      const size_t num_candidate_comps = candidate_comps.size();
+      if (num_candidate_comps == 0) continue;
+
+      // Build aabb tree for this component.
+      submesh_aabb_tree(V,F,Is[i],trees[i],triangle_lists[i],in_Is[i]);
+
+      // Get query points on each candidate component: barycenter of
+      // outer-facet 
+      DerivedV queries(num_candidate_comps, 3);
+      for (size_t j=0; j<num_candidate_comps; j++)
+      {
+        const size_t index = candidate_comps[j];
+        queries.row(j) = get_triangle_center(outer_facets[index]);
+      }
+
+      // Gather closest facets in ith component to each query point and their
+      // orientations
+      const auto& I = Is[i];
+      const auto& tree = trees[i];
+      const auto& in_I = in_Is[i];
+      const auto& triangles = triangle_lists[i];
+
+      Eigen::VectorXi closest_facets, closest_facet_orientations;
+      closest_facet(
+        V,
+        F, 
+        I, 
+        queries,
+        uE2E, 
+        EMAP, 
+        VF,
+        VFi,
+        tree,
+        triangles,
+        in_I,
+        closest_facets, 
+        closest_facet_orientations);
+      // Loop over all candidates
+      for (size_t j=0; j<num_candidate_comps; j++)
+      {
+        const size_t index = candidate_comps[j];
+        const size_t closest_patch = P[closest_facets[j]];
+        const size_t closest_patch_side = closest_facet_orientations[j] ? 0:1;
+        // The cell id of the closest patch
+        const size_t ambient_cell =
+          raw_cells(closest_patch,closest_patch_side);
+        if (ambient_cell != (size_t)outer_cells[i])
+        {
+          // ---> component index inside component i, because the cell of the
+          // closest facet on i to component index is **not** the same as the
+          // "outer cell" of component i: component index is **not** outside of
+          // component i (therefore it's inside).
+          nested_cells[ambient_cell].push_back(outer_cells[index]);
+          ambient_cells[outer_cells[index]].push_back(ambient_cell);
+          ambient_comps[index].push_back(i);
+        }
+      }
+    }
+  }
+
+#ifdef EXTRACT_CELLS_DEBUG
+    log_time("nested_relationship");
+#endif
+
+    const size_t INVALID = std::numeric_limits<size_t>::max();
+    const size_t INFINITE_CELL = num_raw_cells;
+    std::vector<size_t> embedded_cells(num_raw_cells, INVALID);
+    for (size_t i=0; i<num_components; i++) {
+        const size_t outer_cell = outer_cells[i];
+        const auto& ambient_comps_i = ambient_comps[i];
+        const auto& ambient_cells_i = ambient_cells[outer_cell];
+        const size_t num_ambient_comps = ambient_comps_i.size();
+        assert(num_ambient_comps == ambient_cells_i.size());
+        if (num_ambient_comps > 0) {
+            size_t embedded_comp = INVALID;
+            size_t embedded_cell = INVALID;
+            for (size_t j=0; j<num_ambient_comps; j++) {
+                if (ambient_comps[ambient_comps_i[j]].size() ==
+                        num_ambient_comps-1) {
+                    embedded_comp = ambient_comps_i[j];
+                    embedded_cell = ambient_cells_i[j];
+                    break;
+                }
+            }
+            assert(embedded_comp != INVALID);
+            assert(embedded_cell != INVALID);
+            embedded_cells[outer_cell] = embedded_cell;
+        } else {
+            embedded_cells[outer_cell] = INFINITE_CELL;
+        }
+    }
+    for (size_t i=0; i<num_patches; i++) {
+        if (embedded_cells[raw_cells(i,0)] != INVALID) {
+            raw_cells(i,0) = embedded_cells[raw_cells(i, 0)];
+        }
+        if (embedded_cells[raw_cells(i,1)] != INVALID) {
+            raw_cells(i,1) = embedded_cells[raw_cells(i, 1)];
+        }
+    }
+
+    size_t count = 0;
+    std::vector<size_t> mapped_indices(num_raw_cells+1, INVALID);
+    // Always map infinite cell to index 0.
+    mapped_indices[INFINITE_CELL] = count;
+    count++;
+
+    for (size_t i=0; i<num_patches; i++) {
+        const size_t old_positive_cell_id = raw_cells(i, 0);
+        const size_t old_negative_cell_id = raw_cells(i, 1);
+        size_t positive_cell_id, negative_cell_id;
+        if (mapped_indices[old_positive_cell_id] == INVALID) {
+            mapped_indices[old_positive_cell_id] = count;
+            positive_cell_id = count;
+            count++;
+        } else {
+            positive_cell_id = mapped_indices[old_positive_cell_id];
+        }
+        if (mapped_indices[old_negative_cell_id] == INVALID) {
+            mapped_indices[old_negative_cell_id] = count;
+            negative_cell_id = count;
+            count++;
+        } else {
+            negative_cell_id = mapped_indices[old_negative_cell_id];
+        }
+        raw_cells(i, 0) = positive_cell_id;
+        raw_cells(i, 1) = negative_cell_id;
+    }
+    cells = raw_cells;
+#ifdef EXTRACT_CELLS_DEBUG
+    log_time("finalize");
+#endif
+    return count;
+}
+
+template<
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedP,
+  typename DeriveduE,
+  typename uE2EType,
+  typename DerivedEMAP,
+  typename DerivedC>
+IGL_INLINE size_t igl::copyleft::cgal::extract_cells_single_component(
+  const Eigen::PlainObjectBase<DerivedV>& V,
+  const Eigen::PlainObjectBase<DerivedF>& F,
+  const Eigen::PlainObjectBase<DerivedP>& P,
+  const Eigen::PlainObjectBase<DeriveduE>& uE,
+  const std::vector<std::vector<uE2EType> >& uE2E,
+  const Eigen::PlainObjectBase<DerivedEMAP>& EMAP,
+  Eigen::PlainObjectBase<DerivedC>& cells)
+{
+  const size_t num_faces = F.rows();
+  // Input:
+  //   index  index into #F*3 list of undirect edges
+  // Returns index into face
+  const auto edge_index_to_face_index = [&num_faces](size_t index)
+  {
+    return index % num_faces;
+  };
+  // Determine if a face (containing undirected edge {s,d} is consistently
+  // oriented with directed edge {s,d} (or otherwise it is with {d,s})
+  // 
+  // Inputs:
+  //   fid  face index into F
+  //   s  source index of edge
+  //   d  destination index of edge
+  // Returns true if face F(fid,:) is consistent with {s,d}
+  const auto is_consistent = 
+    [&F](const size_t fid, const size_t s, const size_t d) -> bool
+  {
+    if ((size_t)F(fid, 0) == s && (size_t)F(fid, 1) == d) return false;
+    if ((size_t)F(fid, 1) == s && (size_t)F(fid, 2) == d) return false;
+    if ((size_t)F(fid, 2) == s && (size_t)F(fid, 0) == d) return false;
+
+    if ((size_t)F(fid, 0) == d && (size_t)F(fid, 1) == s) return true;
+    if ((size_t)F(fid, 1) == d && (size_t)F(fid, 2) == s) return true;
+    if ((size_t)F(fid, 2) == d && (size_t)F(fid, 0) == s) return true;
+    throw "Invalid face!";
+    return false;
+  };
+
+  const size_t num_unique_edges = uE.rows();
+  const size_t num_patches = P.maxCoeff() + 1;
+
+  // Build patch-patch adjacency list.
+  std::vector<std::map<size_t, size_t> > patch_adj(num_patches);
+  for (size_t i=0; i<num_unique_edges; i++) {
+    const size_t s = uE(i,0);
+    const size_t d = uE(i,1);
+    const auto adj_faces = uE2E[i];
+    const size_t num_adj_faces = adj_faces.size();
+    if (num_adj_faces > 2) {
+      for (size_t j=0; j<num_adj_faces; j++) {
+        const size_t patch_j = P[edge_index_to_face_index(adj_faces[j])];
+        for (size_t k=j+1; k<num_adj_faces; k++) {
+          const size_t patch_k = P[edge_index_to_face_index(adj_faces[k])];
+          if (patch_adj[patch_j].find(patch_k) == patch_adj[patch_j].end()) {
+            patch_adj[patch_j].insert({patch_k, i});
+          }
+          if (patch_adj[patch_k].find(patch_j) == patch_adj[patch_k].end()) {
+            patch_adj[patch_k].insert({patch_j, i});
+          }
+        }
+      }
+    }
+  }
+
+
+  const int INVALID = std::numeric_limits<int>::max();
+  std::vector<size_t> cell_labels(num_patches * 2);
+  for (size_t i=0; i<num_patches; i++) cell_labels[i] = i;
+  std::vector<std::set<size_t> > equivalent_cells(num_patches*2);
+  std::vector<bool> processed(num_unique_edges, false);
+
+  size_t label_count=0;
+  for (size_t i=0; i<num_patches; i++) {
+    for (const auto& entry : patch_adj[i]) {
+      const size_t neighbor_patch = entry.first;
+      const size_t uei = entry.second;
+      if (processed[uei]) continue;
+      processed[uei] = true;
+
+      const auto& adj_faces = uE2E[uei];
+      const size_t num_adj_faces = adj_faces.size();
+      assert(num_adj_faces > 2);
+
+      const size_t s = uE(uei,0);
+      const size_t d = uE(uei,1);
+
+      std::vector<int> signed_adj_faces;
+      for (auto ej : adj_faces)
+      {
+        const size_t fid = edge_index_to_face_index(ej);
+        bool cons = is_consistent(fid, s, d);
+        signed_adj_faces.push_back((fid+1)*(cons ? 1:-1));
+      }
+      {
+        // Sort adjacent faces cyclically around {s,d}
+        Eigen::VectorXi order;
+        // order[f] will reveal the order of face f in signed_adj_faces
+        order_facets_around_edge(V, F, s, d, signed_adj_faces, order);
+        for (size_t j=0; j<num_adj_faces; j++) {
+          const size_t curr_idx = j;
+          const size_t next_idx = (j+1)%num_adj_faces;
+          const size_t curr_patch_idx =
+            P[edge_index_to_face_index(adj_faces[order[curr_idx]])];
+          const size_t next_patch_idx =
+            P[edge_index_to_face_index(adj_faces[order[next_idx]])];
+          const bool curr_cons = signed_adj_faces[order[curr_idx]] > 0;
+          const bool next_cons = signed_adj_faces[order[next_idx]] > 0;
+          const size_t curr_cell_idx = curr_patch_idx*2 + (curr_cons?0:1);
+          const size_t next_cell_idx = next_patch_idx*2 + (next_cons?1:0);
+          equivalent_cells[curr_cell_idx].insert(next_cell_idx);
+          equivalent_cells[next_cell_idx].insert(curr_cell_idx);
+        }
+      }
+    }
+  }
+
+  size_t count=0;
+  cells.resize(num_patches, 2);
+  cells.setConstant(INVALID);
+  const auto extract_equivalent_cells = [&](size_t i) {
+    if (cells(i/2, i%2) != INVALID) return;
+    std::queue<size_t> Q;
+    Q.push(i);
+    cells(i/2, i%2) = count;
+    while (!Q.empty()) {
+      const size_t index = Q.front();
+      Q.pop();
+      for (const auto j : equivalent_cells[index]) {
+        if (cells(j/2, j%2) == INVALID) {
+          cells(j/2, j%2) = count;
+          Q.push(j);
+        }
+      }
+    }
+    count++;
+  };
+  for (size_t i=0; i<num_patches; i++) {
+    extract_equivalent_cells(i*2);
+    extract_equivalent_cells(i*2+1);
+  }
+
+  assert((cells.array() != INVALID).all());
+  return count;
+}
+
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template unsigned long igl::copyleft::cgal::extract_cells<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, unsigned long, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<std::vector<unsigned long, std::allocator<unsigned long> >, std::allocator<std::vector<unsigned long, std::allocator<unsigned long> > > > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+// generated by autoexplicit.sh
+template unsigned long igl::copyleft::cgal::extract_cells<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, unsigned long, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<std::vector<unsigned long, std::allocator<unsigned long> >, std::allocator<std::vector<unsigned long, std::allocator<unsigned long> > > > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+template unsigned long igl::copyleft::cgal::extract_cells<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, unsigned long, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<std::vector<unsigned long, std::allocator<unsigned long> >, std::allocator<std::vector<unsigned long, std::allocator<unsigned long> > > > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+template unsigned long igl::copyleft::cgal::extract_cells<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+#ifdef WIN32
+template unsigned __int64 igl::copyleft::cgal::extract_cells<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, unsigned __int64, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class std::vector<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>, class std::allocator<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> &);
+template unsigned __int64 igl::copyleft::cgal::extract_cells<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, unsigned __int64, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class std::vector<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>, class std::allocator<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> &);
+template unsigned __int64 igl::copyleft::cgal::extract_cells<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, 3, 1, -1, 3>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, unsigned __int64, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 3, 1, -1, 3>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class std::vector<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>, class std::allocator<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> &);
+#endif
+#endif

src/igl/copyleft/cgal/extract_cells.h

@@ -0,0 +1,116 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+//
+#ifndef IGL_COPYLEFT_CGAL_EXTRACT_CELLS
+#define IGL_COPYLEFT_CGAL_EXTRACT_CELLS
+
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <vector>
+
+namespace igl {
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Extract connected 3D space partitioned by mesh (V, F).
+      //
+      // Inputs:
+      //   V  #V by 3 array of vertices.
+      //   F  #F by 3 array of faces.
+      //
+      // Output:
+      //   cells  #F by 2 array of cell indices.  cells(i,0) represents the
+      //          cell index on the positive side of face i, and cells(i,1)
+      //          represents cell index of the negqtive side.
+      //          By convension cell with index 0 is the infinite cell.
+      // Returns the number of cells
+      template<
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedC >
+      IGL_INLINE size_t extract_cells(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        Eigen::PlainObjectBase<DerivedC>& cells);
+
+      // Extract connected 3D space partitioned by mesh (V, F).
+      //
+      // Inputs:
+      //   V  #V by 3 array of vertices.
+      //   F  #F by 3 array of faces.
+      //   P  #F list of patch indices.
+      //   E  #E by 2 array of vertex indices, one edge per row.
+      //  uE    #uE by 2 list of vertex_indices, represents undirected edges.
+      //  uE2E  #uE list of lists that maps uE to E. (a one-to-many map)
+      //  EMAP  #F*3 list of indices into uE.
+      //
+      // Output:
+      //   cells  #P by 2 array of cell indices.  cells(i,0) represents the
+      //          cell index on the positive side of patch i, and cells(i,1)
+      //          represents cell index of the negqtive side.
+      //          By convension cell with index 0 is the infinite cell.
+      template<
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedP,
+        typename DerivedE,
+        typename DeriveduE,
+        typename uE2EType,
+        typename DerivedEMAP,
+        typename DerivedC >
+      IGL_INLINE size_t extract_cells(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        const Eigen::PlainObjectBase<DerivedP>& P,
+        const Eigen::PlainObjectBase<DerivedE>& E,
+        const Eigen::PlainObjectBase<DeriveduE>& uE,
+        const std::vector<std::vector<uE2EType> >& uE2E,
+        const Eigen::PlainObjectBase<DerivedEMAP>& EMAP,
+        Eigen::PlainObjectBase<DerivedC>& cells);
+
+      // Extract connected 3D space partitioned by mesh (V,F) composed of
+      // **possibly multiple components** (the name of this function is
+      // dubious).
+      //
+      // Inputs:
+      //   V  #V by 3 array of vertices.
+      //   F  #F by 3 array of faces.
+      //   P  #F list of patch indices.
+      //   E  #E by 2 array of vertex indices, one edge per row.
+      //  uE    #uE by 2 list of vertex_indices, represents undirected edges.
+      //  uE2E  #uE list of lists that maps uE to E. (a one-to-many map)
+      //  EMAP  #F*3 list of indices into uE.
+      // Output:
+      //  cells  #P by 2 array of cell indices.  cells(i,0) represents the
+      //    cell index on the positive side of patch i, and cells(i,1)
+      //    represents cell index of the negative side.
+      template<
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedP,
+        typename DeriveduE,
+        typename uE2EType,
+        typename DerivedEMAP,
+        typename DerivedC >
+      IGL_INLINE size_t extract_cells_single_component(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        const Eigen::PlainObjectBase<DerivedP>& P,
+        const Eigen::PlainObjectBase<DeriveduE>& uE,
+        const std::vector<std::vector<uE2EType> >& uE2E,
+        const Eigen::PlainObjectBase<DerivedEMAP>& EMAP,
+        Eigen::PlainObjectBase<DerivedC>& cells);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "extract_cells.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/extract_feature.cpp

@@ -0,0 +1,123 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "extract_feature.h"
+#include <igl/unique_edge_map.h>
+#include <CGAL/Kernel/global_functions.h>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+
+template<
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedE >
+IGL_INLINE void igl::copyleft::cgal::extract_feature(
+    const Eigen::PlainObjectBase<DerivedV>& V,
+    const Eigen::PlainObjectBase<DerivedF>& F,
+    const double tol,
+    Eigen::PlainObjectBase<DerivedE>& feature_edges) {
+
+  using IndexType = typename DerivedE::Scalar;
+  DerivedE E, uE;
+  Eigen::VectorXi EMAP;
+  std::vector<std::vector<IndexType> > uE2E;
+  igl::unique_edge_map(F, E, uE, EMAP, uE2E);
+
+  igl::copyleft::cgal::extract_feature(V, F, tol, E, uE, uE2E, feature_edges);
+}
+
+template<
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedE >
+IGL_INLINE void igl::copyleft::cgal::extract_feature(
+    const Eigen::PlainObjectBase<DerivedV>& V,
+    const Eigen::PlainObjectBase<DerivedF>& F,
+    const double tol,
+    const Eigen::PlainObjectBase<DerivedE>& E,
+    const Eigen::PlainObjectBase<DerivedE>& uE,
+    const std::vector<std::vector<typename DerivedE::Scalar> >& uE2E,
+    Eigen::PlainObjectBase<DerivedE>& feature_edges) {
+
+  assert(V.cols() == 3);
+  assert(F.cols() == 3);
+  using Scalar = typename DerivedV::Scalar;
+  using IndexType = typename DerivedE::Scalar;
+  using Vertex = Eigen::Matrix<Scalar, 3, 1>;
+  using Kernel = typename CGAL::Exact_predicates_exact_constructions_kernel;
+  using Point = typename Kernel::Point_3;
+
+  const size_t num_unique_edges = uE.rows();
+  const size_t num_faces = F.rows();
+  // NOTE: CGAL's definition of dihedral angle measures the angle between two
+  // facets instead of facet normals.
+  const double cos_tol = cos(igl::PI - tol);
+  std::vector<size_t> result; // Indices into uE
+
+  auto is_non_manifold = [&uE2E](size_t ei) -> bool {
+    return uE2E[ei].size() > 2;
+  };
+
+  auto is_boundary = [&uE2E](size_t ei) -> bool {
+    return uE2E[ei].size() == 1;
+  };
+
+  auto opposite_vertex = [&uE, &F](size_t ei, size_t fi) -> IndexType {
+    const size_t v0 = uE(ei, 0);
+    const size_t v1 = uE(ei, 1);
+    for (size_t i=0; i<3; i++) {
+      const size_t v = F(fi, i);
+      if (v != v0 && v != v1) { return v; }
+    }
+    throw "Input face must be topologically degenerate!";
+  };
+
+  auto is_feature = [&V, &F, &uE, &uE2E, &opposite_vertex, num_faces](
+      size_t ei, double cos_tol) -> bool {
+    auto adj_faces = uE2E[ei];
+    assert(adj_faces.size() == 2);
+    const Vertex v0 = V.row(uE(ei, 0));
+    const Vertex v1 = V.row(uE(ei, 1));
+    const Vertex v2 = V.row(opposite_vertex(ei, adj_faces[0] % num_faces));
+    const Vertex v3 = V.row(opposite_vertex(ei, adj_faces[1] % num_faces));
+    const Point p0(v0[0], v0[1], v0[2]);
+    const Point p1(v1[0], v1[1], v1[2]);
+    const Point p2(v2[0], v2[1], v2[2]);
+    const Point p3(v3[0], v3[1], v3[2]);
+    const auto ori = CGAL::orientation(p0, p1, p2, p3);
+    switch (ori) {
+      case CGAL::POSITIVE:
+        return CGAL::compare_dihedral_angle(p0, p1, p2, p3, cos_tol) ==
+          CGAL::SMALLER;
+      case CGAL::NEGATIVE:
+        return CGAL::compare_dihedral_angle(p0, p1, p3, p2, cos_tol) ==
+          CGAL::SMALLER;
+      case CGAL::COPLANAR:
+        if (!CGAL::collinear(p0, p1, p2) && !CGAL::collinear(p0, p1, p3)) {
+          return CGAL::compare_dihedral_angle(p0, p1, p2, p3, cos_tol) ==
+            CGAL::SMALLER;
+        } else {
+          throw "Dihedral angle (and feature edge) is not well defined for"
+              " degenerate triangles!";
+        }
+      default:
+        throw "Unknown CGAL orientation";
+    }
+  };
+
+  for (size_t i=0; i<num_unique_edges; i++) {
+    if (is_boundary(i) || is_non_manifold(i) || is_feature(i, cos_tol)) {
+      result.push_back(i);
+    }
+  }
+
+  const size_t num_feature_edges = result.size();
+  feature_edges.resize(num_feature_edges, 2);
+  for (size_t i=0; i<num_feature_edges; i++) {
+    feature_edges.row(i) = uE.row(result[i]);
+  }
+}

src/igl/copyleft/cgal/extract_feature.h

@@ -0,0 +1,90 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef IGL_COPYLEFT_CGAL_EXTRACT_FEATURE_H
+#define IGL_COPYLEFT_CGAL_EXTRACT_FEATURE_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <vector>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Extract feature edges based on dihedral angle.
+      // Here, dihedral angle is defined as the angle between surface
+      // __normals__ as described in
+      // http://mathworld.wolfram.com/DihedralAngle.html
+      //
+      // Non-manifold and boundary edges are automatically considered as
+      // features.
+      //
+      // Inputs:
+      //   V   #V by 3 array of vertices.
+      //   F   #F by 3 array of faces.
+      //   tol Edges with dihedral angle larger than this are considered
+      //       as features.  Angle is measured in radian.
+      //
+      // Output:
+      //   feature_edges: #E by 2 array of edges.  Each edge satisfies at
+      //      least one of the following criteria:
+      //
+      //      * Edge has dihedral angle larger than tol.
+      //      * Edge is boundary.
+      //      * Edge is non-manifold (i.e. it has more than 2 adjacent
+      //        faces).
+      template <
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedE>
+      IGL_INLINE void extract_feature(
+            const Eigen::PlainObjectBase<DerivedV>& V,
+            const Eigen::PlainObjectBase<DerivedF>& F,
+            const double tol,
+            Eigen::PlainObjectBase<DerivedE>& feature_edges);
+
+      // Inputs:
+      //   V    #V by 3 array of vertices.
+      //   F    #F by 3 array of faces.
+      //   tol  Edges with dihedral angle larger than this are considered
+      //        as features.  Angle is measured in radian.
+      //   E    #E by 2 array of directed edges.
+      //   uE   #uE by 2 array of undirected edges.
+      //   uE2E #uE list of lists mapping undirected edges to all corresponding
+      //        directed edges.
+      //
+      // Output:
+      //   feature_edges: #E by 2 array of edges.  Each edge satisfies at
+      //      least one of the following criteria:
+      //
+      //      * Edge has dihedral angle larger than tol.
+      //      * Edge is boundary.
+      //      * Edge is non-manifold (i.e. it has more than 2 adjacent
+      //        faces).
+      template <
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedE>
+      IGL_INLINE void extract_feature(
+            const Eigen::PlainObjectBase<DerivedV>& V,
+            const Eigen::PlainObjectBase<DerivedF>& F,
+            const double tol,
+            const Eigen::PlainObjectBase<DerivedE>& E,
+            const Eigen::PlainObjectBase<DerivedE>& uE,
+            const std::vector<std::vector<typename DerivedE::Scalar> >& uE2E,
+            Eigen::PlainObjectBase<DerivedE>& feature_edges);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "extract_feature.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/fast_winding_number.cpp

@@ -0,0 +1,82 @@
+#include "../../fast_winding_number.h"
+#include "../../octree.h"
+#include "../../knn.h"
+#include "../../parallel_for.h"
+#include "point_areas.h"
+#include <vector>
+
+namespace igl {
+  namespace copyleft{
+    namespace cgal{
+      template <typename DerivedP, typename DerivedN, typename DerivedQ,
+        typename BetaType, typename DerivedWN>
+      IGL_INLINE void fast_winding_number(const Eigen::MatrixBase<DerivedP>& P,
+                                          const Eigen::MatrixBase<DerivedN>& N,
+                                          const Eigen::MatrixBase<DerivedQ>& Q,
+                                          const int expansion_order,
+                                          const BetaType beta,
+                                          Eigen::PlainObjectBase<DerivedWN>& WN
+                                          ){
+        typedef typename DerivedWN::Scalar real;
+        typedef typename Eigen::Matrix<real,Eigen::Dynamic,Eigen::Dynamic>
+                                                                  RealMatrix;
+        
+        std::vector<std::vector<int> > point_indices;
+        Eigen::Matrix<int,Eigen::Dynamic,8> CH;
+        Eigen::Matrix<real,Eigen::Dynamic,3> CN;
+        Eigen::Matrix<real,Eigen::Dynamic,1> W;
+        Eigen::MatrixXi I;
+        Eigen::Matrix<real,Eigen::Dynamic,1> A;
+        
+        octree(P,point_indices,CH,CN,W);
+        knn(P,21,point_indices,CH,CN,W,I);
+        point_areas(P,I,N,A);
+        
+        Eigen::Matrix<real,Eigen::Dynamic,Eigen::Dynamic> EC;
+        Eigen::Matrix<real,Eigen::Dynamic,3> CM;
+        Eigen::Matrix<real,Eigen::Dynamic,1> R;
+        
+        igl::fast_winding_number(P,N,A,point_indices,CH,
+                                 expansion_order,CM,R,EC);
+        igl::fast_winding_number(P,N,A,point_indices,CH,
+                                 CM,R,EC,Q,beta,WN);
+      }
+      
+      template <typename DerivedP, typename DerivedN,
+        typename DerivedQ, typename DerivedWN>
+      IGL_INLINE void fast_winding_number(
+                                          const Eigen::MatrixBase<DerivedP>& P,
+                                          const Eigen::MatrixBase<DerivedN>& N,
+                                          const Eigen::MatrixBase<DerivedQ>& Q,
+                                          Eigen::PlainObjectBase<DerivedWN>& WN
+                                          ){
+        fast_winding_number(P,N,Q,2,2.0,WN);
+      }
+    }
+  }
+}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+

src/igl/copyleft/cgal/fast_winding_number.h

@@ -0,0 +1,66 @@
+#ifndef IGL_COPYLEFT_CGAL_FAST_WINDING_NUMBER
+#define IGL_COPYLEFT_CGAL_FAST_WINDING_NUMBER
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <vector>
+namespace igl
+{
+  // Evaluate the fast winding number for point data, without known areas. The
+  // areas are calculated using igl::knn and igl::copyleft::cgal::point_areas.
+  //
+  // This function performes the precomputation and evaluation all in one.
+  // If you need to acess the precomuptation for repeated evaluations, use the
+  // two functions designed for exposed precomputation, which are the first two
+  // functions see in igl/fast_winding_number.h
+  //
+  // Inputs:
+  //   P  #P by 3 list of point locations
+  //   N  #P by 3 list of point normals
+  //   Q  #Q by 3 list of query points for the winding number
+  //   beta  This is a Barnes-Hut style accuracy term that separates near feild
+  //         from far field. The higher the beta, the more accurate and slower
+  //         the evaluation. We reccommend using a beta value of 2.
+  //   expansion_order    the order of the taylor expansion. We support 0,1,2.
+  // Outputs:
+  //   WN  #Q by 1 list of windinng number values at each query point
+  //
+  template <typename DerivedP, typename DerivedN, typename DerivedQ,
+    typename BetaType, typename DerivedWN>
+  IGL_INLINE void fast_winding_number(const Eigen::MatrixBase<DerivedP>& P,
+                                      const Eigen::MatrixBase<DerivedN>& N,
+                                      const Eigen::MatrixBase<DerivedQ>& Q,
+                                      const int expansion_order,
+                                      const BetaType beta,
+                                      Eigen::PlainObjectBase<DerivedWN>& WN
+                                      );
+  
+  // Evaluate the fast winding number for point data, without known areas. The
+  // areas are calculated using igl::knn and
+  // igl::point_areas. This function uses the default expansion
+  // order and beta (both are set to 2).
+  //
+  // This function performes the precomputation and evaluation all in one.
+  // If you need to acess the precomuptation for repeated evaluations, use the
+  // two functions designed for exposed precomputation (described above).
+  
+  // Inputs:
+  //   P  #P by 3 list of point locations
+  //   N  #P by 3 list of point normals
+  //   Q  #Q by 3 list of query points for the winding number
+  // Outputs:
+  //   WN  #Q by 1 list of windinng number values at each query point
+  //
+  template <typename DerivedP, typename DerivedN, typename DerivedQ,
+    typename DerivedWN>
+  IGL_INLINE void fast_winding_number(const Eigen::MatrixBase<DerivedP>& P,
+                                      const Eigen::MatrixBase<DerivedN>& N,
+                                      const Eigen::MatrixBase<DerivedQ>& Q,
+                                      Eigen::PlainObjectBase<DerivedWN>& WN
+                                      );
+}
+#ifndef IGL_STATIC_LIBRARY
+#  include "fast_winding_number.cpp"
+#endif
+
+#endif
+

src/igl/copyleft/cgal/half_space_box.cpp

@@ -0,0 +1,123 @@
+#include "half_space_box.h"
+#include "assign_scalar.h"
+#include <CGAL/Point_3.h>
+#include <CGAL/Vector_3.h>
+
+template <typename DerivedV>
+IGL_INLINE void igl::copyleft::cgal::half_space_box(
+  const CGAL::Plane_3<CGAL::Epeck> & P,
+  const Eigen::MatrixBase<DerivedV> & V,
+  Eigen::Matrix<CGAL::Epeck::FT,8,3> & BV,
+  Eigen::Matrix<int,12,3> & BF)
+{
+  typedef CGAL::Plane_3<CGAL::Epeck> Plane;
+  typedef CGAL::Point_3<CGAL::Epeck> Point;
+  typedef CGAL::Vector_3<CGAL::Epeck> Vector;
+  typedef CGAL::Epeck::FT EScalar;
+  Eigen::Matrix<typename DerivedV::Scalar,1,3> avg(0,0,0);
+  for(int v = 0;v<V.rows();v++) for(int c = 0;c<V.cols();c++) avg(c) += V(v,c);
+  avg /= V.rows();
+
+  Point o3(avg(0),avg(1),avg(2));
+  Point o2 = P.projection(o3);
+  Vector u;
+  EScalar max_sqrd = -1;
+  for(int v = 0;v<V.rows();v++)
+  {
+    Vector v2 = P.projection(Point(V(v,0),V(v,1),V(v,2))) - o2;
+    const EScalar sqrd = v2.squared_length();
+    if(max_sqrd<0 || sqrd < max_sqrd)
+    {
+      u = v2;
+      max_sqrd = sqrd;
+    }
+  }
+  // L1 bbd 
+  const EScalar bbd = 
+    (EScalar(V.col(0).maxCoeff())- EScalar(V.col(0).minCoeff())) + 
+    (EScalar(V.col(1).maxCoeff())- EScalar(V.col(1).minCoeff())) + 
+    (EScalar(V.col(2).maxCoeff())- EScalar(V.col(2).minCoeff()));
+  Vector n = P.orthogonal_vector();
+  // now we have a center o2 and a vector u to the farthest point on the plane 
+  std::vector<Point> vBV;vBV.reserve(8);
+  Vector v = CGAL::cross_product(u,n);
+  // Scale u,v,n to be longer than bbd
+  const auto & longer_than = [](const EScalar min_sqr, Vector & x)
+  {
+    assert(x.squared_length() > 0);
+    while(x.squared_length() < min_sqr)
+    {
+      x = 2.*x;
+    }
+  };
+  longer_than(bbd*bbd,u);
+  longer_than(bbd*bbd,v);
+  longer_than(bbd*bbd,n);
+  vBV.emplace_back( o2 + u + v);
+  vBV.emplace_back( o2 - u + v);
+  vBV.emplace_back( o2 - u - v);
+  vBV.emplace_back( o2 + u - v);
+  vBV.emplace_back( o2 + u + v - n);
+  vBV.emplace_back( o2 - u + v - n);
+  vBV.emplace_back( o2 - u - v - n);
+  vBV.emplace_back( o2 + u - v - n);
+  BV.resize(8,3);
+  for(int b = 0;b<8;b++)
+  {
+    igl::copyleft::cgal::assign_scalar(vBV[b].x(),BV(b,0));
+    igl::copyleft::cgal::assign_scalar(vBV[b].y(),BV(b,1));
+    igl::copyleft::cgal::assign_scalar(vBV[b].z(),BV(b,2));
+  }
+  BF.resize(12,3);
+  BF<<
+    1,0,2,
+    2,0,3,
+    4,5,6,
+    4,6,7,
+    0,1,4,
+    4,1,5,
+    1,2,5,
+    5,2,6,
+    2,3,6,
+    6,3,7,
+    3,0,7,
+    7,0,4;
+}
+
+template <typename Derivedp, typename Derivedn, typename DerivedV>
+IGL_INLINE void igl::copyleft::cgal::half_space_box(
+  const Eigen::MatrixBase<Derivedp> & p,
+  const Eigen::MatrixBase<Derivedn> & n,
+  const Eigen::MatrixBase<DerivedV> & V,
+  Eigen::Matrix<CGAL::Epeck::FT,8,3> & BV,
+  Eigen::Matrix<int,12,3> & BF)
+{
+  typedef CGAL::Plane_3<CGAL::Epeck> Plane;
+  typedef CGAL::Point_3<CGAL::Epeck> Point;
+  typedef CGAL::Vector_3<CGAL::Epeck> Vector;
+  Plane P(Point(p(0),p(1),p(2)),Vector(n(0),n(1),n(2)));
+  return half_space_box(P,V,BV,BF);
+}
+
+template <typename Derivedequ, typename DerivedV>
+IGL_INLINE void igl::copyleft::cgal::half_space_box(
+  const Eigen::MatrixBase<Derivedequ> & equ,
+  const Eigen::MatrixBase<DerivedV> & V,
+  Eigen::Matrix<CGAL::Epeck::FT,8,3> & BV,
+  Eigen::Matrix<int,12,3> & BF)
+{
+  typedef CGAL::Plane_3<CGAL::Epeck> Plane;
+  Plane P(equ(0),equ(1),equ(2),equ(3));
+  return half_space_box(P,V,BV,BF);
+}
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::half_space_box<Eigen::Matrix<double, -1, 3, 1, -1, 3> >(CGAL::Plane_3<CGAL::Epeck> const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 1, -1, 3> > const&, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3>&, Eigen::Matrix<int, 12, 3, 0, 12, 3>&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::half_space_box<Eigen::Matrix<float, -1, 3, 1, -1, 3> >(CGAL::Plane_3<CGAL::Epeck> const&, Eigen::MatrixBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> > const&, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3>&, Eigen::Matrix<int, 12, 3, 0, 12, 3>&);
+template void igl::copyleft::cgal::half_space_box<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 1, 4, 1, 1, 4>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 1, 4, 1, 1, 4> > const&, Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3>&, Eigen::Matrix<int, 12, 3, 0, 12, 3>&);
+template void igl::copyleft::cgal::half_space_box<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 1, 4, 1, 1, 4>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 4, 0, -1, 4> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 1, 4, 1, 1, 4> > const&, Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 4, 0, -1, 4> > const&, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3>&, Eigen::Matrix<int, 12, 3, 0, 12, 3>&);
+template void igl::copyleft::cgal::half_space_box<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 1, 4, 1, 1, 4>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 1, 4, 1, 1, 4> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3>&, Eigen::Matrix<int, 12, 3, 0, 12, 3>&);
+template void igl::copyleft::cgal::half_space_box<Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3>&, Eigen::Matrix<int, 12, 3, 0, 12, 3>&);
+#endif

src/igl/copyleft/cgal/half_space_box.h

@@ -0,0 +1,63 @@
+#ifndef IGL_COPYLEFT_CGAL_HALF_SPACE_BOX_H
+#define IGL_COPYLEFT_CGAL_HALF_SPACE_BOX_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/Plane_3.h>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Construct a mesh of box (BV,BF) so that it contains the intersection of
+      // the half-space under the plane (P) and the bounding box of V, and does not
+      // contain any of the half-space above (P).
+      //
+      // Inputs:
+      //   P  plane so that normal points away from half-space
+      //   V  #V by 3 list of vertex positions
+      // Outputs:
+      //   BV  #BV by 3 list of box vertex positions
+      //   BF  #BF b3 list of box triangle indices into BV
+      template <typename DerivedV>
+      IGL_INLINE void half_space_box(
+        const CGAL::Plane_3<CGAL::Epeck> & P,
+        const Eigen::MatrixBase<DerivedV> & V,
+        Eigen::Matrix<CGAL::Epeck::FT,8,3> & BV,
+        Eigen::Matrix<int,12,3> & BF);
+      // Inputs:
+      //   p  3d point on plane
+      //   n  3d vector of normal of plane pointing away from inside
+      //   V  #V by 3 list of vertex positions
+      // Outputs:
+      //   BV  #BV by 3 list of box vertex positions
+      //   BF  #BF b3 list of box triangle indices into BV
+      template <typename Derivedp, typename Derivedn, typename DerivedV>
+      IGL_INLINE void half_space_box(
+        const Eigen::MatrixBase<Derivedp> & p,
+        const Eigen::MatrixBase<Derivedn> & n,
+        const Eigen::MatrixBase<DerivedV> & V,
+        Eigen::Matrix<CGAL::Epeck::FT,8,3> & BV,
+        Eigen::Matrix<int,12,3> & BF);
+      // Inputs:
+      //   equ  plane equation: a*x+b*y+c*z + d = 0
+      //   V  #V by 3 list of vertex positions
+      // Outputs:
+      //   BV  #BV by 3 list of box vertex positions
+      //   BF  #BF b3 list of box triangle indices into BV
+      template <typename Derivedequ, typename DerivedV>
+      IGL_INLINE void half_space_box(
+        const Eigen::MatrixBase<Derivedequ> & equ,
+        const Eigen::MatrixBase<DerivedV> & V,
+        Eigen::Matrix<CGAL::Epeck::FT,8,3> & BV,
+        Eigen::Matrix<int,12,3> & BF);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "half_space_box.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/hausdorff.cpp

@@ -0,0 +1,39 @@
+#include "hausdorff.h"
+#include "../../hausdorff.h"
+#include <functional>
+
+template <
+  typename DerivedV,
+  typename Kernel,
+  typename Scalar>
+IGL_INLINE void igl::copyleft::cgal::hausdorff(
+  const Eigen::MatrixBase<DerivedV>& V,
+  const CGAL::AABB_tree<
+    CGAL::AABB_traits<Kernel, 
+      CGAL::AABB_triangle_primitive<Kernel, 
+        typename std::vector<CGAL::Triangle_3<Kernel> >::iterator
+      >
+    >
+  > & treeB,
+  const std::vector<CGAL::Triangle_3<Kernel> > & /*TB*/,
+  Scalar & l,
+  Scalar & u)
+{
+  // Not sure why using `auto` here doesn't work with the `hausdorff` function
+  // parameter but explicitly naming the type does...
+  const std::function<double(const double &,const double &,const double &)> 
+    dist_to_B = [&treeB](
+    const double & x, const double & y, const double & z)->double
+  {
+    CGAL::Point_3<Kernel> query(x,y,z);
+    typename CGAL::AABB_tree<
+      CGAL::AABB_traits<Kernel, 
+        CGAL::AABB_triangle_primitive<Kernel, 
+          typename std::vector<CGAL::Triangle_3<Kernel> >::iterator
+        >
+      >
+    >::Point_and_primitive_id pp = treeB.closest_point_and_primitive(query);
+    return std::sqrt((query-pp.first).squared_length());
+  };
+  return igl::hausdorff(V,dist_to_B,l,u);
+}

src/igl/copyleft/cgal/hausdorff.h

@@ -0,0 +1,62 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_HAUSDORFF_H
+#define IGL_COPYLEFT_CGAL_HAUSDORFF_H
+#include "../../igl_inline.h"
+
+#include <Eigen/Dense>
+#include "CGAL_includes.hpp"
+#include <vector>
+
+namespace igl 
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Compute lower and upper bounds (l,u) on the Hausdorff distance between a triangle
+      // (V) and a pointset (e.g., mesh, triangle soup) given by a distance function
+      // handle (dist_to_B).
+      //
+      // Inputs:
+      //   V   3 by 3 list of corner positions so that V.row(i) is the position of the
+      //     ith corner
+      //   treeB  CGAL's AABB tree containing triangle soup (VB,FB)
+      //   TB  list of CGAL triangles in order of FB (for determining which was found
+      //     in computation)
+      // Outputs:
+      //   l  lower bound on Hausdorff distance 
+      //   u  upper bound on Hausdorff distance
+      //
+      template <
+        typename DerivedV,
+        typename Kernel,
+        typename Scalar>
+      IGL_INLINE void hausdorff(
+        const Eigen::MatrixBase<DerivedV>& V,
+        const CGAL::AABB_tree<
+          CGAL::AABB_traits<Kernel, 
+            CGAL::AABB_triangle_primitive<Kernel, 
+              typename std::vector<CGAL::Triangle_3<Kernel> >::iterator
+            >
+          >
+        > & treeB,
+        const std::vector<CGAL::Triangle_3<Kernel> > & TB,
+        Scalar & l,
+        Scalar & u);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "hausdorff.cpp"
+#endif
+
+#endif
+
+

src/igl/copyleft/cgal/incircle.cpp

@@ -0,0 +1,39 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Qingan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "incircle.h"
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+template<typename Scalar>
+IGL_INLINE short igl::copyleft::cgal::incircle(
+    const Scalar pa[2],
+    const Scalar pb[2],
+    const Scalar pc[2],
+    const Scalar pd[2])
+{
+  typedef CGAL::Exact_predicates_exact_constructions_kernel Epeck;
+  typedef CGAL::Exact_predicates_inexact_constructions_kernel Epick;
+  typedef typename std::conditional<std::is_same<Scalar, Epeck::FT>::value,
+          Epeck, Epick>::type Kernel;
+
+  switch(CGAL::side_of_oriented_circle(
+        typename Kernel::Point_2(pa[0], pa[1]),
+        typename Kernel::Point_2(pb[0], pb[1]),
+        typename Kernel::Point_2(pc[0], pc[1]),
+        typename Kernel::Point_2(pd[0], pd[1]))) {
+    case CGAL::ON_POSITIVE_SIDE:
+      return 1;
+    case CGAL::ON_NEGATIVE_SIDE:
+      return -1;
+    case CGAL::ON_ORIENTED_BOUNDARY:
+      return 0;
+    default:
+      throw "Invalid incircle result";
+  }
+}

src/igl/copyleft/cgal/incircle.h

@@ -0,0 +1,39 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Qingan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef IGL_COPYLEFT_CGAL_INCIRCLE_H
+#define IGL_COPYLEFT_CGAL_INCIRCLE_H
+
+#include "../../igl_inline.h"
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Inputs:
+      //   pa,pb,pc,pd  2D points.
+      // Output:
+      //   1 if pd is inside of the oriented circle formed by pa,pb,pc.
+      //   0 if pd is co-circular with pa,pb,pc.
+      //  -1 if pd is outside of the oriented circle formed by pa,pb,pc.
+      template <typename Scalar>
+      IGL_INLINE short incircle(
+          const Scalar pa[2],
+          const Scalar pb[2],
+          const Scalar pc[2],
+          const Scalar pd[2]);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "incircle.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/insert_into_cdt.cpp

@@ -0,0 +1,68 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2016 Alec Jacobson
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "insert_into_cdt.h"
+#include <CGAL/Point_3.h>
+#include <CGAL/Segment_3.h>
+#include <CGAL/Triangle_3.h>
+
+template <typename Kernel>
+IGL_INLINE void igl::copyleft::cgal::insert_into_cdt(
+  const CGAL::Object & obj,
+  const CGAL::Plane_3<Kernel> & P,
+  CGAL::Constrained_triangulation_plus_2<
+    CGAL::Constrained_Delaunay_triangulation_2<
+      Kernel,
+      CGAL::Triangulation_data_structure_2<
+        CGAL::Triangulation_vertex_base_2<Kernel>,
+        CGAL::Constrained_triangulation_face_base_2< Kernel>
+      >,
+      CGAL::Exact_intersections_tag
+    >
+  >
+  & cdt)
+{
+  typedef CGAL::Point_3<Kernel>    Point_3;
+  typedef CGAL::Segment_3<Kernel>  Segment_3;
+  typedef CGAL::Triangle_3<Kernel> Triangle_3;
+
+  if(const Segment_3 *iseg = CGAL::object_cast<Segment_3 >(&obj))
+  {
+    // Add segment constraint
+    cdt.insert_constraint( P.to_2d(iseg->vertex(0)),P.to_2d(iseg->vertex(1)));
+  }else if(const Point_3 *ipoint = CGAL::object_cast<Point_3 >(&obj))
+  {
+    // Add point
+    cdt.insert(P.to_2d(*ipoint));
+  } else if(const Triangle_3 *itri = CGAL::object_cast<Triangle_3 >(&obj))
+  {
+    // Add 3 segment constraints
+    cdt.insert_constraint( P.to_2d(itri->vertex(0)),P.to_2d(itri->vertex(1)));
+    cdt.insert_constraint( P.to_2d(itri->vertex(1)),P.to_2d(itri->vertex(2)));
+    cdt.insert_constraint( P.to_2d(itri->vertex(2)),P.to_2d(itri->vertex(0)));
+  } else if(const std::vector<Point_3 > *polyp =
+      CGAL::object_cast< std::vector<Point_3 > >(&obj))
+  {
+    const std::vector<Point_3 > & poly = *polyp;
+    const size_t m = poly.size();
+    assert(m>=2);
+    for(size_t p = 0;p<m;p++)
+    {
+      const size_t np = (p+1)%m;
+      cdt.insert_constraint(P.to_2d(poly[p]),P.to_2d(poly[np]));
+    }
+  }else {
+    throw std::runtime_error("Unknown intersection object!");
+  }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+template void igl::copyleft::cgal::insert_into_cdt<CGAL::Epick>(CGAL::Object const&, CGAL::Plane_3<CGAL::Epick> const&, CGAL::Constrained_triangulation_plus_2<CGAL::Constrained_Delaunay_triangulation_2<CGAL::Epick, CGAL::Triangulation_data_structure_2<CGAL::Triangulation_vertex_base_2<CGAL::Epick, CGAL::Triangulation_ds_vertex_base_2<void> >, CGAL::Constrained_triangulation_face_base_2<CGAL::Epick, CGAL::Triangulation_face_base_2<CGAL::Epick, CGAL::Triangulation_ds_face_base_2<void> > > >, CGAL::Exact_intersections_tag> >&);
+template void igl::copyleft::cgal::insert_into_cdt<CGAL::Epeck>(CGAL::Object const&, CGAL::Plane_3<CGAL::Epeck> const&, CGAL::Constrained_triangulation_plus_2<CGAL::Constrained_Delaunay_triangulation_2<CGAL::Epeck, CGAL::Triangulation_data_structure_2<CGAL::Triangulation_vertex_base_2<CGAL::Epeck, CGAL::Triangulation_ds_vertex_base_2<void> >, CGAL::Constrained_triangulation_face_base_2<CGAL::Epeck, CGAL::Triangulation_face_base_2<CGAL::Epeck, CGAL::Triangulation_ds_face_base_2<void> > > >, CGAL::Exact_intersections_tag> >&);
+#endif

src/igl/copyleft/cgal/insert_into_cdt.h

@@ -0,0 +1,60 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2016 Alec Jacobson
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_INSERT_INTO_CDT_H
+#define IGL_COPYLEFT_CGAL_INSERT_INTO_CDT_H
+#include "../../igl_inline.h"
+
+#include <CGAL/double.h> // Workaround https://github.com/CGAL/cgal/issues/2182 with CGAL 4.10-1
+#include <CGAL/Plane_3.h>
+#include <CGAL/Constrained_Delaunay_triangulation_2.h>
+#include <CGAL/Constrained_triangulation_plus_2.h>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Given a current 2D constrained Delaunay triangulation (cdt), insert a
+      // 3D "object" (e.g., resulting from intersecting two triangles) into the
+      // cdt, by projecting it via the given plane (P) and adding appropriate
+      // constraints.
+      //
+      // Inputs:
+      //   obj  CGAL::Object representing a vertex, segment, or (convex)
+      //     polygon. All vertices should lie on the plane P. If not, then this
+      //     adds the _projection_ of this object to the cdt and that might not
+      //     be what you wanted to do.
+      //   P  plane obj lies on and upon which the cdt is being performed
+      //   cdt  current CDT, see output
+      // Outputs:
+      //   cdt  CDT updated to contain constraints for the given object
+      //
+      template <typename Kernel>
+      IGL_INLINE void insert_into_cdt(
+        const CGAL::Object & obj,
+        const CGAL::Plane_3<Kernel> & P,
+        CGAL::Constrained_triangulation_plus_2<
+          CGAL::Constrained_Delaunay_triangulation_2<
+            Kernel,
+            CGAL::Triangulation_data_structure_2<
+              CGAL::Triangulation_vertex_base_2<Kernel>,
+              CGAL::Constrained_triangulation_face_base_2< Kernel>
+            >,
+            CGAL::Exact_intersections_tag
+          >
+        >
+        & cdt);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "insert_into_cdt.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/insphere.cpp

@@ -0,0 +1,41 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Qingan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "insphere.h"
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+template<typename Scalar>
+IGL_INLINE short igl::copyleft::cgal::insphere(
+    const Scalar pa[3],
+    const Scalar pb[3],
+    const Scalar pc[3],
+    const Scalar pd[3],
+    const Scalar pe[3])
+{
+  typedef CGAL::Exact_predicates_exact_constructions_kernel Epeck;
+  typedef CGAL::Exact_predicates_inexact_constructions_kernel Epick;
+  typedef typename std::conditional<std::is_same<Scalar, Epeck::FT>::value,
+          Epeck, Epick>::type Kernel;
+
+  switch(CGAL::side_of_oriented_sphere(
+        typename Kernel::Point_3(pa[0], pa[1], pa[2]),
+        typename Kernel::Point_3(pb[0], pb[1], pb[2]),
+        typename Kernel::Point_3(pc[0], pc[1], pc[2]),
+        typename Kernel::Point_3(pd[0], pd[1], pd[2]),
+        typename Kernel::Point_3(pe[0], pe[1], pe[2]))) {
+    case CGAL::ON_POSITIVE_SIDE:
+      return 1;
+    case CGAL::ON_NEGATIVE_SIDE:
+      return -1;
+    case CGAL::ON_ORIENTED_BOUNDARY:
+      return 0;
+    default:
+      throw "Invalid incircle result";
+  }
+}

src/igl/copyleft/cgal/insphere.h

@@ -0,0 +1,40 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Qingan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef IGL_COPYLEFT_CGAL_INSPHERE_H
+#define IGL_COPYLEFT_CGAL_INSPHERE_H
+
+#include "../../igl_inline.h"
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Inputs:
+      //   pa,pb,pc,pd,pe  3D points.
+      // Output:
+      //   1 if pe is inside of the oriented sphere formed by pa,pb,pc,pd.
+      //   0 if pe is co-spherical with pa,pb,pc,pd.
+      //  -1 if pe is outside of the oriented sphere formed by pa,pb,pc,pd.
+      template <typename Scalar>
+      IGL_INLINE short insphere(
+          const Scalar pa[3],
+          const Scalar pb[3],
+          const Scalar pc[3],
+          const Scalar pd[3],
+          const Scalar pe[3]);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "insphere.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/intersect_other.cpp

@@ -0,0 +1,289 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "intersect_other.h"
+#include "CGAL_includes.hpp"
+#include "mesh_to_cgal_triangle_list.h"
+#include "remesh_intersections.h"
+#include "../../slice_mask.h"
+#include "../../remove_unreferenced.h"
+
+#ifndef IGL_FIRST_HIT_EXCEPTION
+#define IGL_FIRST_HIT_EXCEPTION 10
+#endif
+
+// Un-exposed helper functions
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      template <typename DerivedF>
+      static IGL_INLINE void push_result(
+        const Eigen::PlainObjectBase<DerivedF> & F,
+        const int f,
+        const int f_other,
+        const CGAL::Object & result,
+        std::map<
+          typename DerivedF::Index,
+          std::vector<std::pair<typename DerivedF::Index, CGAL::Object> > > &
+          offending)
+        //std::map<
+        //  std::pair<typename DerivedF::Index,typename DerivedF::Index>,
+        //  std::vector<typename DerivedF::Index> > & edge2faces)
+      {
+        typedef typename DerivedF::Index Index;
+        typedef std::pair<Index,Index> EMK;
+        if(offending.count(f) == 0)
+        {
+          // first time marking, initialize with new id and empty list
+          offending[f] = {};
+          for(Index e = 0; e<3;e++)
+          {
+            // append face to edge's list
+            Index i = F(f,(e+1)%3) < F(f,(e+2)%3) ? F(f,(e+1)%3) : F(f,(e+2)%3);
+            Index j = F(f,(e+1)%3) < F(f,(e+2)%3) ? F(f,(e+2)%3) : F(f,(e+1)%3);
+            //edge2faces[EMK(i,j)].push_back(f);
+          }
+        }
+        offending[f].push_back({f_other,result});
+      }
+      template <
+        typename Kernel,
+        typename DerivedVA,
+        typename DerivedFA,
+        typename DerivedVB,
+        typename DerivedFB,
+        typename DerivedIF,
+        typename DerivedVVAB,
+        typename DerivedFFAB,
+        typename DerivedJAB,
+        typename DerivedIMAB>
+      static IGL_INLINE bool intersect_other_helper(
+        const Eigen::PlainObjectBase<DerivedVA> & VA,
+        const Eigen::PlainObjectBase<DerivedFA> & FA,
+        const Eigen::PlainObjectBase<DerivedVB> & VB,
+        const Eigen::PlainObjectBase<DerivedFB> & FB,
+        const RemeshSelfIntersectionsParam & params,
+        Eigen::PlainObjectBase<DerivedIF> & IF,
+        Eigen::PlainObjectBase<DerivedVVAB> & VVAB,
+        Eigen::PlainObjectBase<DerivedFFAB> & FFAB,
+        Eigen::PlainObjectBase<DerivedJAB>  & JAB,
+        Eigen::PlainObjectBase<DerivedIMAB> & IMAB)
+      {
+
+        using namespace std;
+        using namespace Eigen;
+
+        typedef typename DerivedFA::Index Index;
+        // 3D Primitives
+        typedef CGAL::Point_3<Kernel>    Point_3;
+        typedef CGAL::Segment_3<Kernel>  Segment_3; 
+        typedef CGAL::Triangle_3<Kernel> Triangle_3; 
+        typedef CGAL::Plane_3<Kernel>    Plane_3;
+        typedef CGAL::Tetrahedron_3<Kernel> Tetrahedron_3; 
+        // 2D Primitives
+        typedef CGAL::Point_2<Kernel>    Point_2;
+        typedef CGAL::Segment_2<Kernel>  Segment_2; 
+        typedef CGAL::Triangle_2<Kernel> Triangle_2; 
+        // 2D Constrained Delaunay Triangulation types
+        typedef CGAL::Triangulation_vertex_base_2<Kernel>  TVB_2;
+        typedef CGAL::Constrained_triangulation_face_base_2<Kernel> CTAB_2;
+        typedef CGAL::Triangulation_data_structure_2<TVB_2,CTAB_2> TDS_2;
+        typedef CGAL::Exact_intersections_tag Itag;
+        // Axis-align boxes for all-pairs self-intersection detection
+        typedef std::vector<Triangle_3> Triangles;
+        typedef typename Triangles::iterator TrianglesIterator;
+        typedef typename Triangles::const_iterator TrianglesConstIterator;
+        typedef 
+          CGAL::Box_intersection_d::Box_with_handle_d<double,3,TrianglesIterator> 
+          Box;
+        typedef 
+          std::map<Index,std::vector<std::pair<Index,CGAL::Object> > > 
+          OffendingMap;
+        typedef std::map<std::pair<Index,Index>,std::vector<Index> >  EdgeMap;
+        typedef std::pair<Index,Index> EMK;
+
+        Triangles TA,TB;
+        // Compute and process self intersections
+        mesh_to_cgal_triangle_list(VA,FA,TA);
+        mesh_to_cgal_triangle_list(VB,FB,TB);
+        // http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Box_intersection_d/Chapter_main.html#Section_63.5 
+        // Create the corresponding vector of bounding boxes
+        std::vector<Box> A_boxes,B_boxes;
+        const auto box_up = [](Triangles & T, std::vector<Box> & boxes) -> void
+        {
+          boxes.reserve(T.size());
+          for ( 
+            TrianglesIterator tit = T.begin(); 
+            tit != T.end(); 
+            ++tit)
+          {
+            boxes.push_back(Box(tit->bbox(), tit));
+          }
+        };
+        box_up(TA,A_boxes);
+        box_up(TB,B_boxes);
+        OffendingMap offendingA,offendingB;
+        //EdgeMap edge2facesA,edge2facesB;
+
+        std::list<int> lIF;
+        const auto cb = [&](const Box &a, const Box &b) -> void
+        {
+          using namespace std;
+          // index in F and T
+          int fa = a.handle()-TA.begin();
+          int fb = b.handle()-TB.begin();
+          const Triangle_3 & A = *a.handle();
+          const Triangle_3 & B = *b.handle();
+          if(CGAL::do_intersect(A,B))
+          {
+            // There was an intersection
+            lIF.push_back(fa);
+            lIF.push_back(fb);
+            if(params.first_only)
+            {
+              throw IGL_FIRST_HIT_EXCEPTION;
+            }
+            if(!params.detect_only)
+            {
+              CGAL::Object result = CGAL::intersection(A,B);
+
+              push_result(FA,fa,fb,result,offendingA);
+              push_result(FB,fb,fa,result,offendingB);
+            }
+          }
+        };
+        try{
+          CGAL::box_intersection_d(
+            A_boxes.begin(), A_boxes.end(),
+            B_boxes.begin(), B_boxes.end(),
+            cb);
+        }catch(int e)
+        {
+          // Rethrow if not FIRST_HIT_EXCEPTION
+          if(e != IGL_FIRST_HIT_EXCEPTION)
+          {
+            throw e;
+          }
+          // Otherwise just fall through
+        }
+
+        // Convert lIF to Eigen matrix
+        assert(lIF.size()%2 == 0);
+        IF.resize(lIF.size()/2,2);
+        {
+          int i=0;
+          for(
+            list<int>::const_iterator ifit = lIF.begin();
+            ifit!=lIF.end();
+            )
+          {
+            IF(i,0) = (*ifit);
+            ifit++; 
+            IF(i,1) = (*ifit);
+            ifit++;
+            i++;
+          }
+        }
+        if(!params.detect_only)
+        {
+          // Obsolete, now remesh_intersections expects a single mesh
+          // remesh_intersections(VA,FA,TA,offendingA,VVA,FFA,JA,IMA);
+          // remesh_intersections(VB,FB,TB,offendingB,VVB,FFB,JB,IMB);
+          // Combine mesh and offending maps
+          DerivedVA VAB(VA.rows()+VB.rows(),3);
+          VAB<<VA,VB;
+          DerivedFA FAB(FA.rows()+FB.rows(),3);
+          FAB<<FA,(FB.array()+VA.rows());
+          Triangles TAB;
+          TAB.reserve(TA.size()+TB.size());
+          TAB.insert(TAB.end(),TA.begin(),TA.end());
+          TAB.insert(TAB.end(),TB.begin(),TB.end());
+          OffendingMap offending;
+          //offending.reserve(offendingA.size() + offendingB.size());
+          for (const auto itr : offendingA)
+          {
+            // Remap offenders in FB to FAB
+            auto offenders = itr.second;
+            for(auto & offender : offenders)
+            {
+              offender.first += FA.rows();
+            }
+            offending[itr.first] = offenders;
+          }
+          for (const auto itr : offendingB)
+          {
+            // Store offenders for FB according to place in FAB
+            offending[FA.rows() + itr.first] = itr.second;
+          }
+
+          remesh_intersections(
+            VAB,FAB,TAB,offending,params.stitch_all,VVAB,FFAB,JAB,IMAB);
+        }
+
+        return IF.rows() > 0;
+      }
+    }
+  }
+}
+
+template <
+  typename DerivedVA,
+  typename DerivedFA,
+  typename DerivedVB,
+  typename DerivedFB,
+  typename DerivedIF,
+  typename DerivedVVAB,
+  typename DerivedFFAB,
+  typename DerivedJAB,
+  typename DerivedIMAB>
+IGL_INLINE bool igl::copyleft::cgal::intersect_other(
+    const Eigen::PlainObjectBase<DerivedVA> & VA,
+    const Eigen::PlainObjectBase<DerivedFA> & FA,
+    const Eigen::PlainObjectBase<DerivedVB> & VB,
+    const Eigen::PlainObjectBase<DerivedFB> & FB,
+    const RemeshSelfIntersectionsParam & params,
+    Eigen::PlainObjectBase<DerivedIF> & IF,
+    Eigen::PlainObjectBase<DerivedVVAB> & VVAB,
+    Eigen::PlainObjectBase<DerivedFFAB> & FFAB,
+    Eigen::PlainObjectBase<DerivedJAB>  & JAB,
+    Eigen::PlainObjectBase<DerivedIMAB> & IMAB)
+{
+  if(params.detect_only)
+  {
+    return intersect_other_helper<CGAL::Epick>
+      (VA,FA,VB,FB,params,IF,VVAB,FFAB,JAB,IMAB);
+  }else
+  {
+    return intersect_other_helper<CGAL::Epeck>
+      (VA,FA,VB,FB,params,IF,VVAB,FFAB,JAB,IMAB);
+  }
+}
+
+IGL_INLINE bool igl::copyleft::cgal::intersect_other(
+  const Eigen::MatrixXd & VA,
+  const Eigen::MatrixXi & FA,
+  const Eigen::MatrixXd & VB,
+  const Eigen::MatrixXi & FB,
+  const bool first_only,
+  Eigen::MatrixXi & IF)
+{
+  Eigen::MatrixXd VVAB;
+  Eigen::MatrixXi FFAB;
+  Eigen::VectorXi JAB,IMAB;
+  return intersect_other(
+    VA,FA,VB,FB,{true,first_only},IF,VVAB,FFAB,JAB,IMAB);
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template bool igl::copyleft::cgal::intersect_other<Eigen::Matrix<double, -1, -1, 0, -1, -1>,   Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>,   Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>,   Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1,   -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&,   Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&,   Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&,   Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&,   igl::copyleft::cgal::RemeshSelfIntersectionsParam const&,   Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&,   Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> >&,   Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&,   Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&,   Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template bool igl::copyleft::cgal::intersect_other<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::copyleft::cgal::RemeshSelfIntersectionsParam const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+#endif

src/igl/copyleft/cgal/intersect_other.h

@@ -0,0 +1,91 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_INTERSECT_OTHER_H
+#define IGL_COPYLEFT_CGAL_INTERSECT_OTHER_H
+#include "../../igl_inline.h"
+#include "RemeshSelfIntersectionsParam.h"
+
+#include <Eigen/Dense>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // INTERSECT_OTHER Given a triangle mesh (VA,FA) and another mesh (VB,FB)
+      // find all pairs of intersecting faces. Note that self-intersections are
+      // ignored.
+      // 
+      // Inputs:
+      //   VA  #V by 3 list of vertex positions
+      //   FA  #F by 3 list of triangle indices into VA
+      //   VB  #V by 3 list of vertex positions
+      //   FB  #F by 3 list of triangle indices into VB
+      //   params   whether to detect only and then whether to only find first
+      //     intersection
+      // Outputs:
+      //   IF  #intersecting face pairs by 2 list of intersecting face pairs,
+      //     indexing FA and FB
+      //   VVAB  #VVAB by 3 list of vertex positions
+      //   FFAB  #FFAB by 3 list of triangle indices into VVA
+      //   JAB  #FFAB list of indices into [FA;FB] denoting birth triangle
+      //   IMAB  #VVAB list of indices stitching duplicates (resulting from
+      //     mesh intersections) together
+      template <
+        typename DerivedVA,
+        typename DerivedFA,
+        typename DerivedVB,
+        typename DerivedFB,
+        typename DerivedIF,
+        typename DerivedVVAB,
+        typename DerivedFFAB,
+        typename DerivedJAB,
+        typename DerivedIMAB>
+      IGL_INLINE bool intersect_other(
+        const Eigen::PlainObjectBase<DerivedVA> & VA,
+        const Eigen::PlainObjectBase<DerivedFA> & FA,
+        const Eigen::PlainObjectBase<DerivedVB> & VB,
+        const Eigen::PlainObjectBase<DerivedFB> & FB,
+        const RemeshSelfIntersectionsParam & params,
+        Eigen::PlainObjectBase<DerivedIF> & IF,
+        Eigen::PlainObjectBase<DerivedVVAB> & VVAB,
+        Eigen::PlainObjectBase<DerivedFFAB> & FFAB,
+        Eigen::PlainObjectBase<DerivedJAB>  & JAB,
+        Eigen::PlainObjectBase<DerivedIMAB> & IMAB);
+      // Legacy wrapper for detect only using common types.
+      //
+      // Inputs:
+      //   VA  #V by 3 list of vertex positions
+      //   FA  #F by 3 list of triangle indices into VA
+      //   VB  #V by 3 list of vertex positions
+      //   FB  #F by 3 list of triangle indices into VB
+      //   first_only  whether to only detect the first intersection.
+      // Outputs:
+      //   IF  #intersecting face pairs by 2 list of intersecting face pairs,
+      //     indexing FA and FB
+      // Returns true if any intersections were found
+      //
+      // See also: remesh_self_intersections
+      IGL_INLINE bool intersect_other(
+        const Eigen::MatrixXd & VA,
+        const Eigen::MatrixXi & FA,
+        const Eigen::MatrixXd & VB,
+        const Eigen::MatrixXi & FB,
+        const bool first_only,
+        Eigen::MatrixXi & IF);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "intersect_other.cpp"
+#endif
+  
+#endif
+

src/igl/copyleft/cgal/intersect_with_half_space.cpp

@@ -0,0 +1,88 @@
+#include "intersect_with_half_space.h"
+#include "mesh_boolean.h"
+#include "half_space_box.h"
+
+template <
+  typename DerivedV,
+  typename DerivedF,
+  typename Derivedp,
+  typename Derivedn,
+  typename DerivedVC,
+  typename DerivedFC,
+  typename DerivedJ>
+IGL_INLINE bool igl::copyleft::cgal::intersect_with_half_space(
+  const Eigen::MatrixBase<DerivedV > & V,
+  const Eigen::MatrixBase<DerivedF > & F,
+  const Eigen::MatrixBase<Derivedp > & p,
+  const Eigen::MatrixBase<Derivedn > & n,
+  Eigen::PlainObjectBase<DerivedVC > & VC,
+  Eigen::PlainObjectBase<DerivedFC > & FC,
+  Eigen::PlainObjectBase<DerivedJ > & J)
+{
+  typedef CGAL::Plane_3<CGAL::Epeck> Plane;
+  typedef CGAL::Point_3<CGAL::Epeck> Point;
+  typedef CGAL::Vector_3<CGAL::Epeck> Vector;
+  Plane P(Point(p(0),p(1),p(2)),Vector(n(0),n(1),n(2)));
+  return intersect_with_half_space(V,F,P,VC,FC,J);
+}
+
+template <
+  typename DerivedV,
+  typename DerivedF,
+  typename Derivedequ,
+  typename DerivedVC,
+  typename DerivedFC,
+  typename DerivedJ>
+IGL_INLINE bool igl::copyleft::cgal::intersect_with_half_space(
+  const Eigen::MatrixBase<DerivedV > & V,
+  const Eigen::MatrixBase<DerivedF > & F,
+  const Eigen::MatrixBase<Derivedequ > & equ,
+  Eigen::PlainObjectBase<DerivedVC > & VC,
+  Eigen::PlainObjectBase<DerivedFC > & FC,
+  Eigen::PlainObjectBase<DerivedJ > & J)
+{
+  typedef CGAL::Plane_3<CGAL::Epeck> Plane;
+  Plane P(equ(0),equ(1),equ(2),equ(3));
+  return intersect_with_half_space(V,F,P,VC,FC,J);
+}
+
+template <
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedVC,
+  typename DerivedFC,
+  typename DerivedJ>
+IGL_INLINE bool igl::copyleft::cgal::intersect_with_half_space(
+  const Eigen::MatrixBase<DerivedV > & V,
+  const Eigen::MatrixBase<DerivedF > & F,
+  const CGAL::Plane_3<CGAL::Epeck> & P,
+  Eigen::PlainObjectBase<DerivedVC > & VC,
+  Eigen::PlainObjectBase<DerivedFC > & FC,
+  Eigen::PlainObjectBase<DerivedJ > & J)
+{
+  Eigen::Matrix<CGAL::Epeck::FT,8,3> BV;
+  Eigen::Matrix<int,12,3> BF;
+  half_space_box(P,V,BV,BF);
+  // Disturbingly, (BV,BF) must be first argument
+  const bool ret = mesh_boolean(BV,BF,V,F,MESH_BOOLEAN_TYPE_INTERSECT,VC,FC,J);
+  // But now J is wrong...
+  std::for_each(
+    J.data(),
+    J.data()+J.size(),
+    [&BF,&F](typename DerivedJ::Scalar & j)
+      {j = (j<BF.rows()?F.rows()+j:j-BF.rows());}
+    );
+  return ret;
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template bool igl::copyleft::cgal::intersect_with_half_space<Eigen::Matrix<double, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+// generated by autoexplicit.sh
+template bool igl::copyleft::cgal::intersect_with_half_space<Eigen::Matrix<double, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::CwiseUnaryOp<Eigen::internal::scalar_opposite_op<double>, Eigen::Matrix<double, 1, 3, 1, 1, 3> const>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::CwiseUnaryOp<Eigen::internal::scalar_opposite_op<double>, Eigen::Matrix<double, 1, 3, 1, 1, 3> const> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+// generated by autoexplicit.sh
+template bool igl::copyleft::cgal::intersect_with_half_space<Eigen::Matrix<float, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<float, 1, 3, 1, 1, 3>, Eigen::Matrix<float, 1, 3, 1, 1, 3>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<float, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<float, 1, 3, 1, 1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+// generated by autoexplicit.sh
+template bool igl::copyleft::cgal::intersect_with_half_space<Eigen::Matrix<float, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<float, 1, 3, 1, 1, 3>, Eigen::CwiseUnaryOp<Eigen::internal::scalar_opposite_op<float>, Eigen::Matrix<float, 1, 3, 1, 1, 3> const>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<float, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::CwiseUnaryOp<Eigen::internal::scalar_opposite_op<float>, Eigen::Matrix<float, 1, 3, 1, 1, 3> const> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+#endif

src/igl/copyleft/cgal/intersect_with_half_space.h

@@ -0,0 +1,96 @@
+#ifndef IGL_COPYLEFT_CGAL_INTERSECT_WITH_HALF_SPACE_H
+#define IGL_COPYLEFT_CGAL_INTERSECT_WITH_HALF_SPACE_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/Plane_3.h>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Intersect a PWN mesh with a half-space. Point on plane, normal pointing
+      // outward.
+      //
+      // Inputs:
+      //   V  #V by 3 list of mesh vertex positions
+      //   p  3d point on plane
+      //   n  3d vector of normal of plane pointing away from inside
+      // Outputs:
+      //   VC  #VC by 3 list of vertex positions of boolean result mesh
+      //   FC  #FC by 3 list of triangle indices into VC
+      //   J  #FC list of indices into [F;F.rows()+[1;2]] revealing "birth"
+      //     facet
+      template <
+        typename DerivedV,
+        typename DerivedF,
+        typename Derivedp,
+        typename Derivedn,
+        typename DerivedVC,
+        typename DerivedFC,
+        typename DerivedJ>
+      IGL_INLINE bool intersect_with_half_space(
+        const Eigen::MatrixBase<DerivedV > & V,
+        const Eigen::MatrixBase<DerivedF > & F,
+        const Eigen::MatrixBase<Derivedp > & p,
+        const Eigen::MatrixBase<Derivedn > & n,
+        Eigen::PlainObjectBase<DerivedVC > & VC,
+        Eigen::PlainObjectBase<DerivedFC > & FC,
+        Eigen::PlainObjectBase<DerivedJ > & J);
+      // Intersect a PWN mesh with a half-space. Plane equation.
+      //
+      // Inputs:
+      //   V  #V by 3 list of mesh vertex positions
+      //   equ  plane equation: P(x,y,z) = a*x+b*y+c*z + d = 0, P(x,y,z) < 0 is
+      //     _inside_.
+      // Outputs:
+      //   VC  #VC by 3 list of vertex positions of boolean result mesh
+      //   FC  #FC by 3 list of triangle indices into VC
+      //   J  #FC list of indices into [F;F.rows()+[1;2]] revealing "birth" facet
+      template <
+        typename DerivedV,
+        typename DerivedF,
+        typename Derivedequ,
+        typename DerivedVC,
+        typename DerivedFC,
+        typename DerivedJ>
+      IGL_INLINE bool intersect_with_half_space(
+        const Eigen::MatrixBase<DerivedV > & V,
+        const Eigen::MatrixBase<DerivedF > & F,
+        const Eigen::MatrixBase<Derivedequ > & equ,
+        Eigen::PlainObjectBase<DerivedVC > & VC,
+        Eigen::PlainObjectBase<DerivedFC > & FC,
+        Eigen::PlainObjectBase<DerivedJ > & J);
+      // Intersect a PWN mesh with a half-space. CGAL Plane.
+      //
+      // Inputs:
+      //   V  #V by 3 list of mesh vertex positions
+      //   P  plane 
+      // Outputs:
+      //   VC  #VC by 3 list of vertex positions of boolean result mesh
+      //   FC  #FC by 3 list of triangle indices into VC
+      //   J  #FC list of indices into [F;F.rows()+[1;2]] revealing "birth" facet
+      template <
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedVC,
+        typename DerivedFC,
+        typename DerivedJ>
+      IGL_INLINE bool intersect_with_half_space(
+        const Eigen::MatrixBase<DerivedV > & V,
+        const Eigen::MatrixBase<DerivedF > & F,
+        const CGAL::Plane_3<CGAL::Epeck> & P,
+        Eigen::PlainObjectBase<DerivedVC > & VC,
+        Eigen::PlainObjectBase<DerivedFC > & FC,
+        Eigen::PlainObjectBase<DerivedJ > & J);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "intersect_with_half_space.cpp"
+#endif
+
+#endif

src/igl/copyleft/cgal/lexicographic_triangulation.cpp

@@ -0,0 +1,24 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+//                    Qingan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "lexicographic_triangulation.h"
+#include "../../lexicographic_triangulation.h"
+#include "orient2D.h"
+
+template<
+  typename DerivedP,
+  typename DerivedF
+  >
+IGL_INLINE void igl::copyleft::cgal::lexicographic_triangulation(
+    const Eigen::PlainObjectBase<DerivedP>& P,
+    Eigen::PlainObjectBase<DerivedF>& F)
+{
+  typedef typename DerivedP::Scalar Scalar;
+  igl::lexicographic_triangulation(P, orient2D<Scalar>, F);
+}

src/igl/copyleft/cgal/lexicographic_triangulation.h

@@ -0,0 +1,47 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+//                    Qingan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef IGL_COPYLEFT_CGAL_LEXICOGRAPHIC_TRIANGULATION_H
+#define IGL_COPYLEFT_CGAL_LEXICOGRAPHIC_TRIANGULATION_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+
+      // Given a set of points in 2D, return a lexicographic triangulation of these
+      // points.
+      //
+      // Inputs:
+      //   P  #P by 2 list of vertex positions
+      //
+      // Outputs:
+      //   F  #F by 3 of faces in lexicographic triangulation.
+      template<
+        typename DerivedP,
+        typename DerivedF
+        >
+      IGL_INLINE void lexicographic_triangulation(
+          const Eigen::PlainObjectBase<DerivedP>& P,
+          Eigen::PlainObjectBase<DerivedF>& F);
+    }
+  }
+}
+
+
+
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "lexicographic_triangulation.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/list_to_matrix.cpp

@@ -0,0 +1,15 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2017 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "../../list_to_matrix.h"
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#ifdef IGL_STATIC_LIBRARY
+#undef IGL_STATIC_LIBRARY
+#include "../../list_to_matrix.cpp"
+template bool igl::list_to_matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>,   Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>   >(std::vector<std::vector<CGAL::Lazy_exact_nt<CGAL::Gmpq>,   std::allocator<CGAL::Lazy_exact_nt<CGAL::Gmpq> > >,   std::allocator<std::vector<CGAL::Lazy_exact_nt<CGAL::Gmpq>,   std::allocator<CGAL::Lazy_exact_nt<CGAL::Gmpq> > > > > const&,   Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3,   0, -1, 3> >&);
+#endif

src/igl/copyleft/cgal/mesh_boolean.cpp

@@ -0,0 +1,466 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+//                    Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+//
+#include "mesh_boolean.h"
+#include "assign.h"
+#include "extract_cells.h"
+#include "mesh_boolean_type_to_funcs.h"
+#include "propagate_winding_numbers.h"
+#include "relabel_small_immersed_cells.h"
+#include "remesh_self_intersections.h"
+#include "string_to_mesh_boolean_type.h"
+#include "../../combine.h"
+#include "../../cumsum.h"
+#include "../../extract_manifold_patches.h"
+#include "../../get_seconds.h"
+#include "../../remove_unreferenced.h"
+#include "../../resolve_duplicated_faces.h"
+#include "../../slice.h"
+#include "../../unique_edge_map.h"
+#include "../../unique_simplices.h"
+
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <algorithm>
+
+//#define MESH_BOOLEAN_TIMING
+//#define DOUBLE_CHECK_EXACT_OUTPUT
+//#define SMALL_CELL_REMOVAL
+
+template <
+  typename DerivedVA,
+  typename DerivedFA,
+  typename DerivedVB,
+  typename DerivedFB,
+  typename DerivedVC,
+  typename DerivedFC,
+  typename DerivedJ>
+IGL_INLINE bool igl::copyleft::cgal::mesh_boolean(
+    const Eigen::MatrixBase<DerivedVA > & VA,
+    const Eigen::MatrixBase<DerivedFA > & FA,
+    const Eigen::MatrixBase<DerivedVB > & VB,
+    const Eigen::MatrixBase<DerivedFB > & FB,
+    const MeshBooleanType & type,
+    Eigen::PlainObjectBase<DerivedVC > & VC,
+    Eigen::PlainObjectBase<DerivedFC > & FC,
+    Eigen::PlainObjectBase<DerivedJ > & J)
+{
+  std::function<int(const int, const int)> keep;
+  std::function<int(const Eigen::Matrix<int,1,Eigen::Dynamic>) > wind_num_op;
+  mesh_boolean_type_to_funcs(type,wind_num_op,keep);
+  return mesh_boolean(VA,FA,VB,FB,wind_num_op,keep,VC,FC,J);
+}
+template <
+  typename DerivedVA,
+  typename DerivedFA,
+  typename DerivedVB,
+  typename DerivedFB,
+  typename DerivedVC,
+  typename DerivedFC,
+  typename DerivedJ>
+IGL_INLINE bool igl::copyleft::cgal::mesh_boolean(
+  const Eigen::MatrixBase<DerivedVA > & VA,
+  const Eigen::MatrixBase<DerivedFA > & FA,
+  const Eigen::MatrixBase<DerivedVB > & VB,
+  const Eigen::MatrixBase<DerivedFB > & FB,
+  const std::string & type_str,
+  Eigen::PlainObjectBase<DerivedVC > & VC,
+  Eigen::PlainObjectBase<DerivedFC > & FC,
+  Eigen::PlainObjectBase<DerivedJ > & J)
+{
+  return mesh_boolean(
+    VA,FA,VB,FB,string_to_mesh_boolean_type(type_str),VC,FC,J);
+}
+
+template <
+  typename DerivedVA,
+  typename DerivedFA,
+  typename DerivedVB,
+  typename DerivedFB,
+  typename DerivedVC,
+  typename DerivedFC,
+  typename DerivedJ>
+IGL_INLINE bool igl::copyleft::cgal::mesh_boolean(
+    const Eigen::MatrixBase<DerivedVA> & VA,
+    const Eigen::MatrixBase<DerivedFA> & FA,
+    const Eigen::MatrixBase<DerivedVB> & VB,
+    const Eigen::MatrixBase<DerivedFB> & FB,
+    const std::function<int(const Eigen::Matrix<int,1,Eigen::Dynamic>) >& wind_num_op,
+    const std::function<int(const int, const int)> & keep,
+    Eigen::PlainObjectBase<DerivedVC > & VC,
+    Eigen::PlainObjectBase<DerivedFC > & FC,
+    Eigen::PlainObjectBase<DerivedJ > & J) 
+{
+  // Generate combined mesh (VA,FA,VB,FB) -> (V,F)
+  Eigen::Matrix<size_t,2,1> sizes(FA.rows(),FB.rows());
+  // TODO: This is a precision template **bug** that results in failure to
+  // compile. If DerivedVA::Scalar is double and DerivedVB::Scalar is
+  // CGAL::Epeck::FT then the following assignment will not compile. This
+  // implies that VA must have the trumping precision (and a valid assignment
+  // operator from VB's type).
+  Eigen::Matrix<typename DerivedVA::Scalar,Eigen::Dynamic,3> VV(VA.rows() + VB.rows(), 3);
+  DerivedFC FF(FA.rows() + FB.rows(), 3);
+  // Can't use comma initializer
+  for(int a = 0;a<VA.rows();a++)
+  {
+    for(int d = 0;d<3;d++) VV(a,d) = VA(a,d);
+  }
+  for(int b = 0;b<VB.rows();b++)
+  {
+    for(int d = 0;d<3;d++) VV(VA.rows()+b,d) = VB(b,d);
+  }
+  FF.block(0, 0, FA.rows(), 3) = FA;
+  // Eigen struggles to assign nothing to nothing and will assert if FB is empty
+  if(FB.rows() > 0)
+  {
+    FF.block(FA.rows(), 0, FB.rows(), 3) = FB.array() + VA.rows();
+  }
+  return mesh_boolean(VV,FF,sizes,wind_num_op,keep,VC,FC,J);
+}
+
+template <
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedVC,
+  typename DerivedFC,
+  typename DerivedJ>
+IGL_INLINE bool igl::copyleft::cgal::mesh_boolean(
+    const std::vector<DerivedV > & Vlist,
+    const std::vector<DerivedF > & Flist,
+    const std::function<int(const Eigen::Matrix<int,1,Eigen::Dynamic>) >& wind_num_op,
+    const std::function<int(const int, const int)> & keep,
+    Eigen::PlainObjectBase<DerivedVC > & VC,
+    Eigen::PlainObjectBase<DerivedFC > & FC,
+    Eigen::PlainObjectBase<DerivedJ > & J)
+{
+  DerivedV VV;
+  DerivedF FF;
+  Eigen::Matrix<size_t,Eigen::Dynamic,1> Vsizes,Fsizes;
+  igl::combine(Vlist,Flist,VV,FF,Vsizes,Fsizes);
+  return mesh_boolean(VV,FF,Fsizes,wind_num_op,keep,VC,FC,J);
+}
+
+template <
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedVC,
+  typename DerivedFC,
+  typename DerivedJ>
+IGL_INLINE bool igl::copyleft::cgal::mesh_boolean(
+    const std::vector<DerivedV > & Vlist,
+    const std::vector<DerivedF > & Flist,
+    const MeshBooleanType & type,
+    Eigen::PlainObjectBase<DerivedVC > & VC,
+    Eigen::PlainObjectBase<DerivedFC > & FC,
+    Eigen::PlainObjectBase<DerivedJ > & J)
+{
+  DerivedV VV;
+  DerivedF FF;
+  Eigen::Matrix<size_t,Eigen::Dynamic,1> Vsizes,Fsizes;
+  igl::combine(Vlist,Flist,VV,FF,Vsizes,Fsizes);
+  std::function<int(const int, const int)> keep;
+  std::function<int(const Eigen::Matrix<int,1,Eigen::Dynamic>) > wind_num_op;
+  mesh_boolean_type_to_funcs(type,wind_num_op,keep);
+  return mesh_boolean(VV,FF,Fsizes,wind_num_op,keep,VC,FC,J);
+}
+
+template <
+  typename DerivedVV,
+  typename DerivedFF,
+  typename Derivedsizes,
+  typename DerivedVC,
+  typename DerivedFC,
+  typename DerivedJ>
+IGL_INLINE bool igl::copyleft::cgal::mesh_boolean(
+    const Eigen::MatrixBase<DerivedVV > & VV,
+    const Eigen::MatrixBase<DerivedFF > & FF,
+    const Eigen::MatrixBase<Derivedsizes> & sizes,
+    const std::function<int(const Eigen::Matrix<int,1,Eigen::Dynamic>) >& wind_num_op,
+    const std::function<int(const int, const int)> & keep,
+    Eigen::PlainObjectBase<DerivedVC > & VC,
+    Eigen::PlainObjectBase<DerivedFC > & FC,
+    Eigen::PlainObjectBase<DerivedJ > & J)
+{
+#ifdef MESH_BOOLEAN_TIMING
+  const auto & tictoc = []() -> double
+  {
+    static double t_start = igl::get_seconds();
+    double diff = igl::get_seconds()-t_start;
+    t_start += diff;
+    return diff;
+  };
+  const auto log_time = [&](const std::string& label) -> void {
+    std::cout << "mesh_boolean." << label << ": "
+      << tictoc() << std::endl;
+  };
+  tictoc();
+#endif
+  typedef typename DerivedVC::Scalar Scalar;
+  typedef CGAL::Epeck Kernel;
+  typedef Kernel::FT ExactScalar;
+  typedef Eigen::Matrix<Scalar,Eigen::Dynamic,3> MatrixX3S;
+  typedef Eigen::Matrix<typename DerivedJ::Scalar,Eigen::Dynamic,1> VectorXJ;
+  typedef Eigen::Matrix<
+    ExactScalar,
+    Eigen::Dynamic,
+    Eigen::Dynamic,
+    DerivedVC::IsRowMajor> MatrixXES;
+  MatrixXES V;
+  DerivedFC F;
+  VectorXJ  CJ;
+  {
+    Eigen::VectorXi I;
+    igl::copyleft::cgal::RemeshSelfIntersectionsParam params;
+    params.stitch_all = true;
+    MatrixXES Vr;
+    DerivedFC Fr;
+    Eigen::MatrixXi IF;
+    igl::copyleft::cgal::remesh_self_intersections(
+        VV, FF, params, Vr, Fr, IF, CJ, I);
+    assert(I.size() == Vr.rows());
+    // Merge coinciding vertices into non-manifold vertices.
+    std::for_each(Fr.data(), Fr.data()+Fr.size(),
+          [&I](typename DerivedFC::Scalar& a) { a=I[a]; });
+      // Remove unreferenced vertices.
+      Eigen::VectorXi UIM;
+      igl::remove_unreferenced(Vr, Fr, V, F, UIM);
+   }
+#ifdef MESH_BOOLEAN_TIMING
+  log_time("resolve_self_intersection");
+#endif
+
+  // Compute edges of (F) --> (E,uE,EMAP,uE2E)
+  Eigen::MatrixXi E, uE;
+  Eigen::VectorXi EMAP;
+  std::vector<std::vector<size_t> > uE2E;
+  igl::unique_edge_map(F, E, uE, EMAP, uE2E);
+
+  // Compute patches (F,EMAP,uE2E) --> (P)
+  Eigen::VectorXi P;
+  const size_t num_patches = igl::extract_manifold_patches(F, EMAP, uE2E, P);
+#ifdef MESH_BOOLEAN_TIMING
+  log_time("patch_extraction");
+#endif
+
+  // Compute cells (V,F,P,E,uE,EMAP) -> (per_patch_cells)
+  Eigen::MatrixXi per_patch_cells;
+  const size_t num_cells =
+    igl::copyleft::cgal::extract_cells(
+        V, F, P, E, uE, uE2E, EMAP, per_patch_cells);
+#ifdef MESH_BOOLEAN_TIMING
+  log_time("cell_extraction");
+#endif
+
+  // Compute winding numbers on each side of each facet.
+  const size_t num_faces = F.rows();
+  // W(f,:) --> [w1out,w1in,w2out,w2in, ... wnout,wnint] winding numbers above
+  // and below each face w.r.t. each input mesh, so that W(f,2*i) is the
+  // winding number above face f w.r.t. input i, and W(f,2*i+1) is the winding
+  // number below face f w.r.t. input i.
+  Eigen::MatrixXi W;
+  // labels(f) = i means that face f comes from mesh i
+  Eigen::VectorXi labels(num_faces);
+  // cumulative sizes
+  Derivedsizes cumsizes;
+  igl::cumsum(sizes,1,cumsizes);
+  const size_t num_inputs = sizes.size();
+  std::transform(
+    CJ.data(), 
+    CJ.data()+CJ.size(), 
+    labels.data(),
+    // Determine which input mesh birth face i comes from
+    [&num_inputs,&cumsizes](int i)->int
+    { 
+      for(int k = 0;k<num_inputs;k++)
+      {
+        if(i<cumsizes(k)) return k;
+      }
+      assert(false && "Birth parent index out of range");
+      return -1;
+    });
+  bool valid = true;
+  if (num_faces > 0) 
+  {
+    valid = valid & 
+      igl::copyleft::cgal::propagate_winding_numbers(
+          V, F, uE, uE2E, num_patches, P, num_cells, per_patch_cells, labels, W);
+  } else 
+  {
+    W.resize(0, 2*num_inputs);
+  }
+  assert((size_t)W.rows() == num_faces);
+  // If W doesn't have enough columns, pad with zeros
+  if (W.cols() <= 2*num_inputs) 
+  {
+    const int old_ncols = W.cols();
+    W.conservativeResize(num_faces,2*num_inputs);
+    W.rightCols(2*num_inputs-old_ncols).setConstant(0);
+  }
+  assert((size_t)W.cols() == 2*num_inputs);
+#ifdef MESH_BOOLEAN_TIMING
+  log_time("propagate_input_winding_number");
+#endif
+
+  // Compute resulting winding number.
+  Eigen::MatrixXi Wr(num_faces, 2);
+  for (size_t i=0; i<num_faces; i++) 
+  {
+    // Winding number vectors above and below
+    Eigen::RowVectorXi w_out(1,num_inputs), w_in(1,num_inputs);
+    for(size_t k =0;k<num_inputs;k++)
+    {
+      w_out(k) = W(i,2*k+0);
+      w_in(k) = W(i,2*k+1);
+    }
+    Wr(i,0) = wind_num_op(w_out);
+    Wr(i,1) = wind_num_op(w_in);
+  }
+#ifdef MESH_BOOLEAN_TIMING
+  log_time("compute_output_winding_number");
+#endif
+
+#ifdef SMALL_CELL_REMOVAL
+  igl::copyleft::cgal::relabel_small_immersed_cells(
+    V, F, num_patches, P, num_cells, per_patch_cells, 1e-3, Wr);
+#endif
+
+  // Extract boundary separating inside from outside.
+  auto index_to_signed_index = [&](size_t i, bool ori) -> int
+  {
+    return (i+1)*(ori?1:-1);
+  };
+  //auto signed_index_to_index = [&](int i) -> size_t {
+  //    return abs(i) - 1;
+  //};
+  std::vector<int> selected;
+  for(size_t i=0; i<num_faces; i++) 
+  {
+    auto should_keep = keep(Wr(i,0), Wr(i,1));
+    if (should_keep > 0) 
+    {
+      selected.push_back(index_to_signed_index(i, true));
+    } else if (should_keep < 0) 
+    {
+      selected.push_back(index_to_signed_index(i, false));
+    }
+  }
+
+  const size_t num_selected = selected.size();
+  DerivedFC kept_faces(num_selected, 3);
+  DerivedJ  kept_face_indices(num_selected, 1);
+  for (size_t i=0; i<num_selected; i++) 
+  {
+    size_t idx = abs(selected[i]) - 1;
+    if (selected[i] > 0) 
+    {
+      kept_faces.row(i) = F.row(idx);
+    } else 
+    {
+      kept_faces.row(i) = F.row(idx).reverse();
+    }
+    kept_face_indices(i, 0) = CJ[idx];
+  }
+#ifdef MESH_BOOLEAN_TIMING
+  log_time("extract_output");
+#endif
+
+  // Finally, remove duplicated faces and unreferenced vertices.
+  {
+    DerivedFC G;
+    DerivedJ JJ;
+    igl::resolve_duplicated_faces(kept_faces, G, JJ);
+    igl::slice(kept_face_indices, JJ, 1, J);
+
+#ifdef DOUBLE_CHECK_EXACT_OUTPUT
+    {
+      // Sanity check on exact output.
+      igl::copyleft::cgal::RemeshSelfIntersectionsParam params;
+      params.detect_only = true;
+      params.first_only = true;
+      MatrixXES dummy_VV;
+      DerivedFC dummy_FF, dummy_IF;
+      Eigen::VectorXi dummy_J, dummy_IM;
+      igl::copyleft::cgal::SelfIntersectMesh<
+        Kernel,
+        MatrixXES, DerivedFC,
+        MatrixXES, DerivedFC,
+        DerivedFC,
+        Eigen::VectorXi,
+        Eigen::VectorXi
+      > checker(V, G, params,
+          dummy_VV, dummy_FF, dummy_IF, dummy_J, dummy_IM);
+      if (checker.count != 0) 
+      {
+        throw "Self-intersection not fully resolved.";
+      }
+    }
+#endif
+
+    MatrixX3S Vs;
+    assign(V,Vs);
+    Eigen::VectorXi newIM;
+    igl::remove_unreferenced(Vs,G,VC,FC,newIM);
+  }
+#ifdef MESH_BOOLEAN_TIMING
+  log_time("clean_up");
+#endif
+  return valid;
+}
+
+template <
+  typename DerivedVA,
+  typename DerivedFA,
+  typename DerivedVB,
+  typename DerivedFB,
+  typename DerivedVC,
+  typename DerivedFC>
+IGL_INLINE bool igl::copyleft::cgal::mesh_boolean(
+  const Eigen::MatrixBase<DerivedVA > & VA,
+  const Eigen::MatrixBase<DerivedFA > & FA,
+  const Eigen::MatrixBase<DerivedVB > & VB,
+  const Eigen::MatrixBase<DerivedFB > & FB,
+  const MeshBooleanType & type,
+  Eigen::PlainObjectBase<DerivedVC > & VC,
+  Eigen::PlainObjectBase<DerivedFC > & FC) 
+{
+  Eigen::Matrix<typename DerivedFC::Index, Eigen::Dynamic,1> J;
+  return igl::copyleft::cgal::mesh_boolean(VA,FA,VB,FB,type,VC,FC,J);
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3>, Eigen::Matrix<int, 12, 3, 0, 12, 3>, Eigen::Matrix<double, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, 12, 3, 0, 12, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, igl::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+// generated by autoexplicit.sh
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 1, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+// generated by autoexplicit.sh
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<float, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+// generated by autoexplicit.sh
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+// generated by autoexplicit.sh
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<float, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<float, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+// generated by autoexplicit.sh
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3>, Eigen::Matrix<int, 12, 3, 0, 12, 3>, Eigen::Matrix<float, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, 12, 3, 0, 12, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, igl::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<float, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3>, Eigen::Matrix<int, 12, 3, 0, 12, 3>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, 12, 3, 0, 12, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3>, Eigen::Matrix<int, 12, 3, 0, 12, 3>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 4, 0, -1, 4>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 4, 0, -1, 4>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, 12, 3, 0, 12, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 4, 0, -1, 4> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 4, 0, -1, 4> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<long, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> >&);
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3>, Eigen::Matrix<int, 12, 3, 0, 12, 3>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, 12, 3, 0, 12, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, igl::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(std::vector<Eigen::Matrix<double, -1, -1, 0, -1, -1>, std::allocator<Eigen::Matrix<double, -1, -1, 0, -1, -1> > > const&, std::vector<Eigen::Matrix<int, -1, -1, 0, -1, -1>, std::allocator<Eigen::Matrix<int, -1, -1, 0, -1, -1> > > const&, std::function<int (Eigen::Matrix<int, 1, -1, 1, 1, -1>)> const&, std::function<int (int, int)> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template bool igl::copyleft::cgal::mesh_boolean<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(std::vector<Eigen::Matrix<double, -1, -1, 0, -1, -1>, std::allocator<Eigen::Matrix<double, -1, -1, 0, -1, -1> > > const&, std::vector<Eigen::Matrix<int, -1, -1, 0, -1, -1>, std::allocator<Eigen::Matrix<int, -1, -1, 0, -1, -1> > > const&, igl::MeshBooleanType const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+#ifdef WIN32
+template bool igl::copyleft::cgal::mesh_boolean<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, 3, 0, -1, 3>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, 3, 0, -1, 3>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, 3, 0, -1, 3>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>>(class Eigen::MatrixBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, 3, 0, -1, 3>> const &, class Eigen::MatrixBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::MatrixBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, 3, 0, -1, 3>> const &, class Eigen::MatrixBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, enum igl::MeshBooleanType const &, class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, 3, 0, -1, 3>> &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> &, class Eigen::PlainObjectBase<class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>> &);
+#endif
+#endif

src/igl/copyleft/cgal/mesh_boolean.h

@@ -0,0 +1,229 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+//                    Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+//
+#ifndef IGL_COPYLEFT_CGAL_MESH_BOOLEAN_H
+#define IGL_COPYLEFT_CGAL_MESH_BOOLEAN_H
+
+#include "../../igl_inline.h"
+#include "../../MeshBooleanType.h"
+#include <Eigen/Core>
+#include <functional>
+#include <vector>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      //  MESH_BOOLEAN Compute boolean csg operations on "solid", consistently
+      //  oriented meshes.
+      //
+      //  Inputs:
+      //    VA  #VA by 3 list of vertex positions of first mesh
+      //    FA  #FA by 3 list of triangle indices into VA
+      //    VB  #VB by 3 list of vertex positions of second mesh
+      //    FB  #FB by 3 list of triangle indices into VB
+      //    type  type of boolean operation
+      //  Outputs:
+      //    VC  #VC by 3 list of vertex positions of boolean result mesh
+      //    FC  #FC by 3 list of triangle indices into VC
+      //    J  #FC list of indices into [FA;FA.rows()+FB] revealing "birth" facet
+      //  Returns true if inputs induce a piecewise constant winding number
+      //  field and type is valid
+      //
+      //  See also: mesh_boolean_cork, intersect_other,
+      //  remesh_self_intersections
+      template <
+        typename DerivedVA,
+        typename DerivedFA,
+        typename DerivedVB,
+        typename DerivedFB,
+        typename DerivedVC,
+        typename DerivedFC,
+        typename DerivedJ>
+      IGL_INLINE bool mesh_boolean(
+        const Eigen::MatrixBase<DerivedVA > & VA,
+        const Eigen::MatrixBase<DerivedFA > & FA,
+        const Eigen::MatrixBase<DerivedVB > & VB,
+        const Eigen::MatrixBase<DerivedFB > & FB,
+        const MeshBooleanType & type,
+        Eigen::PlainObjectBase<DerivedVC > & VC,
+        Eigen::PlainObjectBase<DerivedFC > & FC,
+        Eigen::PlainObjectBase<DerivedJ > & J);
+      template <
+        typename DerivedVA,
+        typename DerivedFA,
+        typename DerivedVB,
+        typename DerivedFB,
+        typename DerivedVC,
+        typename DerivedFC,
+        typename DerivedJ>
+      IGL_INLINE bool mesh_boolean(
+        const Eigen::MatrixBase<DerivedVA > & VA,
+        const Eigen::MatrixBase<DerivedFA > & FA,
+        const Eigen::MatrixBase<DerivedVB > & VB,
+        const Eigen::MatrixBase<DerivedFB > & FB,
+        const std::string & type_str,
+        Eigen::PlainObjectBase<DerivedVC > & VC,
+        Eigen::PlainObjectBase<DerivedFC > & FC,
+        Eigen::PlainObjectBase<DerivedJ > & J);
+      //
+      //  Inputs:
+      //    VA  #VA by 3 list of vertex positions of first mesh
+      //    FA  #FA by 3 list of triangle indices into VA
+      //    VB  #VB by 3 list of vertex positions of second mesh
+      //    FB  #FB by 3 list of triangle indices into VB
+      //    wind_num_op  function handle for filtering winding numbers from
+      //      tuples of integer values to [0,1] outside/inside values
+      //    keep  function handle for determining if a patch should be "kept"
+      //      in the output based on the winding number on either side
+      //  Outputs:
+      //    VC  #VC by 3 list of vertex positions of boolean result mesh
+      //    FC  #FC by 3 list of triangle indices into VC
+      //    J  #FC list of indices into [FA;FB] revealing "birth" facet
+      //  Returns true iff inputs induce a piecewise constant winding number
+      //    field
+      //
+      //  See also: mesh_boolean_cork, intersect_other,
+      //  remesh_self_intersections
+      template <
+        typename DerivedVA,
+        typename DerivedFA,
+        typename DerivedVB,
+        typename DerivedFB,
+        typename DerivedVC,
+        typename DerivedFC,
+        typename DerivedJ>
+      IGL_INLINE bool mesh_boolean(
+          const Eigen::MatrixBase<DerivedVA> & VA,
+          const Eigen::MatrixBase<DerivedFA> & FA,
+          const Eigen::MatrixBase<DerivedVB> & VB,
+          const Eigen::MatrixBase<DerivedFB> & FB,
+          const std::function<int(const Eigen::Matrix<int,1,Eigen::Dynamic>) >& wind_num_op,
+          const std::function<int(const int, const int)> & keep,
+          Eigen::PlainObjectBase<DerivedVC > & VC,
+          Eigen::PlainObjectBase<DerivedFC > & FC,
+          Eigen::PlainObjectBase<DerivedJ > & J);
+      //  MESH_BOOLEAN Variadic boolean operations
+      //
+      //  Inputs:
+      //    Vlist  k-long list of lists of mesh vertex positions
+      //    Flist  k-long list of lists of mesh face indices, so that Flist[i] indexes
+      //      vertices in Vlist[i]
+      //    wind_num_op  function handle for filtering winding numbers from
+      //      n-tuples of integer values to [0,1] outside/inside values
+      //    keep  function handle for determining if a patch should be "kept"
+      //      in the output based on the winding number on either side
+      //  Outputs:
+      //    VC  #VC by 3 list of vertex positions of boolean result mesh
+      //    FC  #FC by 3 list of triangle indices into VC
+      //    J  #FC list of indices into [Flist[0];Flist[1];...;Flist[k]]
+      //      revealing "birth" facet
+      //  Returns true iff inputs induce a piecewise constant winding number
+      //    field
+      //
+      //  See also: mesh_boolean_cork, intersect_other,
+      //  remesh_self_intersections
+      template <
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedVC,
+        typename DerivedFC,
+        typename DerivedJ>
+      IGL_INLINE bool mesh_boolean(
+          const std::vector<DerivedV > & Vlist,
+          const std::vector<DerivedF > & Flist,
+          const std::function<int(const Eigen::Matrix<int,1,Eigen::Dynamic>) >& wind_num_op,
+          const std::function<int(const int, const int)> & keep,
+          Eigen::PlainObjectBase<DerivedVC > & VC,
+          Eigen::PlainObjectBase<DerivedFC > & FC,
+          Eigen::PlainObjectBase<DerivedJ > & J);
+      template <
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedVC,
+        typename DerivedFC,
+        typename DerivedJ>
+      IGL_INLINE bool mesh_boolean(
+          const std::vector<DerivedV > & Vlist,
+          const std::vector<DerivedF > & Flist,
+          const MeshBooleanType & type,
+          Eigen::PlainObjectBase<DerivedVC > & VC,
+          Eigen::PlainObjectBase<DerivedFC > & FC,
+          Eigen::PlainObjectBase<DerivedJ > & J);
+      // Given a merged mesh (V,F) and list of sizes of inputs
+      //
+      // Inputs:
+      //   V  #V by 3 list of merged mesh vertex positions
+      //   F  #F by 3 list of merged mesh face indices so that first sizes(0)
+      //     faces come from the first input, and the next sizes(1) faces come
+      //     from the second input, and so on.
+      //   sizes  #inputs list of sizes so that sizes(i) is the #faces in the
+      //     ith input
+      //    wind_num_op  function handle for filtering winding numbers from
+      //      tuples of integer values to [0,1] outside/inside values
+      //    keep  function handle for determining if a patch should be "kept"
+      //      in the output based on the winding number on either side
+      //  Outputs:
+      //    VC  #VC by 3 list of vertex positions of boolean result mesh
+      //    FC  #FC by 3 list of triangle indices into VC
+      //    J  #FC list of birth parent indices
+      // 
+      template <
+        typename DerivedVV,
+        typename DerivedFF,
+        typename Derivedsizes,
+        typename DerivedVC,
+        typename DerivedFC,
+        typename DerivedJ>
+      IGL_INLINE bool mesh_boolean(
+          const Eigen::MatrixBase<DerivedVV > & VV,
+          const Eigen::MatrixBase<DerivedFF > & FF,
+          const Eigen::MatrixBase<Derivedsizes> & sizes,
+          const std::function<int(const Eigen::Matrix<int,1,Eigen::Dynamic>) >& wind_num_op,
+          const std::function<int(const int, const int)> & keep,
+          Eigen::PlainObjectBase<DerivedVC > & VC,
+          Eigen::PlainObjectBase<DerivedFC > & FC,
+          Eigen::PlainObjectBase<DerivedJ > & J);
+      //  Inputs:
+      //    VA  #VA by 3 list of vertex positions of first mesh
+      //    FA  #FA by 3 list of triangle indices into VA
+      //    VB  #VB by 3 list of vertex positions of second mesh
+      //    FB  #FB by 3 list of triangle indices into VB
+      //    type  type of boolean operation
+      //  Outputs:
+      //    VC  #VC by 3 list of vertex positions of boolean result mesh
+      //    FC  #FC by 3 list of triangle indices into VC
+      //  Returns true ff inputs induce a piecewise constant winding number
+      //    field and type is valid
+      template <
+        typename DerivedVA,
+        typename DerivedFA,
+        typename DerivedVB,
+        typename DerivedFB,
+        typename DerivedVC,
+        typename DerivedFC>
+      IGL_INLINE bool mesh_boolean(
+          const Eigen::MatrixBase<DerivedVA > & VA,
+          const Eigen::MatrixBase<DerivedFA > & FA,
+          const Eigen::MatrixBase<DerivedVB > & VB,
+          const Eigen::MatrixBase<DerivedFB > & FB,
+          const MeshBooleanType & type,
+          Eigen::PlainObjectBase<DerivedVC > & VC,
+          Eigen::PlainObjectBase<DerivedFC > & FC);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "mesh_boolean.cpp"
+#endif
+
+#endif

src/igl/copyleft/cgal/mesh_boolean_type_to_funcs.cpp

@@ -0,0 +1,39 @@
+#include "mesh_boolean_type_to_funcs.h"
+#include "BinaryWindingNumberOperations.h"
+
+IGL_INLINE void igl::copyleft::cgal::mesh_boolean_type_to_funcs(
+  const MeshBooleanType & type,
+  std::function<int(const Eigen::Matrix<int,1,Eigen::Dynamic>) >& wind_num_op,
+  std::function<int(const int, const int)> & keep)
+{
+  switch (type) 
+  {
+    case MESH_BOOLEAN_TYPE_UNION:
+      wind_num_op = BinaryUnion();
+      keep = KeepInside();
+      return;
+    case MESH_BOOLEAN_TYPE_INTERSECT:
+      wind_num_op = BinaryIntersect();
+      keep = KeepInside();
+      return;
+    case MESH_BOOLEAN_TYPE_MINUS:
+      wind_num_op = BinaryMinus();
+      keep = KeepInside();
+      return;
+    case MESH_BOOLEAN_TYPE_XOR:
+      wind_num_op = BinaryXor();
+      keep = KeepInside();
+      return;
+    case MESH_BOOLEAN_TYPE_RESOLVE:
+      wind_num_op = BinaryResolve();
+      keep = KeepAll();
+      return;
+    default:
+      assert(false && "Unsupported boolean type.");
+      return;
+  }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+#endif

src/igl/copyleft/cgal/mesh_boolean_type_to_funcs.h

@@ -0,0 +1,37 @@
+#ifndef IGL_COPYLEFT_CGAL_MESH_BOOLEAN_TYPE_TO_FUNCS_H
+#define IGL_COPYLEFT_CGAL_MESH_BOOLEAN_TYPE_TO_FUNCS_H
+
+#include "../../igl_inline.h"
+#include "../../MeshBooleanType.h"
+#include <Eigen/Core>
+#include <functional>
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Convert a MeshBooleanType enum to a pair of winding number conversion
+      // function and "keep" function used by mesh_boolean
+      //
+      // Inputs:
+      //   type  MeshBooleanType enum value
+      // Outputs:
+      //    wind_num_op  function handle for filtering winding numbers from
+      //      tuples of integer values to [0,1] outside/inside values
+      //    keep  function handle for determining if a patch should be "kept"
+      //      in the output based on the winding number on either side
+      //
+      // See also: string_to_mesh_boolean_type
+      IGL_INLINE void mesh_boolean_type_to_funcs(
+        const MeshBooleanType & type,
+        std::function<int(const Eigen::Matrix<int,1,Eigen::Dynamic>) >& 
+          wind_num_op,
+        std::function<int(const int, const int)> & keep);
+    }
+  }
+}
+#ifndef IGL_STATIC_LIBRARY
+#  include "mesh_boolean_type_to_funcs.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/mesh_to_cgal_triangle_list.cpp

@@ -0,0 +1,76 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "mesh_to_cgal_triangle_list.h"
+#include "assign.h"
+
+#include <cassert>
+
+template <
+  typename DerivedV,
+  typename DerivedF,
+  typename Kernel>
+IGL_INLINE void igl::copyleft::cgal::mesh_to_cgal_triangle_list(
+  const Eigen::MatrixBase<DerivedV> & V,
+  const Eigen::MatrixBase<DerivedF> & F,
+  std::vector<CGAL::Triangle_3<Kernel> > & T)
+{
+  typedef CGAL::Point_3<Kernel>    Point_3;
+  typedef CGAL::Triangle_3<Kernel> Triangle_3; 
+  // Must be 3D
+  assert(V.cols() == 3);
+  // **Copy** to convert to output type (this is especially/only needed if the
+  // input type DerivedV::Scalar is CGAL::Epeck
+  Eigen::Matrix<
+    typename Kernel::FT,
+    DerivedV::RowsAtCompileTime,
+    DerivedV::ColsAtCompileTime> 
+    KV(V.rows(),V.cols());
+  assign(V,KV);
+  // Must be triangles
+  assert(F.cols() == 3);
+  T.reserve(F.rows());
+  // Loop over faces
+  for(int f = 0;f<(int)F.rows();f++)
+  {
+    T.push_back(
+      Triangle_3(
+        Point_3( KV(F(f,0),0), KV(F(f,0),1), KV(F(f,0),2)),
+        Point_3( KV(F(f,1),0), KV(F(f,1),1), KV(F(f,1),2)),
+        Point_3( KV(F(f,2),0), KV(F(f,2),1), KV(F(f,2),2))));
+  }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, CGAL::Epick>(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, std::vector<CGAL::Triangle_3<CGAL::Epick>, std::allocator<CGAL::Triangle_3<CGAL::Epick> > >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, CGAL::Epeck>(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, std::vector<CGAL::Triangle_3<CGAL::Epeck>, std::allocator<CGAL::Triangle_3<CGAL::Epeck> > >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, CGAL::Epick>(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<CGAL::Triangle_3<CGAL::Epick>, std::allocator<CGAL::Triangle_3<CGAL::Epick> > >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, CGAL::Epeck>(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<CGAL::Triangle_3<CGAL::Epeck>, std::allocator<CGAL::Triangle_3<CGAL::Epeck> > >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, CGAL::Epick>(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<CGAL::Triangle_3<CGAL::Epick>, std::allocator<CGAL::Triangle_3<CGAL::Epick> > >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, CGAL::Epeck>(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<CGAL::Triangle_3<CGAL::Epeck>, std::allocator<CGAL::Triangle_3<CGAL::Epeck> > >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, CGAL::Epick>(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<CGAL::Triangle_3<CGAL::Epick>, std::allocator<CGAL::Triangle_3<CGAL::Epick> > >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, CGAL::Epeck>(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<CGAL::Triangle_3<CGAL::Epeck>, std::allocator<CGAL::Triangle_3<CGAL::Epeck> > >&);
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, CGAL::Epeck>(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, std::vector<CGAL::Triangle_3<CGAL::Epeck>, std::allocator<CGAL::Triangle_3<CGAL::Epeck> > >&);
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, CGAL::Epick>(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, std::vector<CGAL::Triangle_3<CGAL::Epick>, std::allocator<CGAL::Triangle_3<CGAL::Epick> > >&);
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, CGAL::Epeck>(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<CGAL::Triangle_3<CGAL::Epeck>, std::allocator<CGAL::Triangle_3<CGAL::Epeck> > >&);
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, CGAL::Epick>(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<CGAL::Triangle_3<CGAL::Epick>, std::allocator<CGAL::Triangle_3<CGAL::Epick> > >&);
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, CGAL::Epeck>(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, std::vector<CGAL::Triangle_3<CGAL::Epeck>, std::allocator<CGAL::Triangle_3<CGAL::Epeck> > >&);
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, CGAL::Epick>(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, std::vector<CGAL::Triangle_3<CGAL::Epick>, std::allocator<CGAL::Triangle_3<CGAL::Epick> > >&);
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, CGAL::Epick>(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<CGAL::Triangle_3<CGAL::Epick>, std::allocator<CGAL::Triangle_3<CGAL::Epick> > >&);
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, CGAL::Epeck>(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<CGAL::Triangle_3<CGAL::Epeck>, std::allocator<CGAL::Triangle_3<CGAL::Epeck> > >&);
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, CGAL::Epick>(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<CGAL::Triangle_3<CGAL::Epick>, std::allocator<CGAL::Triangle_3<CGAL::Epick> > >&);
+template void igl::copyleft::cgal::mesh_to_cgal_triangle_list<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, CGAL::Epeck>(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 8, 3, 0, 8, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<CGAL::Triangle_3<CGAL::Epeck>, std::allocator<CGAL::Triangle_3<CGAL::Epeck> > >&);
+#endif

src/igl/copyleft/cgal/mesh_to_cgal_triangle_list.h

@@ -0,0 +1,44 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_MESH_TO_CGAL_TRIANGLE_LIST_H
+#define IGL_COPYLEFT_CGAL_MESH_TO_CGAL_TRIANGLE_LIST_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include "CGAL_includes.hpp"
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Convert a mesh (V,F) to a list of CGAL triangles
+      //
+      // Templates:
+      //   Kernal  CGAL computation and construction kernel (e.g.
+      //     CGAL::Exact_predicates_exact_constructions_kernel)
+      // Inputs:
+      //   V  #V by 3 list of vertex positions
+      //   F  #F by 3 list of triangle indices
+      // Outputs:
+      //   T  #F list of CGAL triangles
+      template <
+        typename DerivedV,
+        typename DerivedF,
+        typename Kernel>
+      IGL_INLINE void mesh_to_cgal_triangle_list(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedF> & F,
+        std::vector<CGAL::Triangle_3<Kernel> > & T);
+    }
+  }
+}
+#ifndef IGL_STATIC_LIBRARY
+#  include "mesh_to_cgal_triangle_list.cpp"
+#endif
+
+#endif

src/igl/copyleft/cgal/mesh_to_polyhedron.cpp

@@ -0,0 +1,54 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "mesh_to_polyhedron.h"
+#include <CGAL/Polyhedron_3.h>
+#include <CGAL/Polyhedron_incremental_builder_3.h>
+
+
+template <typename Polyhedron>
+IGL_INLINE bool igl::copyleft::cgal::mesh_to_polyhedron(
+  const Eigen::MatrixXd & V,
+  const Eigen::MatrixXi & F,
+  Polyhedron & poly)
+{
+  typedef typename Polyhedron::HalfedgeDS HalfedgeDS;
+  // Postcondition: hds is a valid polyhedral surface.
+  CGAL::Polyhedron_incremental_builder_3<HalfedgeDS> B(poly.hds());
+  B.begin_surface(V.rows(),F.rows());
+  typedef typename HalfedgeDS::Vertex   Vertex;
+  typedef typename Vertex::Point Point;
+  assert(V.cols() == 3 && "V must be #V by 3");
+  for(int v = 0;v<V.rows();v++)
+  {
+    B.add_vertex(Point(V(v,0),V(v,1),V(v,2)));
+  }
+  assert(F.cols() == 3 && "F must be #F by 3");
+  for(int f=0;f<F.rows();f++)
+  {
+    B.begin_facet();
+    for(int c = 0;c<3;c++)
+    {
+      B.add_vertex_to_facet(F(f,c));
+    }
+    B.end_facet();
+  }
+  if(B.error())
+  {
+    B.rollback();
+    return false;
+  }
+  B.end_surface();
+  return poly.is_valid();
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+#include <CGAL/Simple_cartesian.h>
+#include <CGAL/Polyhedron_items_with_id_3.h>
+template bool igl::copyleft::cgal::mesh_to_polyhedron<CGAL::Polyhedron_3<CGAL::Simple_cartesian<double>, CGAL::Polyhedron_items_with_id_3, CGAL::HalfedgeDS_default, std::allocator<int> > >(Eigen::Matrix<double, -1, -1, 0, -1, -1> const&, Eigen::Matrix<int, -1, -1, 0, -1, -1> const&, CGAL::Polyhedron_3<CGAL::Simple_cartesian<double>, CGAL::Polyhedron_items_with_id_3, CGAL::HalfedgeDS_default, std::allocator<int> >&);
+#endif

src/igl/copyleft/cgal/mesh_to_polyhedron.h

@@ -0,0 +1,42 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_MESH_TO_POLYHEDRON_H
+#define IGL_COPYLEFT_CGAL_MESH_TO_POLYHEDRON_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Convert a mesh (V,F) to a CGAL Polyhedron
+      //
+      // Templates:
+      //   Polyhedron  CGAL Polyhedron type (e.g. Polyhedron_3)
+      // Inputs:
+      //   V  #V by 3 list of vertex positions
+      //   F  #F by 3 list of triangle indices
+      // Outputs:
+      //   poly  cgal polyhedron
+      // Returns true only if (V,F) can be converted to a valid polyhedron (i.e. if
+      // (V,F) is vertex and edge manifold).
+      template <typename Polyhedron>
+      IGL_INLINE bool mesh_to_polyhedron(
+        const Eigen::MatrixXd & V,
+        const Eigen::MatrixXi & F,
+        Polyhedron & poly);
+    }
+  }
+}
+#ifndef IGL_STATIC_LIBRARY
+#  include "mesh_to_polyhedron.cpp"
+#endif
+
+#endif

src/igl/copyleft/cgal/minkowski_sum.cpp

@@ -0,0 +1,395 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "minkowski_sum.h"
+#include "mesh_boolean.h"
+
+#include "../../slice.h"
+#include "../../slice_mask.h"
+#include "../../LinSpaced.h"
+#include "../../unique_rows.h"
+#include "../../get_seconds.h"
+#include "../../edges.h"
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <cassert>
+#include <vector>
+#include <iostream>
+
+
+template <
+  typename DerivedVA,
+  typename DerivedFA,
+  typename DerivedVB,
+  typename DerivedFB,
+  typename DerivedW,
+  typename DerivedG,
+  typename DerivedJ>
+IGL_INLINE void igl::copyleft::cgal::minkowski_sum(
+  const Eigen::MatrixBase<DerivedVA> & VA,
+  const Eigen::MatrixBase<DerivedFA> & FA,
+  const Eigen::MatrixBase<DerivedVB> & VB,
+  const Eigen::MatrixBase<DerivedFB> & FB,
+  const bool resolve_overlaps,
+  Eigen::PlainObjectBase<DerivedW> & W,
+  Eigen::PlainObjectBase<DerivedG> & G,
+  Eigen::PlainObjectBase<DerivedJ> & J)
+{
+  using namespace std;
+  using namespace Eigen;
+  assert(FA.cols() == 3 && "FA must contain a closed triangle mesh");
+  assert(FB.cols() <= FA.cols() && 
+    "FB must contain lower diemnsional simplices than FA");
+  const auto tictoc = []()->double
+  {
+    static double t_start;
+    double now = igl::get_seconds();
+    double interval = now-t_start;
+    t_start = now;
+    return interval;
+  };
+  tictoc();
+  Matrix<typename DerivedFB::Scalar,Dynamic,2> EB;
+  edges(FB,EB);
+  Matrix<typename DerivedFA::Scalar,Dynamic,2> EA(0,2);
+  if(FB.cols() == 3)
+  {
+    edges(FA,EA);
+  }
+  // number of copies of A along edges of B
+  const int n_ab = EB.rows();
+  // number of copies of B along edges of A
+  const int n_ba = EA.rows();
+
+  vector<DerivedW> vW(n_ab + n_ba);
+  vector<DerivedG> vG(n_ab + n_ba);
+  vector<DerivedJ> vJ(n_ab + n_ba);
+  vector<int> offsets(n_ab + n_ba + 1);
+  offsets[0] = 0;
+  // sweep A along edges of B
+  for(int e = 0;e<n_ab;e++)
+  {
+    Matrix<typename DerivedJ::Scalar,Dynamic,1> eJ;
+    minkowski_sum(
+      VA,
+      FA,
+      VB.row(EB(e,0)).eval(),
+      VB.row(EB(e,1)).eval(),
+      false,
+      vW[e],
+      vG[e],
+      eJ);
+    assert(vG[e].rows() == eJ.rows());
+    assert(eJ.cols() == 1);
+    vJ[e].resize(vG[e].rows(),2);
+    vJ[e].col(0) = eJ;
+    vJ[e].col(1).setConstant(e);
+    offsets[e+1] = offsets[e] + vW[e].rows();
+  }
+  // sweep B along edges of A
+  for(int e = 0;e<n_ba;e++)
+  {
+    Matrix<typename DerivedJ::Scalar,Dynamic,1> eJ;
+    const int ee = n_ab+e;
+    minkowski_sum(
+      VB,
+      FB,
+      VA.row(EA(e,0)).eval(),
+      VA.row(EA(e,1)).eval(),
+      false,
+      vW[ee],
+      vG[ee],
+      eJ);
+    vJ[ee].resize(vG[ee].rows(),2);
+    vJ[ee].col(0) = eJ.array() + (FA.rows()+1);
+    vJ[ee].col(1).setConstant(ee);
+    offsets[ee+1] = offsets[ee] + vW[ee].rows();
+  }
+  // Combine meshes
+  int n=0,m=0;
+  for_each(vW.begin(),vW.end(),[&n](const DerivedW & w){n+=w.rows();});
+  for_each(vG.begin(),vG.end(),[&m](const DerivedG & g){m+=g.rows();});
+  assert(n == offsets.back());
+
+  W.resize(n,3);
+  G.resize(m,3);
+  J.resize(m,2);
+  {
+    int m_off = 0,n_off = 0;
+    for(int i = 0;i<vG.size();i++)
+    {
+      W.block(n_off,0,vW[i].rows(),3) = vW[i];
+      G.block(m_off,0,vG[i].rows(),3) = vG[i].array()+offsets[i];
+      J.block(m_off,0,vJ[i].rows(),2) = vJ[i];
+      n_off += vW[i].rows();
+      m_off += vG[i].rows();
+    }
+    assert(n == n_off);
+    assert(m == m_off);
+  }
+  if(resolve_overlaps)
+  {
+    Eigen::Matrix<typename DerivedJ::Scalar, Eigen::Dynamic,1> SJ;
+    mesh_boolean(
+      DerivedW(W),
+      DerivedG(G),
+      Matrix<typename DerivedW::Scalar,Dynamic,Dynamic>(),
+      Matrix<typename DerivedG::Scalar,Dynamic,Dynamic>(),
+      MESH_BOOLEAN_TYPE_UNION,
+      W,
+      G,
+      SJ);
+    slice(DerivedJ(J),SJ,1,J);
+  }
+}
+
+template <
+  typename DerivedVA,
+  typename DerivedFA,
+  typename sType, int sCols, int sOptions,
+  typename dType, int dCols, int dOptions,
+  typename DerivedW,
+  typename DerivedG,
+  typename DerivedJ>
+IGL_INLINE void igl::copyleft::cgal::minkowski_sum(
+  const Eigen::MatrixBase<DerivedVA> & VA,
+  const Eigen::MatrixBase<DerivedFA> & FA,
+  const Eigen::Matrix<sType,1,sCols,sOptions> & s,
+  const Eigen::Matrix<dType,1,dCols,dOptions> & d,
+  const bool resolve_overlaps, 
+  Eigen::PlainObjectBase<DerivedW> & W,
+  Eigen::PlainObjectBase<DerivedG> & G,
+  Eigen::PlainObjectBase<DerivedJ> & J)
+{
+  using namespace Eigen;
+  using namespace std;
+  assert(s.cols() == 3 && "s should be a 3d point");
+  assert(d.cols() == 3 && "d should be a 3d point");
+  // silly base case
+  if(FA.size() == 0)
+  {
+    W.resize(0,3);
+    G.resize(0,3);
+    return;
+  }
+  const int dim = VA.cols();
+  assert(dim == 3 && "dim must be 3D");
+  assert(s.size() == 3 && "s must be 3D point");
+  assert(d.size() == 3 && "d must be 3D point");
+  // segment vector
+  const CGAL::Vector_3<CGAL::Epeck> v(d(0)-s(0),d(1)-s(1),d(2)-s(2));
+  // number of vertices
+  const int n = VA.rows();
+  // duplicate vertices at s and d, we'll remove unreferernced later
+  W.resize(2*n,dim);
+  for(int i = 0;i<n;i++)
+  {
+    for(int j = 0;j<dim;j++)
+    {
+      W  (i,j) = VA(i,j) + s(j);
+      W(i+n,j) = VA(i,j) + d(j);
+    }
+  }
+  // number of faces
+  const int m = FA.rows();
+  //// Mask whether positive dot product, or negative: because of exactly zero,
+  //// these are not necessarily complementary
+  // Nevermind, actually P = !N
+  Matrix<bool,Dynamic,1> P(m,1),N(m,1);
+  // loop over faces
+  int mp = 0,mn = 0;
+  for(int f = 0;f<m;f++)
+  {
+    const CGAL::Plane_3<CGAL::Epeck> plane(
+      CGAL::Point_3<CGAL::Epeck>(VA(FA(f,0),0),VA(FA(f,0),1),VA(FA(f,0),2)),
+      CGAL::Point_3<CGAL::Epeck>(VA(FA(f,1),0),VA(FA(f,1),1),VA(FA(f,1),2)),
+      CGAL::Point_3<CGAL::Epeck>(VA(FA(f,2),0),VA(FA(f,2),1),VA(FA(f,2),2)));
+    const auto normal = plane.orthogonal_vector();
+    const auto dt = normal * v;
+    if(dt > 0)
+    {
+      P(f) = true;
+      N(f) = false;
+      mp++;
+    }else
+    //}else if(dt < 0)
+    {
+      P(f) = false;
+      N(f) = true;
+      mn++;
+    //}else
+    //{
+    //  P(f) = false;
+    //  N(f) = false;
+    }
+  }
+
+  typedef Matrix<typename DerivedG::Scalar,Dynamic,Dynamic> MatrixXI;
+  typedef Matrix<typename DerivedG::Scalar,Dynamic,1> VectorXI;
+  MatrixXI GT(mp+mn,3);
+  GT<< slice_mask(FA,N,1), slice_mask((FA.array()+n).eval(),P,1);
+  // J indexes FA for parts at s and m+FA for parts at d
+  J.derived() = igl::LinSpaced<DerivedJ >(m,0,m-1);
+  DerivedJ JT(mp+mn);
+  JT << slice_mask(J,P,1), slice_mask(J,N,1);
+  JT.block(mp,0,mn,1).array()+=m;
+
+  // Original non-co-planar faces with positively oriented reversed
+  MatrixXI BA(mp+mn,3);
+  BA << slice_mask(FA,P,1).rowwise().reverse(), slice_mask(FA,N,1);
+  // Quads along **all** sides
+  MatrixXI GQ((mp+mn)*3,4);
+  GQ<< 
+    BA.col(1), BA.col(0), BA.col(0).array()+n, BA.col(1).array()+n,
+    BA.col(2), BA.col(1), BA.col(1).array()+n, BA.col(2).array()+n,
+    BA.col(0), BA.col(2), BA.col(2).array()+n, BA.col(0).array()+n;
+
+  MatrixXI uGQ;
+  VectorXI S,sI,sJ;
+  // Inputs:
+  //   F  #F by d list of polygons
+  // Outputs:
+  //   S  #uF list of signed incidences for each unique face
+  //  uF  #uF by d list of unique faces
+  //   I  #uF index vector so that uF = sort(F,2)(I,:)
+  //   J  #F index vector so that sort(F,2) = uF(J,:)
+  [](
+      const MatrixXI & F,
+      VectorXI & S,
+      MatrixXI & uF,
+      VectorXI & I,
+      VectorXI & J)
+  {
+    const int m = F.rows();
+    const int d = F.cols();
+    MatrixXI sF = F;
+    const auto MN = sF.rowwise().minCoeff().eval();
+    // rotate until smallest index is first
+    for(int p = 0;p<d;p++)
+    {
+      for(int f = 0;f<m;f++)
+      {
+        if(sF(f,0) != MN(f))
+        {
+          for(int r = 0;r<d-1;r++)
+          {
+            std::swap(sF(f,r),sF(f,r+1));
+          }
+        }
+      }
+    }
+    // swap orienation so that last index is greater than first
+    for(int f = 0;f<m;f++)
+    {
+      if(sF(f,d-1) < sF(f,1))
+      {
+        sF.block(f,1,1,d-1) = sF.block(f,1,1,d-1).reverse().eval();
+      }
+    }
+    Matrix<bool,Dynamic,1> M = Matrix<bool,Dynamic,1>::Zero(m,1);
+    {
+      VectorXI P = igl::LinSpaced<VectorXI >(d,0,d-1);
+      for(int p = 0;p<d;p++)
+      {
+        for(int f = 0;f<m;f++)
+        {
+          bool all = true;
+          for(int r = 0;r<d;r++)
+          {
+            all = all && (sF(f,P(r)) == F(f,r));
+          }
+          M(f) = M(f) || all;
+        }
+        for(int r = 0;r<d-1;r++)
+        {
+          std::swap(P(r),P(r+1));
+        }
+      }
+    }
+    unique_rows(sF,uF,I,J);
+    S = VectorXI::Zero(uF.rows(),1);
+    assert(m == J.rows());
+    for(int f = 0;f<m;f++)
+    {
+      S(J(f)) += M(f) ? 1 : -1;
+    }
+  }(MatrixXI(GQ),S,uGQ,sI,sJ);
+  assert(S.rows() == uGQ.rows());
+  const int nq = (S.array().abs()==2).count();
+  GQ.resize(nq,4);
+  {
+    int k = 0;
+    for(int q = 0;q<uGQ.rows();q++)
+    {
+      switch(S(q))
+      {
+        case -2:
+          GQ.row(k++) = uGQ.row(q).reverse().eval();
+          break;
+        case 2:
+          GQ.row(k++) = uGQ.row(q);
+          break;
+        default:
+        // do not add
+          break;
+      }
+    }
+    assert(nq == k);
+  }
+
+  G.resize(GT.rows()+2*GQ.rows(),3);
+  G<< 
+    GT,
+    GQ.col(0), GQ.col(1), GQ.col(2), 
+    GQ.col(0), GQ.col(2), GQ.col(3);
+  J.resize(JT.rows()+2*GQ.rows(),1);
+  J<<JT,DerivedJ::Constant(2*GQ.rows(),1,2*m+1);
+  if(resolve_overlaps)
+  {
+    Eigen::Matrix<typename DerivedJ::Scalar, Eigen::Dynamic,1> SJ;
+    mesh_boolean(
+      DerivedW(W),DerivedG(G),
+      Matrix<typename DerivedVA::Scalar,Dynamic,Dynamic>(),MatrixXI(),
+      MESH_BOOLEAN_TYPE_UNION,
+      W,G,SJ);
+    J.derived() = slice(DerivedJ(J),SJ,1);
+  }
+}
+
+template <
+  typename DerivedVA,
+  typename DerivedFA,
+  typename sType, int sCols, int sOptions,
+  typename dType, int dCols, int dOptions,
+  typename DerivedW,
+  typename DerivedG,
+  typename DerivedJ>
+IGL_INLINE void igl::copyleft::cgal::minkowski_sum(
+  const Eigen::MatrixBase<DerivedVA> & VA,
+  const Eigen::MatrixBase<DerivedFA> & FA,
+  const Eigen::Matrix<sType,1,sCols,sOptions> & s,
+  const Eigen::Matrix<dType,1,dCols,dOptions> & d,
+  Eigen::PlainObjectBase<DerivedW> & W,
+  Eigen::PlainObjectBase<DerivedG> & G,
+  Eigen::PlainObjectBase<DerivedJ> & J)
+{
+  return minkowski_sum(VA,FA,s,d,true,W,G,J);
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::minkowski_sum<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, CGAL::Lazy_exact_nt<CGAL::Gmpq>, 3, 1, CGAL::Lazy_exact_nt<CGAL::Gmpq>, 3, 1, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 1, 3, 1, 1, 3> const&, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, 1, 3, 1, 1, 3> const&, bool, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::minkowski_sum<
+  Eigen::Matrix<float, -1, 3, 1, -1, 3>, 
+  Eigen::Matrix<int, -1, 3, 1, -1, 3>, 
+  double, 3, 1, 
+  float, 3, 1, 
+  Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, 
+  Eigen::Matrix<int, -1, -1, 0, -1, -1>, 
+  Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::MatrixBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, Eigen::Matrix<double, 1, 3, 1, 1, 3> const&, Eigen::Matrix<float, 1, 3, 1, 1, 3> const&, bool, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+#endif

src/igl/copyleft/cgal/minkowski_sum.h

@@ -0,0 +1,110 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_MINKOWSKI_SUM_H
+#define IGL_COPYLEFT_CGAL_MINKOWSKI_SUM_H
+
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Compute the Minkowski sum of a closed triangle mesh (V,F) and a
+      // set of simplices in 3D.
+      //
+      // Inputs:
+      //   VA  #VA by 3 list of mesh vertices in 3D
+      //   FA  #FA by 3 list of triangle indices into VA
+      //   VB  #VB by 3 list of mesh vertices in 3D
+      //   FB  #FB by ss list of simplex indices into VB, ss<=3
+      //   resolve_overlaps  whether or not to resolve self-union. If false
+      //     then result may contain self-intersections if input mesh is
+      //     non-convex.
+      // Outputs:
+      //   W  #W by 3 list of mesh vertices in 3D
+      //   G  #G by 3 list of triangle indices into W
+      //   J  #G by 2 list of indices into 
+      //   
+      template <
+        typename DerivedVA,
+        typename DerivedFA,
+        typename DerivedVB,
+        typename DerivedFB,
+        typename DerivedW,
+        typename DerivedG,
+        typename DerivedJ>
+      IGL_INLINE void minkowski_sum(
+        const Eigen::MatrixBase<DerivedVA> & VA,
+        const Eigen::MatrixBase<DerivedFA> & FA,
+        const Eigen::MatrixBase<DerivedVB> & VB,
+        const Eigen::MatrixBase<DerivedFB> & FB,
+        const bool resolve_overlaps,
+        Eigen::PlainObjectBase<DerivedW> & W,
+        Eigen::PlainObjectBase<DerivedG> & G,
+        Eigen::PlainObjectBase<DerivedJ> & J);
+      // Compute the Minkowski sum of a closed triangle mesh (V,F) and a
+      // segment [s,d] in 3D.
+      //
+      // Inputs:
+      //   VA  #VA by 3 list of mesh vertices in 3D
+      //   FA  #FA by 3 list of triangle indices into VA
+      //   s  segment source endpoint in 3D
+      //   d  segment source endpoint in 3D
+      //   resolve_overlaps  whether or not to resolve self-union. If false
+      //     then result may contain self-intersections if input mesh is
+      //     non-convex.
+      // Outputs:
+      //   W  #W by 3 list of mesh vertices in 3D
+      //   G  #G by 3 list of triangle indices into W
+      //   J  #G list of indices into [F;#V+F;[s d]] of birth parents
+      //
+      template <
+        typename DerivedVA,
+        typename DerivedFA,
+        typename sType, int sCols, int sOptions,
+        typename dType, int dCols, int dOptions,
+        typename DerivedW,
+        typename DerivedG,
+        typename DerivedJ>
+      IGL_INLINE void minkowski_sum(
+        const Eigen::MatrixBase<DerivedVA> & VA,
+        const Eigen::MatrixBase<DerivedFA> & FA,
+        const Eigen::Matrix<sType,1,sCols,sOptions> & s,
+        const Eigen::Matrix<dType,1,dCols,dOptions> & d,
+        const bool resolve_overlaps,
+        Eigen::PlainObjectBase<DerivedW> & W,
+        Eigen::PlainObjectBase<DerivedG> & G,
+        Eigen::PlainObjectBase<DerivedJ> & J);
+      template <
+        typename DerivedVA,
+        typename DerivedFA,
+        typename sType, int sCols, int sOptions,
+        typename dType, int dCols, int dOptions,
+        typename DerivedW,
+        typename DerivedG,
+        typename DerivedJ>
+      IGL_INLINE void minkowski_sum(
+        const Eigen::MatrixBase<DerivedVA> & VA,
+        const Eigen::MatrixBase<DerivedFA> & FA,
+        const Eigen::Matrix<sType,1,sCols,sOptions> & s,
+        const Eigen::Matrix<dType,1,dCols,dOptions> & d,
+        Eigen::PlainObjectBase<DerivedW> & W,
+        Eigen::PlainObjectBase<DerivedG> & G,
+        Eigen::PlainObjectBase<DerivedJ> & J);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "minkowski_sum.cpp"
+#endif
+
+#endif

src/igl/copyleft/cgal/order_facets_around_edge.cpp

@@ -0,0 +1,428 @@
+#include "order_facets_around_edge.h"
+#include <Eigen/Geometry>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+
+#include <stdexcept>
+
+// adj_faces contains signed index starting from +- 1.
+template<
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedI >
+void igl::copyleft::cgal::order_facets_around_edge(
+    const Eigen::PlainObjectBase<DerivedV>& V,
+    const Eigen::PlainObjectBase<DerivedF>& F,
+    size_t s,
+    size_t d, 
+    const std::vector<int>& adj_faces,
+    Eigen::PlainObjectBase<DerivedI>& order, bool debug)
+{
+  // Although we only need exact predicates in the algorithm,
+  // exact constructions are needed to avoid degeneracies due to
+  // casting to double.
+  typedef CGAL::Exact_predicates_exact_constructions_kernel K;
+  typedef K::Point_3 Point_3;
+  typedef K::Plane_3 Plane_3;
+
+  auto get_face_index = [&](int adj_f)->size_t
+  {
+    return abs(adj_f) - 1;
+  };
+
+  auto get_opposite_vertex = [&](size_t fid)->size_t
+  {
+    typedef typename DerivedF::Scalar Index;
+    if (F(fid, 0) != (Index)s && F(fid, 0) != (Index)d) return F(fid, 0);
+    if (F(fid, 1) != (Index)s && F(fid, 1) != (Index)d) return F(fid, 1);
+    if (F(fid, 2) != (Index)s && F(fid, 2) != (Index)d) return F(fid, 2);
+    assert(false);
+    return -1;
+  };
+
+  // Handle base cases
+  if (adj_faces.size() == 0) 
+  {
+    order.resize(0, 1);
+    return;
+  } else if (adj_faces.size() == 1)
+  {
+    order.resize(1, 1);
+    order(0, 0) = 0;
+    return;
+  } else if (adj_faces.size() == 2)
+  {
+    const size_t o1 = get_opposite_vertex(get_face_index(adj_faces[0]));
+    const size_t o2 = get_opposite_vertex(get_face_index(adj_faces[1]));
+    const Point_3 ps(V(s, 0), V(s, 1), V(s, 2));
+    const Point_3 pd(V(d, 0), V(d, 1), V(d, 2));
+    const Point_3 p1(V(o1, 0), V(o1, 1), V(o1, 2));
+    const Point_3 p2(V(o2, 0), V(o2, 1), V(o2, 2));
+    order.resize(2, 1);
+    switch (CGAL::orientation(ps, pd, p1, p2))
+    {
+      case CGAL::POSITIVE:
+        order(0, 0) = 1;
+        order(1, 0) = 0;
+        break;
+      case CGAL::NEGATIVE:
+        order(0, 0) = 0;
+        order(1, 0) = 1;
+        break;
+      case CGAL::COPLANAR:
+        {
+          switch (CGAL::coplanar_orientation(ps, pd, p1, p2)) {
+            case CGAL::POSITIVE:
+              // Duplicated face, use index to break tie.
+              order(0, 0) = adj_faces[0] < adj_faces[1] ? 0:1;
+              order(1, 0) = adj_faces[0] < adj_faces[1] ? 1:0;
+              break;
+            case CGAL::NEGATIVE:
+              // Coplanar faces, one on each side of the edge.
+              // It is equally valid to order them (0, 1) or (1, 0).
+              // I cannot think of any reason to prefer one to the
+              // other.  So just use (0, 1) ordering by default.
+              order(0, 0) = 0;
+              order(1, 0) = 1;
+              break;
+            case CGAL::COLLINEAR:
+              std::cerr << "Degenerated triangle detected." <<
+                std::endl;
+              assert(false);
+              break;
+            default:
+              assert(false);
+          }
+        }
+        break;
+      default:
+        assert(false);
+    }
+    return;
+  }
+
+  const size_t num_adj_faces = adj_faces.size();
+  const size_t o = get_opposite_vertex( get_face_index(adj_faces[0]));
+  const Point_3 p_s(V(s, 0), V(s, 1), V(s, 2));
+  const Point_3 p_d(V(d, 0), V(d, 1), V(d, 2));
+  const Point_3 p_o(V(o, 0), V(o, 1), V(o, 2));
+  const Plane_3 separator(p_s, p_d, p_o);
+  if (separator.is_degenerate()) {
+    throw std::runtime_error(
+        "Cannot order facets around edge due to degenerated facets");
+  }
+
+  std::vector<Point_3> opposite_vertices;
+  for (size_t i=0; i<num_adj_faces; i++)
+  {
+    const size_t o = get_opposite_vertex( get_face_index(adj_faces[i]));
+    opposite_vertices.emplace_back(
+        V(o, 0), V(o, 1), V(o, 2));
+  }
+
+  std::vector<int> positive_side;
+  std::vector<int> negative_side;
+  std::vector<int> tie_positive_oriented;
+  std::vector<int> tie_negative_oriented;
+
+  std::vector<size_t> positive_side_index;
+  std::vector<size_t> negative_side_index;
+  std::vector<size_t> tie_positive_oriented_index;
+  std::vector<size_t> tie_negative_oriented_index;
+
+  for (size_t i=0; i<num_adj_faces; i++)
+  {
+    const int f = adj_faces[i];
+    const Point_3& p_a = opposite_vertices[i];
+    auto orientation = separator.oriented_side(p_a);
+    switch (orientation) {
+      case CGAL::ON_POSITIVE_SIDE:
+        positive_side.push_back(f);
+        positive_side_index.push_back(i);
+        break;
+      case CGAL::ON_NEGATIVE_SIDE:
+        negative_side.push_back(f);
+        negative_side_index.push_back(i);
+        break;
+      case CGAL::ON_ORIENTED_BOUNDARY:
+        {
+          auto inplane_orientation = CGAL::coplanar_orientation(
+              p_s, p_d, p_o, p_a);
+          switch (inplane_orientation) {
+            case CGAL::POSITIVE:
+              tie_positive_oriented.push_back(f);
+              tie_positive_oriented_index.push_back(i);
+              break;
+            case CGAL::NEGATIVE:
+              tie_negative_oriented.push_back(f);
+              tie_negative_oriented_index.push_back(i);
+              break;
+            case CGAL::COLLINEAR:
+            default:
+              throw std::runtime_error(
+                  "Degenerated facet detected.");
+              break;
+          }
+        }
+        break;
+      default:
+        // Should not be here.
+        throw std::runtime_error("Unknown CGAL state detected.");
+    }
+  }
+  if (debug) {
+    std::cout << "tie positive: " << std::endl;
+    for (auto& f : tie_positive_oriented) {
+      std::cout << get_face_index(f) << " ";
+    }
+    std::cout << std::endl;
+    std::cout << "positive side: " << std::endl;
+    for (auto& f : positive_side) {
+      std::cout << get_face_index(f) << " ";
+    }
+    std::cout << std::endl;
+    std::cout << "tie negative: " << std::endl;
+    for (auto& f : tie_negative_oriented) {
+      std::cout << get_face_index(f) << " ";
+    }
+    std::cout << std::endl;
+    std::cout << "negative side: " << std::endl;
+    for (auto& f : negative_side) {
+      std::cout << get_face_index(f) << " ";
+    }
+    std::cout << std::endl;
+  }
+
+  auto index_sort = [](std::vector<int>& data) -> std::vector<size_t>{
+    const size_t len = data.size();
+    std::vector<size_t> order(len);
+    for (size_t i=0; i<len; i++) { order[i] = i; }
+    auto comp = [&](size_t i, size_t j) { return data[i] < data[j]; };
+    std::sort(order.begin(), order.end(), comp);
+    return order;
+  };
+
+  DerivedI positive_order, negative_order;
+  order_facets_around_edge(V, F, s, d, positive_side, positive_order, debug);
+  order_facets_around_edge(V, F, s, d, negative_side, negative_order, debug);
+  std::vector<size_t> tie_positive_order = index_sort(tie_positive_oriented);
+  std::vector<size_t> tie_negative_order = index_sort(tie_negative_oriented);
+
+  // Copy results into order vector.
+  const size_t tie_positive_size = tie_positive_oriented.size();
+  const size_t tie_negative_size = tie_negative_oriented.size();
+  const size_t positive_size = positive_order.size();
+  const size_t negative_size = negative_order.size();
+
+  order.resize(
+      tie_positive_size + positive_size + tie_negative_size + negative_size,1);
+
+  size_t count=0;
+  for (size_t i=0; i<tie_positive_size; i++)
+  {
+    order(count+i, 0) = tie_positive_oriented_index[tie_positive_order[i]];
+  }
+  count += tie_positive_size;
+
+  for (size_t i=0; i<negative_size; i++) 
+  {
+    order(count+i, 0) = negative_side_index[negative_order(i, 0)];
+  }
+  count += negative_size;
+
+  for (size_t i=0; i<tie_negative_size; i++)
+  {
+    order(count+i, 0) = tie_negative_oriented_index[tie_negative_order[i]];
+  }
+  count += tie_negative_size;
+
+  for (size_t i=0; i<positive_size; i++)
+  {
+    order(count+i, 0) = positive_side_index[positive_order(i, 0)];
+  }
+  count += positive_size;
+  assert(count == num_adj_faces);
+
+  // Find the correct start point.
+  size_t start_idx = 0;
+  for (size_t i=0; i<num_adj_faces; i++)
+  {
+    const Point_3& p_a = opposite_vertices[order(i, 0)];
+    const Point_3& p_b =
+      opposite_vertices[order((i+1)%num_adj_faces, 0)];
+    auto orientation = CGAL::orientation(p_s, p_d, p_a, p_b);
+    if (orientation == CGAL::POSITIVE)
+    {
+      // Angle between triangle (p_s, p_d, p_a) and (p_s, p_d, p_b) is
+      // more than 180 degrees.
+      start_idx = (i+1)%num_adj_faces;
+      break;
+    } else if (orientation == CGAL::COPLANAR &&
+        Plane_3(p_s, p_d, p_a).orthogonal_direction() !=
+        Plane_3(p_s, p_d, p_b).orthogonal_direction())
+    {
+      // All 4 points are coplanar, but p_a and p_b are on each side of
+      // the edge (p_s, p_d).  This means the angle between triangle
+      // (p_s, p_d, p_a) and (p_s, p_d, p_b) is exactly 180 degrees.
+      start_idx = (i+1)%num_adj_faces;
+      break;
+    }
+  }
+  DerivedI circular_order = order;
+  for (size_t i=0; i<num_adj_faces; i++)
+  {
+    order(i, 0) = circular_order((start_idx + i)%num_adj_faces, 0);
+  }
+}
+
+template<
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedI>
+IGL_INLINE
+void igl::copyleft::cgal::order_facets_around_edge(
+  const Eigen::PlainObjectBase<DerivedV>& V,
+  const Eigen::PlainObjectBase<DerivedF>& F,
+  size_t s,
+  size_t d, 
+  const std::vector<int>& adj_faces,
+  const Eigen::PlainObjectBase<DerivedV>& pivot_point,
+  Eigen::PlainObjectBase<DerivedI>& order)
+{
+  assert(V.cols() == 3);
+  assert(F.cols() == 3);
+  assert(pivot_point.cols() == 3);
+  auto signed_index_to_index = [&](int signed_idx)
+  {
+      return abs(signed_idx) -1;
+  };
+  auto get_opposite_vertex_index = [&](size_t fid) -> typename DerivedF::Scalar
+  {
+      typedef typename DerivedF::Scalar Index;
+      if (F(fid, 0) != (Index)s && F(fid, 0) != (Index)d) return F(fid, 0);
+      if (F(fid, 1) != (Index)s && F(fid, 1) != (Index)d) return F(fid, 1);
+      if (F(fid, 2) != (Index)s && F(fid, 2) != (Index)d) return F(fid, 2);
+      assert(false);
+      // avoid warning
+      return -1;
+  };
+
+  {
+    // Check if s, d and pivot are collinear.
+    typedef CGAL::Exact_predicates_exact_constructions_kernel K;
+    K::Point_3 ps(V(s,0), V(s,1), V(s,2));
+    K::Point_3 pd(V(d,0), V(d,1), V(d,2));
+    K::Point_3 pp(pivot_point(0,0), pivot_point(0,1), pivot_point(0,2));
+    if (CGAL::collinear(ps, pd, pp)) {
+        throw std::runtime_error(
+                "Pivot point is collinear with the outer edge!");
+    }
+  }
+
+  const size_t N = adj_faces.size();
+  const size_t num_faces = N + 1; // N adj faces + 1 pivot face
+
+  // Because face indices are used for tie breaking, the original face indices
+  // in the new faces array must be ascending.
+  auto comp = [&](int i, int j) 
+  {
+    return signed_index_to_index(adj_faces[i]) <
+      signed_index_to_index(adj_faces[j]);
+  };
+  std::vector<size_t> adj_order(N);
+  for (size_t i=0; i<N; i++) adj_order[i] = i;
+  std::sort(adj_order.begin(), adj_order.end(), comp);
+
+  DerivedV vertices(num_faces + 2, 3);
+  for (size_t i=0; i<N; i++) 
+  {
+    const size_t fid = signed_index_to_index(adj_faces[adj_order[i]]);
+    vertices.row(i) = V.row(get_opposite_vertex_index(fid));
+  }
+  vertices.row(N  ) = pivot_point;
+  vertices.row(N+1) = V.row(s);
+  vertices.row(N+2) = V.row(d);
+
+  DerivedF faces(num_faces, 3);
+  for (size_t i=0; i<N; i++)
+  {
+    if (adj_faces[adj_order[i]] < 0) 
+    {
+      faces(i,0) = N+1; // s
+      faces(i,1) = N+2; // d
+      faces(i,2) = i  ;
+    } else 
+    {
+      faces(i,0) = N+2; // d
+      faces(i,1) = N+1; // s
+      faces(i,2) = i  ;
+    }
+  }
+  // Last face is the pivot face.
+  faces(N, 0) = N+1;
+  faces(N, 1) = N+2;
+  faces(N, 2) = N;
+
+  std::vector<int> adj_faces_with_pivot(num_faces);
+  for (size_t i=0; i<num_faces; i++)
+  {
+    if ((size_t)faces(i,0) == N+1 && (size_t)faces(i,1) == N+2)
+    {
+        adj_faces_with_pivot[i] = int(i+1) * -1;
+    } else
+    {
+        adj_faces_with_pivot[i] = int(i+1);
+    }
+  }
+
+  DerivedI order_with_pivot;
+  order_facets_around_edge(
+    vertices, faces, N+1, N+2, adj_faces_with_pivot, order_with_pivot);
+
+  assert((size_t)order_with_pivot.size() == num_faces);
+  order.resize(N);
+  size_t pivot_index = num_faces + 1;
+  for (size_t i=0; i<num_faces; i++)
+  {
+    if ((size_t)order_with_pivot[i] == N)
+    {
+      pivot_index = i;
+      break;
+    }
+  }
+  assert(pivot_index < num_faces);
+
+  for (size_t i=0; i<N; i++)
+  {
+    order[i] = adj_order[order_with_pivot[(pivot_index+i+1)%num_faces]];
+  }
+}
+
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::order_facets_around_edge<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, unsigned long, unsigned long, std::vector<int, std::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::order_facets_around_edge<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, unsigned long, unsigned long, std::vector<int, std::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&, bool);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::order_facets_around_edge<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, unsigned long, unsigned long, std::vector<int, std::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::order_facets_around_edge<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, unsigned long, unsigned long, std::vector<int, std::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&, bool);
+template void igl::copyleft::cgal::order_facets_around_edge<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, unsigned long, unsigned long, std::vector<int, std::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&, bool);
+template void igl::copyleft::cgal::order_facets_around_edge<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, unsigned long, unsigned long, std::vector<int, std::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&, bool);
+template void igl::copyleft::cgal::order_facets_around_edge<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, unsigned long, unsigned long, std::vector<int, std::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::order_facets_around_edge<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, unsigned long, unsigned long, std::vector<int, std::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::order_facets_around_edge<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, unsigned long, unsigned long, std::vector<int, std::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::order_facets_around_edge<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, unsigned long, unsigned long, std::vector<int, std::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+#ifdef WIN32
+template void igl::copyleft::cgal::order_facets_around_edge<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, unsigned __int64, unsigned __int64, class std::vector<int, class std::allocator<int>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> &);
+template void igl::copyleft::cgal::order_facets_around_edge<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, unsigned __int64, unsigned __int64, class std::vector<int, class std::allocator<int>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> &, bool);
+template void igl::copyleft::cgal::order_facets_around_edge<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, unsigned __int64, unsigned __int64, class std::vector<int, class std::allocator<int>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> &);
+template void igl::copyleft::cgal::order_facets_around_edge<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, unsigned __int64, unsigned __int64, class std::vector<int, class std::allocator<int>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> &, bool);
+template void igl::copyleft::cgal::order_facets_around_edge<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, 3, 1, -1, 3>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 3, 1, -1, 3>> const &, unsigned __int64, unsigned __int64, class std::vector<int, class std::allocator<int>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> &);
+template void igl::copyleft::cgal::order_facets_around_edge<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, 3, 1, -1, 3>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 3, 1, -1, 3>> const &, unsigned __int64, unsigned __int64, class std::vector<int, class std::allocator<int>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> &, bool);
+template void igl::copyleft::cgal::order_facets_around_edge<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, 3, 0, -1, 3>, class Eigen::Matrix<int, -1, 3, 0, -1, 3>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, 3, 0, -1, 3>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 3, 0, -1, 3>> const &, unsigned __int64, unsigned __int64, class std::vector<int, class std::allocator<int>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, 3, 0, -1, 3>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> &);
+template void igl::copyleft::cgal::order_facets_around_edge<class Eigen::Matrix<double, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<double, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, unsigned __int64, unsigned __int64, class std::vector<int, class std::allocator<int>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<double, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> &);
+template void igl::copyleft::cgal::order_facets_around_edge<class Eigen::Matrix<double, -1, 3, 0, -1, 3>, class Eigen::Matrix<int, -1, 3, 0, -1, 3>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<double, -1, 3, 0, -1, 3>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 3, 0, -1, 3>> const &, unsigned __int64, unsigned __int64, class std::vector<int, class std::allocator<int>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<double, -1, 3, 0, -1, 3>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> &);
+#endif
+#endif

src/igl/copyleft/cgal/order_facets_around_edge.h

@@ -0,0 +1,77 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+//
+#ifndef IGL_COPYLEFT_CGAL_ORDER_FACETS_AROUND_EDGE_H
+#define IGL_COPYLEFT_CGAL_ORDER_FACETS_AROUND_EDGE_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <vector>
+
+namespace igl 
+{
+  namespace copyleft
+  {
+    namespace cgal 
+    {
+      // Given a directed edge, sort its adjacent faces.  Assuming the
+      // directed edge is (s, d).  Sort the adjacent faces clockwise around the
+      // axis (d - s), i.e. left-hand rule.  An adjacent face is consistently
+      // oriented if it contains (d, s) as a directed edge.
+      //
+      // For overlapping faces, break the tie using signed face index, smaller
+      // signed index comes before the larger signed index.  Signed index is
+      // computed as (consistent? 1:-1) * (face_index + 1).
+      //
+      // Inputs:
+      //   V  #V by 3 list of vertices.
+      //   F  #F by 3 list of faces
+      //   s  Index of source vertex.
+      //   d  Index of destination vertex.
+      //   adj_faces  List of adjacent face signed indices.
+      // Output:
+      //   order  List of face indices that orders adjacent faces around edge
+      //     (s, d) clockwise.
+      template<
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedI >
+      IGL_INLINE
+      void order_facets_around_edge(
+          const Eigen::PlainObjectBase<DerivedV>& V,
+          const Eigen::PlainObjectBase<DerivedF>& F,
+          size_t s, 
+          size_t d, 
+          const std::vector<int>& adj_faces,
+          Eigen::PlainObjectBase<DerivedI>& order,
+          bool debug=false);
+
+      // This function is a wrapper around the one above.  Since the ordering
+      // is circular, the pivot point is used to define a starting point.  So
+      // order[0] is the index into adj_face that is immediately after the
+      // pivot face (s, d, pivot point) in clockwise order.
+      template<
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedI>
+      IGL_INLINE
+      void order_facets_around_edge(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        size_t s, 
+        size_t d, 
+        const std::vector<int>& adj_faces,
+        const Eigen::PlainObjectBase<DerivedV>& pivot_point,
+        Eigen::PlainObjectBase<DerivedI>& order);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#include "order_facets_around_edge.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/order_facets_around_edges.cpp

@@ -0,0 +1,332 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "order_facets_around_edges.h"
+#include "order_facets_around_edge.h"
+#include "../../sort_angles.h"
+#include <Eigen/Geometry>
+#include <type_traits>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+
+template<
+    typename DerivedV,
+    typename DerivedF,
+    typename DerivedN,
+    typename DeriveduE,
+    typename uE2EType,
+    typename uE2oEType,
+    typename uE2CType >
+IGL_INLINE
+typename std::enable_if<!std::is_same<typename DerivedV::Scalar,
+typename CGAL::Exact_predicates_exact_constructions_kernel::FT>::value, void>::type
+igl::copyleft::cgal::order_facets_around_edges(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        const Eigen::PlainObjectBase<DerivedN>& N,
+        const Eigen::PlainObjectBase<DeriveduE>& uE,
+        const std::vector<std::vector<uE2EType> >& uE2E,
+        std::vector<std::vector<uE2oEType> >& uE2oE,
+        std::vector<std::vector<uE2CType > >& uE2C ) {
+
+    typedef Eigen::Matrix<typename DerivedN::Scalar, 3, 1> Vector3F;
+    const typename DerivedV::Scalar EPS = 1e-12;
+    const size_t num_faces = F.rows();
+    const size_t num_undirected_edges = uE.rows();
+
+    auto edge_index_to_face_index = [&](size_t ei) { return ei % num_faces; };
+    auto edge_index_to_corner_index = [&](size_t ei) { return ei / num_faces; };
+
+    uE2oE.resize(num_undirected_edges);
+    uE2C.resize(num_undirected_edges);
+
+    for(size_t ui = 0;ui<num_undirected_edges;ui++)
+    {
+        const auto& adj_edges = uE2E[ui];
+        const size_t edge_valance = adj_edges.size();
+        assert(edge_valance > 0);
+
+        const auto ref_edge = adj_edges[0];
+        const auto ref_face = edge_index_to_face_index(ref_edge);
+        Vector3F ref_normal = N.row(ref_face);
+
+        const auto ref_corner_o = edge_index_to_corner_index(ref_edge);
+        const auto ref_corner_s = (ref_corner_o+1)%3;
+        const auto ref_corner_d = (ref_corner_o+2)%3;
+
+        const typename DerivedF::Scalar o = F(ref_face, ref_corner_o);
+        const typename DerivedF::Scalar s = F(ref_face, ref_corner_s);
+        const typename DerivedF::Scalar d = F(ref_face, ref_corner_d);
+
+        Vector3F edge = V.row(d) - V.row(s);
+        auto edge_len = edge.norm();
+        bool degenerated = edge_len < EPS;
+        if (degenerated) {
+            if (edge_valance <= 2) {
+                // There is only one way to order 2 or less faces.
+                edge.setZero();
+            } else {
+                edge.setZero();
+                Eigen::Matrix<typename DerivedN::Scalar, Eigen::Dynamic, 3>
+                    normals(edge_valance, 3);
+                for (size_t fei=0; fei<edge_valance; fei++) {
+                    const auto fe = adj_edges[fei];
+                    const auto f = edge_index_to_face_index(fe);
+                    normals.row(fei) = N.row(f);
+                }
+                for (size_t i=0; i<edge_valance; i++) {
+                    size_t j = (i+1) % edge_valance;
+                    Vector3F ni = normals.row(i);
+                    Vector3F nj = normals.row(j);
+                    edge = ni.cross(nj);
+                    edge_len = edge.norm();
+                    if (edge_len >= EPS) {
+                        edge.normalize();
+                        break;
+                    }
+                }
+
+                // Ensure edge direction are consistent with reference face.
+                Vector3F in_face_vec = V.row(o) - V.row(s);
+                if (edge.cross(in_face_vec).dot(ref_normal) < 0) {
+                    edge *= -1;
+                }
+
+                if (edge.norm() < EPS) {
+                    std::cerr << "=====================================" << std::endl;
+                    std::cerr << "  ui: " << ui << std::endl;
+                    std::cerr << "edge: " << ref_edge << std::endl;
+                    std::cerr << "face: " << ref_face << std::endl;
+                    std::cerr << "  vs: " << V.row(s) << std::endl;
+                    std::cerr << "  vd: " << V.row(d) << std::endl;
+                    std::cerr << "adj face normals: " << std::endl;
+                    std::cerr << normals << std::endl;
+                    std::cerr << "Very degenerated case detected:" << std::endl;
+                    std::cerr << "Near zero edge surrounded by "
+                        << edge_valance << " neearly colinear faces" <<
+                        std::endl;
+                    std::cerr << "=====================================" << std::endl;
+                }
+            }
+        } else {
+            edge.normalize();
+        }
+
+        Eigen::MatrixXd angle_data(edge_valance, 3);
+        std::vector<bool> cons(edge_valance);
+
+        for (size_t fei=0; fei<edge_valance; fei++) {
+            const auto fe = adj_edges[fei];
+            const auto f = edge_index_to_face_index(fe);
+            const auto c = edge_index_to_corner_index(fe);
+            cons[fei] = (d == F(f, (c+1)%3));
+            assert( cons[fei] ||  (d == F(f,(c+2)%3)));
+            assert(!cons[fei] || (s == F(f,(c+2)%3)));
+            assert(!cons[fei] || (d == F(f,(c+1)%3)));
+            Vector3F n = N.row(f);
+            angle_data(fei, 0) = ref_normal.cross(n).dot(edge);
+            angle_data(fei, 1) = ref_normal.dot(n);
+            if (cons[fei]) {
+                angle_data(fei, 0) *= -1;
+                angle_data(fei, 1) *= -1;
+            }
+            angle_data(fei, 0) *= -1; // Sort clockwise.
+            angle_data(fei, 2) = (cons[fei]?1.:-1.)*(f+1);
+        }
+
+        Eigen::VectorXi order;
+        igl::sort_angles(angle_data, order);
+
+        auto& ordered_edges = uE2oE[ui];
+        auto& consistency = uE2C[ui];
+
+        ordered_edges.resize(edge_valance);
+        consistency.resize(edge_valance);
+        for (size_t fei=0; fei<edge_valance; fei++) {
+            ordered_edges[fei] = adj_edges[order[fei]];
+            consistency[fei] = cons[order[fei]];
+        }
+    }
+}
+
+template<
+    typename DerivedV,
+    typename DerivedF,
+    typename DerivedN,
+    typename DeriveduE,
+    typename uE2EType,
+    typename uE2oEType,
+    typename uE2CType >
+IGL_INLINE 
+typename std::enable_if<std::is_same<typename DerivedV::Scalar,
+typename CGAL::Exact_predicates_exact_constructions_kernel::FT>::value, void>::type
+igl::copyleft::cgal::order_facets_around_edges(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        const Eigen::PlainObjectBase<DerivedN>& N,
+        const Eigen::PlainObjectBase<DeriveduE>& uE,
+        const std::vector<std::vector<uE2EType> >& uE2E,
+        std::vector<std::vector<uE2oEType> >& uE2oE,
+        std::vector<std::vector<uE2CType > >& uE2C ) {
+
+    typedef Eigen::Matrix<typename DerivedN::Scalar, 3, 1> Vector3F;
+    typedef Eigen::Matrix<typename DerivedV::Scalar, 3, 1> Vector3E;
+    const typename DerivedV::Scalar EPS = 1e-12;
+    const size_t num_faces = F.rows();
+    const size_t num_undirected_edges = uE.rows();
+
+    auto edge_index_to_face_index = [&](size_t ei) { return ei % num_faces; };
+    auto edge_index_to_corner_index = [&](size_t ei) { return ei / num_faces; };
+
+    uE2oE.resize(num_undirected_edges);
+    uE2C.resize(num_undirected_edges);
+
+    for(size_t ui = 0;ui<num_undirected_edges;ui++)
+    {
+        const auto& adj_edges = uE2E[ui];
+        const size_t edge_valance = adj_edges.size();
+        assert(edge_valance > 0);
+
+        const auto ref_edge = adj_edges[0];
+        const auto ref_face = edge_index_to_face_index(ref_edge);
+        Vector3F ref_normal = N.row(ref_face);
+
+        const auto ref_corner_o = edge_index_to_corner_index(ref_edge);
+        const auto ref_corner_s = (ref_corner_o+1)%3;
+        const auto ref_corner_d = (ref_corner_o+2)%3;
+
+        const typename DerivedF::Scalar o = F(ref_face, ref_corner_o);
+        const typename DerivedF::Scalar s = F(ref_face, ref_corner_s);
+        const typename DerivedF::Scalar d = F(ref_face, ref_corner_d);
+
+        Vector3E exact_edge = V.row(d) - V.row(s);
+        exact_edge.array() /= exact_edge.squaredNorm();
+        Vector3F edge(
+                CGAL::to_double(exact_edge[0]),
+                CGAL::to_double(exact_edge[1]),
+                CGAL::to_double(exact_edge[2]));
+        edge.normalize();
+
+        Eigen::MatrixXd angle_data(edge_valance, 3);
+        std::vector<bool> cons(edge_valance);
+
+        for (size_t fei=0; fei<edge_valance; fei++) {
+            const auto fe = adj_edges[fei];
+            const auto f = edge_index_to_face_index(fe);
+            const auto c = edge_index_to_corner_index(fe);
+            cons[fei] = (d == F(f, (c+1)%3));
+            assert( cons[fei] ||  (d == F(f,(c+2)%3)));
+            assert(!cons[fei] || (s == F(f,(c+2)%3)));
+            assert(!cons[fei] || (d == F(f,(c+1)%3)));
+            Vector3F n = N.row(f);
+            angle_data(fei, 0) = ref_normal.cross(n).dot(edge);
+            angle_data(fei, 1) = ref_normal.dot(n);
+            if (cons[fei]) {
+                angle_data(fei, 0) *= -1;
+                angle_data(fei, 1) *= -1;
+            }
+            angle_data(fei, 0) *= -1; // Sort clockwise.
+            angle_data(fei, 2) = (cons[fei]?1.:-1.)*(f+1);
+        }
+
+        Eigen::VectorXi order;
+        igl::sort_angles(angle_data, order);
+
+        auto& ordered_edges = uE2oE[ui];
+        auto& consistency = uE2C[ui];
+
+        ordered_edges.resize(edge_valance);
+        consistency.resize(edge_valance);
+        for (size_t fei=0; fei<edge_valance; fei++) {
+            ordered_edges[fei] = adj_edges[order[fei]];
+            consistency[fei] = cons[order[fei]];
+        }
+    }
+}
+
+template<
+    typename DerivedV,
+    typename DerivedF,
+    typename DeriveduE,
+    typename uE2EType,
+    typename uE2oEType,
+    typename uE2CType >
+IGL_INLINE void igl::copyleft::cgal::order_facets_around_edges(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        const Eigen::PlainObjectBase<DeriveduE>& uE,
+        const std::vector<std::vector<uE2EType> >& uE2E,
+        std::vector<std::vector<uE2oEType> >& uE2oE,
+        std::vector<std::vector<uE2CType > >& uE2C ) {
+
+    //typedef Eigen::Matrix<typename DerivedV::Scalar, 3, 1> Vector3E;
+    const size_t num_faces = F.rows();
+    const size_t num_undirected_edges = uE.rows();
+
+    auto edge_index_to_face_index = [&](size_t ei) { return ei % num_faces; };
+    auto edge_index_to_corner_index = [&](size_t ei) { return ei / num_faces; };
+
+    uE2oE.resize(num_undirected_edges);
+    uE2C.resize(num_undirected_edges);
+
+    for(size_t ui = 0;ui<num_undirected_edges;ui++)
+    {
+        const auto& adj_edges = uE2E[ui];
+        const size_t edge_valance = adj_edges.size();
+        assert(edge_valance > 0);
+
+        const auto ref_edge = adj_edges[0];
+        const auto ref_face = edge_index_to_face_index(ref_edge);
+
+        const auto ref_corner_o = edge_index_to_corner_index(ref_edge);
+        const auto ref_corner_s = (ref_corner_o+1)%3;
+        const auto ref_corner_d = (ref_corner_o+2)%3;
+
+        //const typename DerivedF::Scalar o = F(ref_face, ref_corner_o);
+        const typename DerivedF::Scalar s = F(ref_face, ref_corner_s);
+        const typename DerivedF::Scalar d = F(ref_face, ref_corner_d);
+
+        std::vector<bool> cons(edge_valance);
+        std::vector<int> adj_faces(edge_valance);
+        for (size_t fei=0; fei<edge_valance; fei++) {
+            const auto fe = adj_edges[fei];
+            const auto f = edge_index_to_face_index(fe);
+            const auto c = edge_index_to_corner_index(fe);
+            cons[fei] = (d == F(f, (c+1)%3));
+            adj_faces[fei] = (f+1) * (cons[fei] ? 1:-1);
+
+            assert( cons[fei] ||  (d == F(f,(c+2)%3)));
+            assert(!cons[fei] || (s == F(f,(c+2)%3)));
+            assert(!cons[fei] || (d == F(f,(c+1)%3)));
+        }
+
+        Eigen::VectorXi order;
+        order_facets_around_edge(V, F, s, d, adj_faces, order);
+        assert((size_t)order.size() == edge_valance);
+
+        auto& ordered_edges = uE2oE[ui];
+        auto& consistency = uE2C[ui];
+
+        ordered_edges.resize(edge_valance);
+        consistency.resize(edge_valance);
+        for (size_t fei=0; fei<edge_valance; fei++) {
+            ordered_edges[fei] = adj_edges[order[fei]];
+            consistency[fei] = cons[order[fei]];
+        }
+    }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::order_facets_around_edges<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, int, int, bool>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > > const&, std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > >&, std::vector<std::vector<bool, std::allocator<bool> >, std::allocator<std::vector<bool, std::allocator<bool> > > >&);
+// generated by autoexplicit.sh
+template std::enable_if<!(std::is_same<Eigen::Matrix<double, -1, -1, 0, -1, -1>::Scalar, CGAL::Lazy_exact_nt<CGAL::Gmpq> >::value), void>::type igl::copyleft::cgal::order_facets_around_edges<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, int, int, bool>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > > const&, std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > >&, std::vector<std::vector<bool, std::allocator<bool> >, std::allocator<std::vector<bool, std::allocator<bool> > > >&);
+template void igl::copyleft::cgal::order_facets_around_edges<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 2, 0, -1, 2>, long, long, bool>(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 2, 0, -1, 2> > const&, std::vector<std::vector<long, std::allocator<long> >, std::allocator<std::vector<long, std::allocator<long> > > > const&, std::vector<std::vector<long, std::allocator<long> >, std::allocator<std::vector<long, std::allocator<long> > > >&, std::vector<std::vector<bool, std::allocator<bool> >, std::allocator<std::vector<bool, std::allocator<bool> > > >&);
+template void igl::copyleft::cgal::order_facets_around_edges<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 2, 0, -1, 2>, long, long, bool>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 2, 0, -1, 2> > const&, std::vector<std::vector<long, std::allocator<long> >, std::allocator<std::vector<long, std::allocator<long> > > > const&, std::vector<std::vector<long, std::allocator<long> >, std::allocator<std::vector<long, std::allocator<long> > > >&, std::vector<std::vector<bool, std::allocator<bool> >, std::allocator<std::vector<bool, std::allocator<bool> > > >&);
+template void igl::copyleft::cgal::order_facets_around_edges<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 2, 0, -1, 2>, long, long, bool>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 2, 0, -1, 2> > const&, std::vector<std::vector<long, std::allocator<long> >, std::allocator<std::vector<long, std::allocator<long> > > > const&, std::vector<std::vector<long, std::allocator<long> >, std::allocator<std::vector<long, std::allocator<long> > > >&, std::vector<std::vector<bool, std::allocator<bool> >, std::allocator<std::vector<bool, std::allocator<bool> > > >&);
+template void igl::copyleft::cgal::order_facets_around_edges<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 2, 0, -1, 2>, long, long, bool>(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 2, 0, -1, 2> > const&, std::vector<std::vector<long, std::allocator<long> >, std::allocator<std::vector<long, std::allocator<long> > > > const&, std::vector<std::vector<long, std::allocator<long> >, std::allocator<std::vector<long, std::allocator<long> > > >&, std::vector<std::vector<bool, std::allocator<bool> >, std::allocator<std::vector<bool, std::allocator<bool> > > >&);
+#endif

src/igl/copyleft/cgal/order_facets_around_edges.h

@@ -0,0 +1,107 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_ORDER_FACETS_AROUND_EDGES_H
+#define IGL_COPYLEFT_CGAL_ORDER_FACETS_AROUND_EDGES_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <vector>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // For each undirected edge, sort its adjacent faces.  Assuming the
+      // undirected edge is (s, d).  Sort the adjacent faces clockwise around the
+      // axis (d - s), i.e. left-hand rule.  An adjacent face is consistently
+      // oriented if it contains (d, s) as a directed edge.
+      //
+      // For overlapping faces, break the tie using signed face index, smaller
+      // signed index comes before the larger signed index.  Signed index is
+      // computed as (consistent? 1:-1) * index.
+      //
+      // Inputs:
+      //   V    #V by 3 list of vertices.
+      //   F    #F by 3 list of faces
+      //   N    #F by 3 list of face normals.
+      //  uE    #uE by 2 list of vertex_indices, represents undirected edges.
+      //  uE2E  #uE list of lists that maps uE to E. (a one-to-many map)
+      //
+      // Outputs:
+      //   uE2oE #uE list of lists that maps uE to an ordered list of E. (a
+      //         one-to-many map)
+      //   uE2C  #uE list of lists of bools indicates whether each face in
+      //         uE2oE[i] is consistently orientated as the ordering.
+      //
+      template<
+          typename DerivedV,
+          typename DerivedF,
+          typename DerivedN,
+          typename DeriveduE,
+          typename uE2EType,
+          typename uE2oEType,
+          typename uE2CType >
+      IGL_INLINE
+      typename std::enable_if<!std::is_same<typename DerivedV::Scalar,
+      typename CGAL::Exact_predicates_exact_constructions_kernel::FT>::value, void>::type
+      order_facets_around_edges(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        const Eigen::PlainObjectBase<DerivedN>& N,
+        const Eigen::PlainObjectBase<DeriveduE>& uE,
+        const std::vector<std::vector<uE2EType> >& uE2E,
+        std::vector<std::vector<uE2oEType> >& uE2oE,
+        std::vector<std::vector<uE2CType > >& uE2C );
+
+      template<
+          typename DerivedV,
+          typename DerivedF,
+          typename DerivedN,
+          typename DeriveduE,
+          typename uE2EType,
+          typename uE2oEType,
+          typename uE2CType >
+      IGL_INLINE 
+      typename std::enable_if<std::is_same<typename DerivedV::Scalar,
+      typename CGAL::Exact_predicates_exact_constructions_kernel::FT>::value, void>::type
+      order_facets_around_edges(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        const Eigen::PlainObjectBase<DerivedN>& N,
+        const Eigen::PlainObjectBase<DeriveduE>& uE,
+        const std::vector<std::vector<uE2EType> >& uE2E,
+        std::vector<std::vector<uE2oEType> >& uE2oE,
+        std::vector<std::vector<uE2CType > >& uE2C );
+
+      // Order faces around each edge. Only exact predicate is used in the algorithm.
+      // Normal is not needed.
+      template<
+          typename DerivedV,
+          typename DerivedF,
+          typename DeriveduE,
+          typename uE2EType,
+          typename uE2oEType,
+          typename uE2CType >
+      IGL_INLINE void order_facets_around_edges(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        const Eigen::PlainObjectBase<DeriveduE>& uE,
+        const std::vector<std::vector<uE2EType> >& uE2E,
+        std::vector<std::vector<uE2oEType> >& uE2oE,
+        std::vector<std::vector<uE2CType > >& uE2C );
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#include "order_facets_around_edges.cpp"
+#endif
+
+#endif

src/igl/copyleft/cgal/orient2D.cpp

@@ -0,0 +1,37 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Qingan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "orient2D.h"
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+template<typename Scalar>
+IGL_INLINE short igl::copyleft::cgal::orient2D(
+    const Scalar pa[2],
+    const Scalar pb[2],
+    const Scalar pc[2])
+{
+  typedef CGAL::Exact_predicates_exact_constructions_kernel Epeck;
+  typedef CGAL::Exact_predicates_inexact_constructions_kernel Epick;
+  typedef typename std::conditional<std::is_same<Scalar, Epeck::FT>::value,
+          Epeck, Epick>::type Kernel;
+
+  switch(CGAL::orientation(
+        typename Kernel::Point_2(pa[0], pa[1]),
+        typename Kernel::Point_2(pb[0], pb[1]),
+        typename Kernel::Point_2(pc[0], pc[1]))) {
+    case CGAL::LEFT_TURN:
+      return 1;
+    case CGAL::RIGHT_TURN:
+      return -1;
+    case CGAL::COLLINEAR:
+      return 0;
+    default:
+      throw "Invalid orientation";
+  }
+}

src/igl/copyleft/cgal/orient2D.h

@@ -0,0 +1,38 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Qingan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef IGL_COPYLEFT_CGAL_ORIENT_2D_H
+#define IGL_COPYLEFT_CGAL_ORIENT_2D_H
+
+#include "../../igl_inline.h"
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Inputs:
+      //   pa,pb,pc   2D points.
+      // Output:
+      //   1 if pa,pb,pc are counterclockwise oriented.
+      //   0 if pa,pb,pc are counterclockwise oriented.
+      //  -1 if pa,pb,pc are clockwise oriented.
+      template <typename Scalar>
+      IGL_INLINE short orient2D(
+          const Scalar pa[2],
+          const Scalar pb[2],
+          const Scalar pc[2]);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "orient2D.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/orient3D.cpp

@@ -0,0 +1,39 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Qingan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "orient3D.h"
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+template<typename Scalar>
+IGL_INLINE short igl::copyleft::cgal::orient3D(
+    const Scalar pa[3],
+    const Scalar pb[3],
+    const Scalar pc[3],
+    const Scalar pd[3])
+{
+  typedef CGAL::Exact_predicates_exact_constructions_kernel Epeck;
+  typedef CGAL::Exact_predicates_inexact_constructions_kernel Epick;
+  typedef typename std::conditional<std::is_same<Scalar, Epeck::FT>::value,
+          Epeck, Epick>::type Kernel;
+
+  switch(CGAL::orientation(
+        typename Kernel::Point_3(pa[0], pa[1], pa[2]),
+        typename Kernel::Point_3(pb[0], pb[1], pb[2]),
+        typename Kernel::Point_3(pc[0], pc[1], pc[2]),
+        typename Kernel::Point_3(pd[0], pd[1], pd[2]))) {
+    case CGAL::POSITIVE:
+      return 1;
+    case CGAL::NEGATIVE:
+      return -1;
+    case CGAL::COPLANAR:
+      return 0;
+    default:
+      throw "Invalid orientation";
+  }
+}

src/igl/copyleft/cgal/orient3D.h

@@ -0,0 +1,39 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Qingan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef IGL_COPYLEFT_CGAL_ORIENT_3D_H
+#define IGL_COPYLEFT_CGAL_ORIENT_3D_H
+
+#include "../../igl_inline.h"
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Inputs:
+      //   pa,pb,pc,pd  3D points.
+      // Output:
+      //   1 if pa,pb,pc,pd forms a tet of positive volume.
+      //   0 if pa,pb,pc,pd are coplanar.
+      //  -1 if pa,pb,pc,pd forms a tet of negative volume.
+      template <typename Scalar>
+      IGL_INLINE short orient3D(
+          const Scalar pa[3],
+          const Scalar pb[3],
+          const Scalar pc[3],
+          const Scalar pd[3]);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "orient3D.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/outer_element.cpp

@@ -0,0 +1,232 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2015 Qingnan Zhou <qnzhou@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "outer_element.h"
+#include <iostream>
+#include <vector>
+
+template <
+     typename DerivedV,
+     typename DerivedF,
+     typename DerivedI,
+     typename IndexType,
+     typename DerivedA
+     >
+IGL_INLINE void igl::copyleft::cgal::outer_vertex(
+        const Eigen::PlainObjectBase<DerivedV> & V,
+        const Eigen::PlainObjectBase<DerivedF> & F,
+        const Eigen::PlainObjectBase<DerivedI> & I,
+        IndexType & v_index,
+        Eigen::PlainObjectBase<DerivedA> & A)
+{
+    // Algorithm:
+    //    Find an outer vertex (i.e. vertex reachable from infinity)
+    //    Return the vertex with the largest X value.
+    //    If there is a tie, pick the one with largest Y value.
+    //    If there is still a tie, pick the one with the largest Z value.
+    //    If there is still a tie, then there are duplicated vertices within the
+    //    mesh, which violates the precondition.
+    typedef typename DerivedF::Scalar Index;
+    const Index INVALID = std::numeric_limits<Index>::max();
+    const size_t num_selected_faces = I.rows();
+    std::vector<size_t> candidate_faces;
+    Index outer_vid = INVALID;
+    typename DerivedV::Scalar outer_val = 0;
+    for (size_t i=0; i<num_selected_faces; i++)
+    {
+        size_t f = I(i);
+        for (size_t j=0; j<3; j++)
+        {
+            Index v = F(f, j);
+            auto vx = V(v, 0);
+            if (outer_vid == INVALID || vx > outer_val)
+            {
+                outer_val = vx;
+                outer_vid = v;
+                candidate_faces = {f};
+            } else if (v == outer_vid)
+            {
+                candidate_faces.push_back(f);
+            } else if (vx == outer_val)
+            {
+                // Break tie.
+                auto vy = V(v,1);
+                auto vz = V(v, 2);
+                auto outer_y = V(outer_vid, 1);
+                auto outer_z = V(outer_vid, 2);
+                assert(!(vy == outer_y && vz == outer_z));
+                bool replace = (vy > outer_y) ||
+                    ((vy == outer_y) && (vz > outer_z));
+                if (replace)
+                {
+                    outer_val = vx;
+                    outer_vid = v;
+                    candidate_faces = {f};
+                }
+            }
+        }
+    }
+
+    assert(outer_vid != INVALID);
+    assert(candidate_faces.size() > 0);
+    v_index = outer_vid;
+    A.resize(candidate_faces.size());
+    std::copy(candidate_faces.begin(), candidate_faces.end(), A.data());
+}
+
+template<
+    typename DerivedV,
+    typename DerivedF,
+    typename DerivedI,
+    typename IndexType,
+    typename DerivedA
+    >
+IGL_INLINE void igl::copyleft::cgal::outer_edge(
+        const Eigen::PlainObjectBase<DerivedV> & V,
+        const Eigen::PlainObjectBase<DerivedF> & F,
+        const Eigen::PlainObjectBase<DerivedI> & I,
+        IndexType & v1,
+        IndexType & v2,
+        Eigen::PlainObjectBase<DerivedA> & A) {
+    // Algorithm:
+    //    Find an outer vertex first.
+    //    Find the incident edge with largest abs slope when projected onto XY plane.
+    //    If there is a tie, check the signed slope and use the positive one.
+    //    If there is still a tie, break it using the projected slope onto ZX plane.
+    //    If there is still a tie, again check the signed slope and use the positive one.
+    //    If there is still a tie, then there are multiple overlapping edges,
+    //    which violates the precondition.
+    typedef typename DerivedV::Scalar Scalar;
+    typedef typename DerivedV::Index Index;
+    typedef typename Eigen::Matrix<Scalar, 3, 1> ScalarArray3;
+    typedef typename Eigen::Matrix<typename DerivedF::Scalar, 3, 1> IndexArray3;
+    const Index INVALID = std::numeric_limits<Index>::max();
+
+    Index outer_vid;
+    Eigen::Matrix<Index,Eigen::Dynamic,1> candidate_faces;
+    outer_vertex(V, F, I, outer_vid, candidate_faces);
+    const ScalarArray3& outer_v = V.row(outer_vid);
+    assert(candidate_faces.size() > 0);
+
+    auto get_vertex_index = [&](const IndexArray3& f, Index vid) -> Index
+    {
+        if (f[0] == vid) return 0;
+        if (f[1] == vid) return 1;
+        if (f[2] == vid) return 2;
+        assert(false);
+        return -1;
+    };
+
+    auto unsigned_value = [](Scalar v) -> Scalar {
+        if (v < 0) return v * -1;
+        else return v;
+    };
+
+    Scalar outer_slope_YX = 0;
+    Scalar outer_slope_ZX = 0;
+    Index outer_opp_vid = INVALID;
+    bool infinite_slope_detected = false;
+    std::vector<Index> incident_faces;
+    auto check_and_update_outer_edge = [&](Index opp_vid, Index fid) -> void {
+        if (opp_vid == outer_opp_vid)
+        {
+            incident_faces.push_back(fid);
+            return;
+        }
+
+        const ScalarArray3 opp_v = V.row(opp_vid);
+        if (!infinite_slope_detected && outer_v[0] != opp_v[0])
+        {
+            // Finite slope
+            const ScalarArray3 diff = opp_v - outer_v;
+            const Scalar slope_YX = diff[1] / diff[0];
+            const Scalar slope_ZX = diff[2] / diff[0];
+            const Scalar u_slope_YX = unsigned_value(slope_YX);
+            const Scalar u_slope_ZX = unsigned_value(slope_ZX);
+            bool update = false;
+            if (outer_opp_vid == INVALID) {
+                update = true;
+            } else {
+                const Scalar u_outer_slope_YX = unsigned_value(outer_slope_YX);
+                if (u_slope_YX > u_outer_slope_YX) {
+                    update = true;
+                } else if (u_slope_YX == u_outer_slope_YX &&
+                        slope_YX > outer_slope_YX) {
+                    update = true;
+                } else if (slope_YX == outer_slope_YX) {
+                    const Scalar u_outer_slope_ZX =
+                        unsigned_value(outer_slope_ZX);
+                    if (u_slope_ZX > u_outer_slope_ZX) {
+                        update = true;
+                    } else if (u_slope_ZX == u_outer_slope_ZX &&
+                            slope_ZX > outer_slope_ZX) {
+                        update = true;
+                    } else if (slope_ZX == u_outer_slope_ZX) {
+                        assert(false);
+                    }
+                }
+            }
+
+            if (update) {
+                outer_opp_vid = opp_vid;
+                outer_slope_YX = slope_YX;
+                outer_slope_ZX = slope_ZX;
+                incident_faces = {fid};
+            }
+        } else if (!infinite_slope_detected)
+        {
+            // Infinite slope
+            outer_opp_vid = opp_vid;
+            infinite_slope_detected = true;
+            incident_faces = {fid};
+        }
+    };
+
+    const size_t num_candidate_faces = candidate_faces.size();
+    for (size_t i=0; i<num_candidate_faces; i++)
+    {
+        const Index fid = candidate_faces(i);
+        const IndexArray3& f = F.row(fid);
+        size_t id = get_vertex_index(f, outer_vid);
+        Index next_vid = f((id+1)%3);
+        Index prev_vid = f((id+2)%3);
+        check_and_update_outer_edge(next_vid, fid);
+        check_and_update_outer_edge(prev_vid, fid);
+    }
+
+    v1 = outer_vid;
+    v2 = outer_opp_vid;
+    A.resize(incident_faces.size());
+    std::copy(incident_faces.begin(), incident_faces.end(), A.data());
+}
+
+
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+template void igl::copyleft::cgal::outer_edge<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<long, -1, 1, 0, -1, 1>, long, Eigen::Matrix<long, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> > const&, long&, long&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::outer_edge<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, long, Eigen::Matrix<long, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, long&, long&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::outer_edge<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<long, -1, 1, 0, -1, 1>, long, Eigen::Matrix<long, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> > const&, long&, long&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::outer_edge<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, long, Eigen::Matrix<long, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, long&, long&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::outer_edge<Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 1, -1, -1>, long, Eigen::Matrix<long, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 1, -1, -1> > const&, long&, long&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::outer_edge<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<long, -1, 1, 0, -1, 1>, long, Eigen::Matrix<long, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> > const&, long&, long&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::outer_edge<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, long, Eigen::Matrix<long, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, long&, long&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::outer_edge<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, long, Eigen::Matrix<long, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, long&, long&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::outer_edge<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, long, Eigen::Matrix<long, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, long&, long&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> >&);
+#ifdef WIN32
+template void igl::copyleft::cgal::outer_edge<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, __int64, class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, __int64 &, __int64 &, class Eigen::PlainObjectBase<class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>> &);
+template void igl::copyleft::cgal::outer_edge<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<long, -1, 1, 0, -1, 1>, __int64, class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<long, -1, 1, 0, -1, 1>> const &, __int64 &, __int64 &, class Eigen::PlainObjectBase<class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>> &);
+template void igl::copyleft::cgal::outer_edge<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, __int64, class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, __int64 &, __int64 &, class Eigen::PlainObjectBase<class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>> &);
+template void igl::copyleft::cgal::outer_edge<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, 3, 1, -1, 3>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, __int64, class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 3, 1, -1, 3>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, __int64 &, __int64 &, class Eigen::PlainObjectBase<class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>> &);
+template void igl::copyleft::cgal::outer_edge<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, 3, 0, -1, 3>, class Eigen::Matrix<int, -1, 3, 0, -1, 3>, class Eigen::Matrix<long, -1, 1, 0, -1, 1>, __int64, class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, 3, 0, -1, 3>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 3, 0, -1, 3>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<long, -1, 1, 0, -1, 1>> const &, __int64 &, __int64 &, class Eigen::PlainObjectBase<class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>> &);
+template void igl::copyleft::cgal::outer_edge<class Eigen::Matrix<double, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, __int64, class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<double, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, __int64 &, __int64 &, class Eigen::PlainObjectBase<class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>> &);
+template void igl::copyleft::cgal::outer_edge<class Eigen::Matrix<double, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, __int64, class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<double, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, __int64 &, __int64 &, class Eigen::PlainObjectBase<class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>> &);
+template void igl::copyleft::cgal::outer_edge<class Eigen::Matrix<double, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, -1, 1, -1, -1>, __int64, class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<double, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 1, -1, -1>> const &, __int64 &, __int64 &, class Eigen::PlainObjectBase<class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>> &);
+template void igl::copyleft::cgal::outer_edge<class Eigen::Matrix<double, -1, 3, 0, -1, 3>, class Eigen::Matrix<int, -1, 3, 0, -1, 3>, class Eigen::Matrix<long, -1, 1, 0, -1, 1>, __int64, class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<double, -1, 3, 0, -1, 3>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 3, 0, -1, 3>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<long, -1, 1, 0, -1, 1>> const &, __int64 &, __int64 &, class Eigen::PlainObjectBase<class Eigen::Matrix<__int64, -1, 1, 0, -1, 1>> &);
+#endif
+#endif

src/igl/copyleft/cgal/outer_element.h

@@ -0,0 +1,83 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Qingan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_OUTER_ELEMENT_H
+#define IGL_COPYLEFT_CGAL_OUTER_ELEMENT_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Find a vertex that is reachable from infinite without crossing any faces.
+      // Such vertex is called "outer vertex."
+      //
+      // Precondition: The input mesh must have all self-intersection resolved and
+      // no duplicated vertices.  See cgal::remesh_self_intersections.h for how to
+      // obtain such input.
+      //
+      // Inputs:
+      //   V  #V by 3 list of vertex positions
+      //   F  #F by 3 list of triangle indices into V
+      //   I  #I list of facets to consider
+      // Outputs:
+      //   v_index  index of outer vertex
+      //   A  #A list of facets incident to the outer vertex
+      template <
+          typename DerivedV,
+          typename DerivedF,
+          typename DerivedI,
+          typename IndexType,
+          typename DerivedA
+          >
+      IGL_INLINE void outer_vertex(
+              const Eigen::PlainObjectBase<DerivedV> & V,
+              const Eigen::PlainObjectBase<DerivedF> & F,
+              const Eigen::PlainObjectBase<DerivedI> & I,
+              IndexType & v_index,
+              Eigen::PlainObjectBase<DerivedA> & A);
+      // Find an edge that is reachable from infinity without crossing any faces.
+      // Such edge is called "outer edge."
+      //
+      // Precondition: The input mesh must have all self-intersection resolved
+      // and no duplicated vertices.  The correctness of the output depends on
+      // the fact that there is no edge overlap.  See
+      // cgal::remesh_self_intersections.h for how to obtain such input.
+      //
+      // Inputs:
+      //   V  #V by 3 list of vertex positions
+      //   F  #F by 3 list of triangle indices into V
+      //   I  #I list of facets to consider
+      // Outputs:
+      //   v1 index of the first end point of outer edge
+      //   v2 index of the second end point of outer edge
+      //   A  #A list of facets incident to the outer edge
+      template<
+          typename DerivedV,
+          typename DerivedF,
+          typename DerivedI,
+          typename IndexType,
+          typename DerivedA
+          >
+      IGL_INLINE void outer_edge(
+              const Eigen::PlainObjectBase<DerivedV> & V,
+              const Eigen::PlainObjectBase<DerivedF> & F,
+              const Eigen::PlainObjectBase<DerivedI> & I,
+              IndexType & v1,
+              IndexType & v2,
+              Eigen::PlainObjectBase<DerivedA> & A);
+
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "outer_element.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/outer_facet.cpp

@@ -0,0 +1,180 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "outer_facet.h"
+#include "outer_element.h"
+#include "order_facets_around_edge.h"
+#include <algorithm>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+
+template<
+    typename DerivedV,
+    typename DerivedF,
+    typename DerivedI,
+    typename IndexType
+    >
+IGL_INLINE void igl::copyleft::cgal::outer_facet(
+        const Eigen::PlainObjectBase<DerivedV> & V,
+        const Eigen::PlainObjectBase<DerivedF> & F,
+        const Eigen::PlainObjectBase<DerivedI> & I,
+        IndexType & f,
+        bool & flipped) {
+
+    // Algorithm:
+    //
+    //    1. Find an outer edge (s, d).
+    //
+    //    2. Order adjacent facets around this edge. Because the edge is an
+    //    outer edge, there exists a plane passing through it such that all its
+    //    adjacent facets lie on the same side. The implementation of
+    //    order_facets_around_edge() will find a natural start facet such that
+    //    The first and last facets according to this order are on the outside.
+    //
+    //    3. Because the vertex s is an outer vertex by construction (see
+    //    implemnetation of outer_edge()). The first adjacent facet is facing
+    //    outside (i.e. flipped=false) if it has positive X normal component.
+    //    If it has zero normal component, it is facing outside if it contains
+    //    directed edge (s, d).  
+
+    //typedef typename DerivedV::Scalar Scalar;
+    typedef typename DerivedV::Index Index;
+
+    Index s,d;
+    Eigen::Matrix<Index,Eigen::Dynamic,1> incident_faces;
+    outer_edge(V, F, I, s, d, incident_faces);
+    assert(incident_faces.size() > 0);
+
+    auto convert_to_signed_index = [&](size_t fid) -> int{
+        if ((F(fid, 0) == s && F(fid, 1) == d) ||
+            (F(fid, 1) == s && F(fid, 2) == d) ||
+            (F(fid, 2) == s && F(fid, 0) == d) ) {
+            return int(fid+1) * -1;
+        } else {
+            return int(fid+1);
+        }
+    };
+
+    auto signed_index_to_index = [&](int signed_id) -> size_t {
+        return size_t(abs(signed_id) - 1);
+    };
+
+    std::vector<int> adj_faces(incident_faces.size());
+    std::transform(incident_faces.data(),
+            incident_faces.data() + incident_faces.size(),
+            adj_faces.begin(),
+            convert_to_signed_index);
+
+    DerivedV pivot_point = V.row(s);
+    pivot_point(0, 0) += 1.0;
+
+    Eigen::VectorXi order;
+    order_facets_around_edge(V, F, s, d, adj_faces, pivot_point, order);
+
+    f = signed_index_to_index(adj_faces[order[0]]);
+    flipped = adj_faces[order[0]] > 0;
+}
+
+
+
+template<
+    typename DerivedV,
+    typename DerivedF,
+    typename DerivedN,
+    typename DerivedI,
+    typename IndexType
+    >
+IGL_INLINE void igl::copyleft::cgal::outer_facet(
+        const Eigen::PlainObjectBase<DerivedV> & V,
+        const Eigen::PlainObjectBase<DerivedF> & F,
+        const Eigen::PlainObjectBase<DerivedN> & N,
+        const Eigen::PlainObjectBase<DerivedI> & I,
+        IndexType & f,
+        bool & flipped) {
+    // Algorithm:
+    //    Find an outer edge.
+    //    Find the incident facet with the largest absolute X normal component.
+    //    If there is a tie, keep the one with positive X component.
+    //    If there is still a tie, pick the face with the larger signed index
+    //    (flipped face has negative index).
+    typedef typename DerivedV::Scalar Scalar;
+    typedef typename DerivedV::Index Index;
+    const size_t INVALID = std::numeric_limits<size_t>::max();
+
+    Index v1,v2;
+    Eigen::Matrix<Index,Eigen::Dynamic,1> incident_faces;
+    outer_edge(V, F, I, v1, v2, incident_faces);
+    assert(incident_faces.size() > 0);
+
+    auto generic_fabs = [&](const Scalar& val) -> const Scalar {
+        if (val >= 0) return val;
+        else return -val;
+    };
+
+    Scalar max_nx = 0;
+    size_t outer_fid = INVALID;
+    const size_t num_incident_faces = incident_faces.size();
+    for (size_t i=0; i<num_incident_faces; i++) 
+    {
+        const auto& fid = incident_faces(i);
+        const Scalar nx = N(fid, 0);
+        if (outer_fid == INVALID) {
+            max_nx = nx;
+            outer_fid = fid;
+        } else {
+            if (generic_fabs(nx) > generic_fabs(max_nx)) {
+                max_nx = nx;
+                outer_fid = fid;
+            } else if (nx == -max_nx && nx > 0) {
+                max_nx = nx;
+                outer_fid = fid;
+            } else if (nx == max_nx) {
+                if ((max_nx >= 0 && outer_fid < fid) ||
+                    (max_nx <  0 && outer_fid > fid)) {
+                    max_nx = nx;
+                    outer_fid = fid;
+                }
+            }
+        }
+    }
+
+    assert(outer_fid != INVALID);
+    f = outer_fid;
+    flipped = max_nx < 0;
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, unsigned long>(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, unsigned long&, bool&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, int>(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, int&, bool&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, unsigned long>(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, unsigned long&, bool&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, int>(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, int&, bool&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, unsigned long>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, unsigned long&, bool&);
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<long, -1, 1, 0, -1, 1>, int>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> > const&, int&, bool&);
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 1, -1, -1>, Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 1, -1, -1>, unsigned long>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 1, -1, -1> > const&, unsigned long&, bool&);
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, int>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, int&, bool&);
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, int>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, int&, bool&);
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<long, -1, 1, 0, -1, 1>, int>(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> > const&, int&, bool&);
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<long, -1, 1, 0, -1, 1>, int>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> > const&, int&, bool&);
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, int>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, int&, bool&);
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, unsigned long>(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, unsigned long&, bool&);
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, int>(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, int&, bool&);
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<long, -1, 1, 0, -1, 1>, int>(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> > const&, int&, bool&);
+template void igl::copyleft::cgal::outer_facet<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, int>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, int&, bool&);
+#ifdef WIN32
+template void igl::copyleft::cgal::outer_facet<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, unsigned __int64>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, unsigned __int64 &, bool &);
+template void igl::copyleft::cgal::outer_facet<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, unsigned __int64>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, unsigned __int64 &, bool &);
+template void igl::copyleft::cgal::outer_facet<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, 3, 1, -1, 3>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, unsigned __int64>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 3, 1, -1, 3>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, unsigned __int64 &, bool &);
+#endif
+#endif

src/igl/copyleft/cgal/outer_facet.h

@@ -0,0 +1,91 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef IGL_COPYLEFT_CGAL_OUTER_FACET_H
+#define IGL_COPYLEFT_CGAL_OUTER_FACET_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+        // Find a facet that is reachable from infinity without crossing any faces.
+        // Such facet is called "outer facet."
+        //
+        // Precondition: The input mesh must have all self-intersection resolved.  I.e
+        // there is no duplicated vertices, no overlapping edge and no intersecting
+        // faces (the only exception is there could be topologically duplicated faces).
+        // See cgal::remesh_self_intersections.h for how to obtain such input.
+        //
+        // This function differ from igl::outer_facet() in the fact this
+        // function is more robust because it does not rely on facet normals.
+        //
+        // Inputs:
+        //   V  #V by 3 list of vertex positions
+        //   F  #F by 3 list of triangle indices into V
+        //   I  #I list of facets to consider
+        // Outputs:
+        //   f  Index of the outer facet.
+        //   flipped  true iff the normal of f points inwards.
+        template<
+            typename DerivedV,
+            typename DerivedF,
+            typename DerivedI,
+            typename IndexType
+            >
+        IGL_INLINE void outer_facet(
+                const Eigen::PlainObjectBase<DerivedV> & V,
+                const Eigen::PlainObjectBase<DerivedF> & F,
+                const Eigen::PlainObjectBase<DerivedI> & I,
+                IndexType & f,
+                bool & flipped);
+
+      // Find a facet that is reachable from infinity without crossing any faces.
+      // Such facet is called "outer facet."
+      //
+      // Precondition: The input mesh must have all self-intersection resolved.
+      // I.e there is no duplicated vertices, no overlapping edge and no
+      // intersecting faces (the only exception is there could be topologically
+      // duplicated faces).  See cgal::remesh_self_intersections.h for how to
+      // obtain such input.
+      //
+      // Inputs:
+      //   V  #V by 3 list of vertex positions
+      //   F  #F by 3 list of triangle indices into V
+      //   N  #N by 3 list of face normals
+      //   I  #I list of facets to consider
+      // Outputs:
+      //   f  Index of the outer facet.
+      //   flipped  true iff the normal of f points inwards.
+      template<
+          typename DerivedV,
+          typename DerivedF,
+          typename DerivedN,
+          typename DerivedI,
+          typename IndexType
+          >
+      IGL_INLINE void outer_facet(
+              const Eigen::PlainObjectBase<DerivedV> & V,
+              const Eigen::PlainObjectBase<DerivedF> & F,
+              const Eigen::PlainObjectBase<DerivedN> & N,
+              const Eigen::PlainObjectBase<DerivedI> & I,
+              IndexType & f,
+              bool & flipped);
+
+    }
+
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "outer_facet.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/outer_hull.cpp

@@ -0,0 +1,535 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "outer_hull.h"
+#include "extract_cells.h"
+#include "remesh_self_intersections.h"
+#include "assign.h"
+#include "../../remove_unreferenced.h"
+
+#include <CGAL/AABB_tree.h>
+#include <CGAL/AABB_traits.h>
+#include <CGAL/AABB_triangle_primitive.h>
+#include <CGAL/intersections.h>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+
+template <
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedHV,
+  typename DerivedHF,
+  typename DerivedJ,
+  typename Derivedflip>
+IGL_INLINE void igl::copyleft::cgal::outer_hull(
+  const Eigen::PlainObjectBase<DerivedV> & V,
+  const Eigen::PlainObjectBase<DerivedF> & F,
+  Eigen::PlainObjectBase<DerivedHV> & HV,
+  Eigen::PlainObjectBase<DerivedHF> & HF,
+  Eigen::PlainObjectBase<DerivedJ> & J,
+  Eigen::PlainObjectBase<Derivedflip> & flip)
+{
+  // Exact types
+  typedef CGAL::Epeck Kernel;
+  typedef Kernel::FT ExactScalar;
+  typedef
+    Eigen::Matrix<
+    ExactScalar,
+    Eigen::Dynamic,
+    Eigen::Dynamic,
+    DerivedHV::IsRowMajor>
+      MatrixXES;
+  // Remesh self-intersections
+  MatrixXES Vr;
+  DerivedHF Fr;
+  DerivedJ Jr;
+  {
+    RemeshSelfIntersectionsParam params;
+    params.stitch_all = true;
+    Eigen::VectorXi I;
+    Eigen::MatrixXi IF;
+    remesh_self_intersections(V, F, params, Vr, Fr, IF, Jr, I);
+    // Merge coinciding vertices into non-manifold vertices.
+    std::for_each(Fr.data(), Fr.data()+Fr.size(),
+      [&I](typename DerivedHF::Scalar& a) { a=I[a]; });
+      // Remove unreferenced vertices.
+    Eigen::VectorXi UIM;
+    remove_unreferenced(MatrixXES(Vr),DerivedHF(Fr), Vr, Fr, UIM);
+  }
+  // Extract cells for each face
+  Eigen::MatrixXi C;
+  extract_cells(Vr,Fr,C);
+  // Extract faces on ambient cell
+  int num_outer = 0;
+  for(int i = 0;i<C.rows();i++)
+  {
+    num_outer += ( C(i,0) == 0 || C(i,1) == 0 ) ? 1 : 0;
+  }
+  HF.resize(num_outer,3);
+  J.resize(num_outer,1);
+  flip.resize(num_outer,1);
+  {
+    int h = 0;
+    for(int i = 0;i<C.rows();i++)
+    {
+      if(C(i,0)==0)
+      {
+        HF.row(h) = Fr.row(i);
+        J(h) = Jr(i);
+        flip(h) = false;
+        h++;
+      }else if(C(i,1) == 0)
+      {
+        HF.row(h) = Fr.row(i).reverse();
+        J(h) = Jr(i);
+        flip(h) = true;
+        h++;
+      }
+    }
+    assert(h == num_outer);
+  }
+  // Remove unreferenced vertices and re-index faces
+  {
+    // Cast to output type
+    DerivedHV Vr_cast;
+    assign(Vr,Vr_cast);
+    Eigen::VectorXi I;
+    remove_unreferenced(Vr_cast,DerivedHF(HF),HV,HF,I);
+  }
+}
+
+#include "points_inside_component.h"
+#include "order_facets_around_edges.h"
+#include "outer_facet.h"
+#include "../../sortrows.h"
+#include "../../facet_components.h"
+#include "../../winding_number.h"
+#include "../../triangle_triangle_adjacency.h"
+#include "../../unique_edge_map.h"
+#include "../../barycenter.h"
+#include "../../per_face_normals.h"
+#include "../../sort_angles.h"
+#include <Eigen/Geometry>
+#include <vector>
+#include <map>
+#include <queue>
+#include <iostream>
+#include <type_traits>
+#include <CGAL/number_utils.h>
+//#define IGL_OUTER_HULL_DEBUG
+
+template <
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedG,
+  typename DerivedJ,
+  typename Derivedflip>
+IGL_INLINE void igl::copyleft::cgal::outer_hull_legacy(
+  const Eigen::PlainObjectBase<DerivedV> & V,
+  const Eigen::PlainObjectBase<DerivedF> & F,
+  Eigen::PlainObjectBase<DerivedG> & G,
+  Eigen::PlainObjectBase<DerivedJ> & J,
+  Eigen::PlainObjectBase<Derivedflip> & flip)
+{
+#ifdef IGL_OUTER_HULL_DEBUG
+  std::cerr << "Extracting outer hull" << std::endl;
+#endif
+  using namespace Eigen;
+  using namespace std;
+  typedef typename DerivedF::Index Index;
+  Matrix<Index,DerivedF::RowsAtCompileTime,1> C;
+  typedef Matrix<typename DerivedV::Scalar,Dynamic,DerivedV::ColsAtCompileTime> MatrixXV;
+  //typedef Matrix<typename DerivedF::Scalar,Dynamic,DerivedF::ColsAtCompileTime> MatrixXF;
+  typedef Matrix<typename DerivedG::Scalar,Dynamic,DerivedG::ColsAtCompileTime> MatrixXG;
+  typedef Matrix<typename DerivedJ::Scalar,Dynamic,DerivedJ::ColsAtCompileTime> MatrixXJ;
+  const Index m = F.rows();
+
+  // UNUSED:
+  //const auto & duplicate_simplex = [&F](const int f, const int g)->bool
+  //{
+  //  return
+  //    (F(f,0) == F(g,0) && F(f,1) == F(g,1) && F(f,2) == F(g,2)) ||
+  //    (F(f,1) == F(g,0) && F(f,2) == F(g,1) && F(f,0) == F(g,2)) ||
+  //    (F(f,2) == F(g,0) && F(f,0) == F(g,1) && F(f,1) == F(g,2)) ||
+  //    (F(f,0) == F(g,2) && F(f,1) == F(g,1) && F(f,2) == F(g,0)) ||
+  //    (F(f,1) == F(g,2) && F(f,2) == F(g,1) && F(f,0) == F(g,0)) ||
+  //    (F(f,2) == F(g,2) && F(f,0) == F(g,1) && F(f,1) == F(g,0));
+  //};
+
+#ifdef IGL_OUTER_HULL_DEBUG
+  cout<<"outer hull..."<<endl;
+#endif
+
+#ifdef IGL_OUTER_HULL_DEBUG
+  cout<<"edge map..."<<endl;
+#endif
+  typedef Matrix<typename DerivedF::Scalar,Dynamic,2> MatrixX2I;
+  typedef Matrix<typename DerivedF::Index,Dynamic,1> VectorXI;
+  //typedef Matrix<typename DerivedV::Scalar, 3, 1> Vector3F;
+  MatrixX2I E,uE;
+  VectorXI EMAP;
+  vector<vector<typename DerivedF::Index> > uE2E;
+  unique_edge_map(F,E,uE,EMAP,uE2E);
+#ifdef IGL_OUTER_HULL_DEBUG
+  for (size_t ui=0; ui<uE.rows(); ui++) {
+      std::cout << ui << ": " << uE2E[ui].size() << " -- (";
+      for (size_t i=0; i<uE2E[ui].size(); i++) {
+          std::cout << uE2E[ui][i] << ", ";
+      }
+      std::cout << ")" << std::endl;
+  }
+#endif
+
+  std::vector<std::vector<typename DerivedF::Index> > uE2oE;
+  std::vector<std::vector<bool> > uE2C;
+  order_facets_around_edges(V, F, uE, uE2E, uE2oE, uE2C);
+  uE2E = uE2oE;
+  VectorXI diIM(3*m);
+  for (auto ue : uE2E) {
+      for (size_t i=0; i<ue.size(); i++) {
+          auto fe = ue[i];
+          diIM[fe] = i;
+      }
+  }
+
+  vector<vector<vector<Index > > > TT,_1;
+  triangle_triangle_adjacency(E,EMAP,uE2E,false,TT,_1);
+  VectorXI counts;
+#ifdef IGL_OUTER_HULL_DEBUG
+  cout<<"facet components..."<<endl;
+#endif
+  facet_components(TT,C,counts);
+  assert(C.maxCoeff()+1 == counts.rows());
+  const size_t ncc = counts.rows();
+  G.resize(0,F.cols());
+  J.resize(0,1);
+  flip.setConstant(m,1,false);
+
+#ifdef IGL_OUTER_HULL_DEBUG
+  cout<<"reindex..."<<endl;
+#endif
+  // H contains list of faces on outer hull;
+  vector<bool> FH(m,false);
+  vector<bool> EH(3*m,false);
+  vector<MatrixXG> vG(ncc);
+  vector<MatrixXJ> vJ(ncc);
+  vector<MatrixXJ> vIM(ncc);
+  //size_t face_count = 0;
+  for(size_t id = 0;id<ncc;id++)
+  {
+    vIM[id].resize(counts[id],1);
+  }
+  // current index into each IM
+  vector<size_t> g(ncc,0);
+  // place order of each face in its respective component
+  for(Index f = 0;f<m;f++)
+  {
+    vIM[C(f)](g[C(f)]++) = f;
+  }
+
+#ifdef IGL_OUTER_HULL_DEBUG
+  cout<<"barycenters..."<<endl;
+#endif
+  // assumes that "resolve" has handled any coplanar cases correctly and nearly
+  // coplanar cases can be sorted based on barycenter.
+  MatrixXV BC;
+  barycenter(V,F,BC);
+
+#ifdef IGL_OUTER_HULL_DEBUG
+  cout<<"loop over CCs (="<<ncc<<")..."<<endl;
+#endif
+  for(Index id = 0;id<(Index)ncc;id++)
+  {
+    auto & IM = vIM[id];
+    // starting face that's guaranteed to be on the outer hull and in this
+    // component
+    int f;
+    bool f_flip;
+#ifdef IGL_OUTER_HULL_DEBUG
+  cout<<"outer facet..."<<endl;
+#endif
+  igl::copyleft::cgal::outer_facet(V,F,IM,f,f_flip);
+#ifdef IGL_OUTER_HULL_DEBUG
+  cout<<"outer facet: "<<f<<endl;
+  //cout << V.row(F(f, 0)) << std::endl;
+  //cout << V.row(F(f, 1)) << std::endl;
+  //cout << V.row(F(f, 2)) << std::endl;
+#endif
+    int FHcount = 1;
+    FH[f] = true;
+    // Q contains list of face edges to continue traversing upong
+    queue<int> Q;
+    Q.push(f+0*m);
+    Q.push(f+1*m);
+    Q.push(f+2*m);
+    flip(f) = f_flip;
+    //std::cout << "face " << face_count++ << ": " << f << std::endl;
+    //std::cout << "f " << F.row(f).array()+1 << std::endl;
+    //cout<<"flip("<<f<<") = "<<(flip(f)?"true":"false")<<endl;
+#ifdef IGL_OUTER_HULL_DEBUG
+  cout<<"BFS..."<<endl;
+#endif
+    while(!Q.empty())
+    {
+      // face-edge
+      const int e = Q.front();
+      Q.pop();
+      // face
+      const int f = e%m;
+      // corner
+      const int c = e/m;
+#ifdef IGL_OUTER_HULL_DEBUG
+      std::cout << "edge: " << e << ", ue: " << EMAP(e) << std::endl;
+      std::cout << "face: " << f << std::endl;
+      std::cout << "corner: " << c << std::endl;
+      std::cout << "consistent: " << uE2C[EMAP(e)][diIM[e]] << std::endl;
+#endif
+      // Should never see edge again...
+      if(EH[e] == true)
+      {
+        continue;
+      }
+      EH[e] = true;
+      // source of edge according to f
+      const int fs = flip(f)?F(f,(c+2)%3):F(f,(c+1)%3);
+      // destination of edge according to f
+      const int fd = flip(f)?F(f,(c+1)%3):F(f,(c+2)%3);
+      // edge valence
+      const size_t val = uE2E[EMAP(e)].size();
+#ifdef IGL_OUTER_HULL_DEBUG
+      //std::cout << "vd: " << V.row(fd) << std::endl;
+      //std::cout << "vs: " << V.row(fs) << std::endl;
+      //std::cout << "edge: " << V.row(fd) - V.row(fs) << std::endl;
+      for (size_t i=0; i<val; i++) {
+          if (i == diIM(e)) {
+              std::cout << "* ";
+          } else {
+              std::cout << "  ";
+          }
+          std::cout << i << ": "
+              << " (e: " << uE2E[EMAP(e)][i] << ", f: "
+              << uE2E[EMAP(e)][i] % m * (uE2C[EMAP(e)][i] ? 1:-1) << ")" << std::endl;
+      }
+#endif
+
+      // is edge consistent with edge of face used for sorting
+      const int e_cons = (uE2C[EMAP(e)][diIM(e)] ? 1: -1);
+      int nfei = -1;
+      // Loop once around trying to find suitable next face
+      for(size_t step = 1; step<val+2;step++)
+      {
+        const int nfei_new = (diIM(e) + 2*val + e_cons*step*(flip(f)?-1:1))%val;
+        const int nf = uE2E[EMAP(e)][nfei_new] % m;
+        {
+#ifdef IGL_OUTER_HULL_DEBUG
+        //cout<<"Next facet: "<<(f+1)<<" --> "<<(nf+1)<<", |"<<
+        //  di[EMAP(e)][diIM(e)]<<" - "<<di[EMAP(e)][nfei_new]<<"| = "<<
+        //    abs(di[EMAP(e)][diIM(e)] - di[EMAP(e)][nfei_new])
+        //    <<endl;
+#endif
+
+
+
+          // Only use this face if not already seen
+          if(!FH[nf])
+          {
+            nfei = nfei_new;
+          //} else {
+          //    std::cout << "skipping face " << nfei_new << " because it is seen before"
+          //        << std::endl;
+          }
+          break;
+        //} else {
+        //    std::cout << di[EMAP(e)][diIM(e)].transpose() << std::endl;
+        //    std::cout << di[EMAP(e)][diIM(nfei_new)].transpose() << std::endl;
+        //    std::cout << "skipping face " << nfei_new << " with identical dihedral angle"
+        //        << std::endl;
+        }
+//#ifdef IGL_OUTER_HULL_DEBUG
+//        cout<<"Skipping co-planar facet: "<<(f+1)<<" --> "<<(nf+1)<<endl;
+//#endif
+      }
+
+      int max_ne = -1;
+      if(nfei >= 0)
+      {
+        max_ne = uE2E[EMAP(e)][nfei];
+      }
+
+      if(max_ne>=0)
+      {
+        // face of neighbor
+        const int nf = max_ne%m;
+#ifdef IGL_OUTER_HULL_DEBUG
+        if(!FH[nf])
+        {
+          // first time seeing face
+          cout<<(f+1)<<" --> "<<(nf+1)<<endl;
+        }
+#endif
+        FH[nf] = true;
+        //std::cout << "face " << face_count++ << ": " << nf << std::endl;
+        //std::cout << "f " << F.row(nf).array()+1 << std::endl;
+        FHcount++;
+        // corner of neighbor
+        const int nc = max_ne/m;
+        const int nd = F(nf,(nc+2)%3);
+        const bool cons = (flip(f)?fd:fs) == nd;
+        flip(nf) = (cons ? flip(f) : !flip(f));
+        //cout<<"flip("<<nf<<") = "<<(flip(nf)?"true":"false")<<endl;
+        const int ne1 = nf+((nc+1)%3)*m;
+        const int ne2 = nf+((nc+2)%3)*m;
+        if(!EH[ne1])
+        {
+          Q.push(ne1);
+        }
+        if(!EH[ne2])
+        {
+          Q.push(ne2);
+        }
+      }
+    }
+
+    {
+      vG[id].resize(FHcount,3);
+      vJ[id].resize(FHcount,1);
+      //nG += FHcount;
+      size_t h = 0;
+      assert(counts(id) == IM.rows());
+      for(int i = 0;i<counts(id);i++)
+      {
+        const size_t f = IM(i);
+        //if(f_flip)
+        //{
+        //  flip(f) = !flip(f);
+        //}
+        if(FH[f])
+        {
+          vG[id].row(h) = (flip(f)?F.row(f).reverse().eval():F.row(f));
+          vJ[id](h,0) = f;
+          h++;
+        }
+      }
+      assert((int)h == FHcount);
+    }
+  }
+
+  // Is A inside B? Assuming A and B are consistently oriented but closed and
+  // non-intersecting.
+  const auto & has_overlapping_bbox = [](
+    const Eigen::PlainObjectBase<DerivedV> & V,
+    const MatrixXG & A,
+    const MatrixXG & B)->bool
+  {
+    const auto & bounding_box = [](
+      const Eigen::PlainObjectBase<DerivedV> & V,
+      const MatrixXG & F)->
+        DerivedV
+    {
+      DerivedV BB(2,3);
+      BB<<
+         1e26,1e26,1e26,
+        -1e26,-1e26,-1e26;
+      const size_t m = F.rows();
+      for(size_t f = 0;f<m;f++)
+      {
+        for(size_t c = 0;c<3;c++)
+        {
+          const auto & vfc = V.row(F(f,c)).eval();
+          BB(0,0) = std::min(BB(0,0), vfc(0,0));
+          BB(0,1) = std::min(BB(0,1), vfc(0,1));
+          BB(0,2) = std::min(BB(0,2), vfc(0,2));
+          BB(1,0) = std::max(BB(1,0), vfc(0,0));
+          BB(1,1) = std::max(BB(1,1), vfc(0,1));
+          BB(1,2) = std::max(BB(1,2), vfc(0,2));
+        }
+      }
+      return BB;
+    };
+    // A lot of the time we're dealing with unrelated, distant components: cull
+    // them.
+    DerivedV ABB = bounding_box(V,A);
+    DerivedV BBB = bounding_box(V,B);
+    if( (BBB.row(0)-ABB.row(1)).maxCoeff()>0  ||
+        (ABB.row(0)-BBB.row(1)).maxCoeff()>0 )
+    {
+      // bounding boxes do not overlap
+      return false;
+    } else {
+      return true;
+    }
+  };
+
+  // Reject components which are completely inside other components
+  vector<bool> keep(ncc,true);
+  size_t nG = 0;
+  // This is O( ncc * ncc * m)
+  for(size_t id = 0;id<ncc;id++)
+  {
+    if (!keep[id]) continue;
+    std::vector<size_t> unresolved;
+    for(size_t oid = 0;oid<ncc;oid++)
+    {
+      if(id == oid || !keep[oid])
+      {
+        continue;
+      }
+      if (has_overlapping_bbox(V, vG[id], vG[oid])) {
+          unresolved.push_back(oid);
+      }
+    }
+    const size_t num_unresolved_components = unresolved.size();
+    DerivedV query_points(num_unresolved_components, 3);
+    for (size_t i=0; i<num_unresolved_components; i++) {
+        const size_t oid = unresolved[i];
+        DerivedF f = vG[oid].row(0);
+        query_points(i,0) = (V(f(0,0), 0) + V(f(0,1), 0) + V(f(0,2), 0))/3.0;
+        query_points(i,1) = (V(f(0,0), 1) + V(f(0,1), 1) + V(f(0,2), 1))/3.0;
+        query_points(i,2) = (V(f(0,0), 2) + V(f(0,1), 2) + V(f(0,2), 2))/3.0;
+    }
+    Eigen::VectorXi inside;
+    igl::copyleft::cgal::points_inside_component(V, vG[id], query_points, inside);
+    assert((size_t)inside.size() == num_unresolved_components);
+    for (size_t i=0; i<num_unresolved_components; i++) {
+        if (inside(i, 0)) {
+            const size_t oid = unresolved[i];
+            keep[oid] = false;
+        }
+    }
+  }
+  for (size_t id = 0; id<ncc; id++) {
+      if (keep[id]) {
+          nG += vJ[id].rows();
+      }
+  }
+
+  // collect G and J across components
+  G.resize(nG,3);
+  J.resize(nG,1);
+  {
+    size_t off = 0;
+    for(Index id = 0;id<(Index)ncc;id++)
+    {
+      if(keep[id])
+      {
+        assert(vG[id].rows() == vJ[id].rows());
+        G.block(off,0,vG[id].rows(),vG[id].cols()) = vG[id];
+        J.block(off,0,vJ[id].rows(),vJ[id].cols()) = vJ[id];
+        off += vG[id].rows();
+      }
+    }
+  }
+}
+
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template void igl::copyleft::cgal::outer_hull<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::outer_hull_legacy< Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > &, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > &, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > &);
+template void igl::copyleft::cgal::outer_hull_legacy< Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+template void igl::copyleft::cgal::outer_hull_legacy<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<long, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::outer_hull_legacy<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<long, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+#endif

src/igl/copyleft/cgal/outer_hull.h

@@ -0,0 +1,84 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_OUTER_HULL_H
+#define IGL_COPYLEFT_CGAL_OUTER_HULL_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Compute the "outer hull" of a piecewise constant winding number induce
+      // triangle mesh (V,F).
+      //
+      // Inputs:
+      //   V  #V by 3 list of vertex positions
+      //   F  #F by 3 list of triangle indices into V
+      // Outputs:
+      //   HV  #HV by 3 list of output vertex positions
+      //   HF  #HF by 3 list of output triangle indices into HV
+      //   J  #HF list of indices into F
+      //   flip  #HF list of whether facet was flipped when added to HF
+      //
+      template <
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedHV,
+        typename DerivedHF,
+        typename DerivedJ,
+        typename Derivedflip>
+      IGL_INLINE void outer_hull(
+        const Eigen::PlainObjectBase<DerivedV> & V,
+        const Eigen::PlainObjectBase<DerivedF> & F,
+        Eigen::PlainObjectBase<DerivedHV> & HV,
+        Eigen::PlainObjectBase<DerivedHF> & HF,
+        Eigen::PlainObjectBase<DerivedJ> & J,
+        Eigen::PlainObjectBase<Derivedflip> & flip);
+      // Compute the "outer hull" of a potentially non-manifold mesh (V,F) whose
+      // intersections have been "resolved" (e.g. using `cork` or
+      // `igl::copyleft::cgal::selfintersect`). The outer hull is defined to be all facets
+      // (regardless of orientation) for which there exists some path from infinity
+      // to the face without intersecting any other facets. For solids, this is the
+      // surface of the solid. In general this includes any thin "wings" or
+      // "flaps".  This implementation largely follows Section 3.6 of "Direct
+      // repair of self-intersecting meshes" [Attene 2014].
+      //
+      // Note: This doesn't require the input mesh to be piecewise constant
+      // winding number, but won't handle multiple non-nested connected
+      // components.
+      //
+      // Inputs:
+      //   V  #V by 3 list of vertex positions
+      //   F  #F by 3 list of triangle indices into V
+      // Outputs:
+      //   G  #G by 3 list of output triangle indices into V
+      //   J  #G list of indices into F
+      //   flip  #F list of whether facet was added to G **and** flipped orientation
+      //     (false for faces not added to G)
+      template <
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedG,
+        typename DerivedJ,
+        typename Derivedflip>
+      IGL_INLINE void outer_hull_legacy(
+        const Eigen::PlainObjectBase<DerivedV> & V,
+        const Eigen::PlainObjectBase<DerivedF> & F,
+        Eigen::PlainObjectBase<DerivedG> & G,
+        Eigen::PlainObjectBase<DerivedJ> & J,
+        Eigen::PlainObjectBase<Derivedflip> & flip);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "outer_hull.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/peel_outer_hull_layers.cpp

@@ -0,0 +1,124 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "peel_outer_hull_layers.h"
+#include "outer_hull.h"
+#include "../../LinSpaced.h"
+#include <vector>
+#include <iostream>
+//#define IGL_PEEL_OUTER_HULL_LAYERS_DEBUG
+#ifdef IGL_PEEL_OUTER_HULL_LAYERS_DEBUG
+#include "../../writePLY.h"
+#include "../../writeDMAT.h"
+#include "../../STR.h"
+#endif
+
+template <
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedI,
+  typename Derivedflip>
+IGL_INLINE size_t igl::copyleft::cgal::peel_outer_hull_layers(
+  const Eigen::PlainObjectBase<DerivedV > & V,
+  const Eigen::PlainObjectBase<DerivedF > & F,
+  Eigen::PlainObjectBase<DerivedI> & I,
+  Eigen::PlainObjectBase<Derivedflip > & flip)
+{
+  using namespace Eigen;
+  using namespace std;
+  typedef typename DerivedF::Index Index;
+  typedef Matrix<typename DerivedF::Scalar,Dynamic,DerivedF::ColsAtCompileTime> MatrixXF;
+  typedef Matrix<Index,Dynamic,1> MatrixXI;
+  typedef Matrix<typename Derivedflip::Scalar,Dynamic,Derivedflip::ColsAtCompileTime> MatrixXflip;
+  const Index m = F.rows();
+#ifdef IGL_PEEL_OUTER_HULL_LAYERS_DEBUG
+  cout<<"peel outer hull layers..."<<endl;
+#endif
+#ifdef IGL_PEEL_OUTER_HULL_LAYERS_DEBUG
+  cout<<"calling outer hull..."<<endl;
+  writePLY(STR("peel-outer-hull-input.ply"),V,F);
+#endif
+
+#ifdef IGL_PEEL_OUTER_HULL_LAYERS_DEBUG
+  cout<<"resize output ..."<<endl;
+#endif
+  // keep track of iteration parity and whether flipped in hull
+  MatrixXF Fr = F;
+  I.resize(m,1);
+  flip.resize(m,1);
+  // Keep track of index map
+  MatrixXI IM = igl::LinSpaced<MatrixXI >(m,0,m-1);
+  // This is O(n * layers)
+  MatrixXI P(m,1);
+  Index iter = 0;
+  while(Fr.size() > 0)
+  {
+    assert(Fr.rows() == IM.rows());
+    // Compute outer hull of current Fr
+    MatrixXF Fo;
+    MatrixXI Jo;
+    MatrixXflip flipr;
+#ifdef IGL_PEEL_OUTER_HULL_LAYERS_DEBUG
+  {
+      cout<<"calling outer hull..." << iter <<endl;
+      std::stringstream ss;
+      ss << "outer_hull_" << iter << ".ply";
+      Eigen::MatrixXd vertices(V.rows(), V.cols());
+      std::transform(V.data(), V.data() + V.rows()*V.cols(),
+              vertices.data(),
+              [](typename DerivedV::Scalar val)
+              {return CGAL::to_double(val); });
+      writePLY(ss.str(), vertices, Fr);
+  }
+#endif
+    outer_hull_legacy(V,Fr,Fo,Jo,flipr);
+#ifdef IGL_PEEL_OUTER_HULL_LAYERS_DEBUG
+  writePLY(STR("outer-hull-output-"<<iter<<".ply"),V,Fo);
+  cout<<"reindex, flip..."<<endl;
+#endif
+    assert(Fo.rows() != 0);
+    assert(Fo.rows() == Jo.rows());
+    // all faces in Fo of Fr
+    vector<bool> in_outer(Fr.rows(),false);
+    for(Index g = 0;g<Jo.rows();g++)
+    {
+      I(IM(Jo(g))) = iter;
+      P(IM(Jo(g))) = iter;
+      in_outer[Jo(g)] = true;
+      flip(IM(Jo(g))) = flipr(Jo(g));
+    }
+    // Fr = Fr - Fo
+    // update IM
+    MatrixXF prev_Fr = Fr;
+    MatrixXI prev_IM = IM;
+    Fr.resize(prev_Fr.rows() - Fo.rows(),F.cols());
+    IM.resize(Fr.rows());
+    {
+      Index g = 0;
+      for(Index f = 0;f<prev_Fr.rows();f++)
+      {
+        if(!in_outer[f])
+        {
+          Fr.row(g) = prev_Fr.row(f);
+          IM(g) = prev_IM(f);
+          g++;
+        }
+      }
+    }
+    iter++;
+  }
+  return iter;
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+template unsigned long igl::copyleft::cgal::peel_outer_hull_layers<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template size_t igl::copyleft::cgal::peel_outer_hull_layers<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+#endif

src/igl/copyleft/cgal/peel_outer_hull_layers.h

@@ -0,0 +1,47 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_PEEL_OUTER_HULL_LAYERS_H
+#define IGL_COPYLEFT_CGAL_PEEL_OUTER_HULL_LAYERS_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Computes necessary generic information for boolean operations by
+      // successively "peeling" off the "outer hull" of a mesh (V,F) resulting from
+      // "resolving" all (self-)intersections.
+      //
+      // Inputs:
+      //   V  #V by 3 list of vertex positions
+      //   F  #F by 3 list of triangle indices into V
+      // Outputs:
+      //   I  #F list of which peel Iation a facet belongs 
+      //   flip  #F list of whether a facet's orientation was flipped when facet
+      //     "peeled" into its associated outer hull layer.
+      // Returns number of peels
+      template <
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedI,
+        typename Derivedflip>
+      IGL_INLINE size_t peel_outer_hull_layers(
+        const Eigen::PlainObjectBase<DerivedV > & V,
+        const Eigen::PlainObjectBase<DerivedF > & F,
+        Eigen::PlainObjectBase<DerivedI > & I,
+        Eigen::PlainObjectBase<Derivedflip > & flip);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "peel_outer_hull_layers.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/peel_winding_number_layers.cpp

@@ -0,0 +1,33 @@
+#include "peel_winding_number_layers.h"
+
+#include <cassert>
+
+#include "propagate_winding_numbers.h"
+
+template<
+typename DerivedV,
+typename DerivedF,
+typename DerivedW >
+IGL_INLINE size_t igl::copyleft::cgal::peel_winding_number_layers(
+        const Eigen::PlainObjectBase<DerivedV > & V,
+        const Eigen::PlainObjectBase<DerivedF > & F,
+        Eigen::PlainObjectBase<DerivedW>& W) {
+    const size_t num_faces = F.rows();
+    Eigen::VectorXi labels(num_faces);
+    labels.setZero();
+
+    Eigen::MatrixXi winding_numbers;
+    igl::copyleft::cgal::propagate_winding_numbers(V, F, labels, winding_numbers);
+    assert(winding_numbers.rows() == num_faces);
+    assert(winding_numbers.cols() == 2);
+
+    int min_w = winding_numbers.minCoeff();
+    int max_w = winding_numbers.maxCoeff();
+    assert(max_w > min_w);
+
+    W.resize(num_faces, 1);
+    for (size_t i=0; i<num_faces; i++) {
+        W(i, 0) = winding_numbers(i, 1);
+    }
+    return max_w - min_w;
+}

src/igl/copyleft/cgal/peel_winding_number_layers.h

@@ -0,0 +1,24 @@
+#ifndef IGL_COPYLEFT_CGAL_PEEL_WINDING_NUMBER_LAYERS_H
+#define IGL_COPYLEFT_CGAL_PEEL_WINDING_NUMBER_LAYERS_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+
+namespace igl {
+  namespace copyleft {
+    namespace cgal {
+        template<
+            typename DerivedV,
+            typename DerivedF,
+            typename DerivedW >
+        IGL_INLINE size_t peel_winding_number_layers(
+                const Eigen::PlainObjectBase<DerivedV > & V,
+                const Eigen::PlainObjectBase<DerivedF > & F,
+                Eigen::PlainObjectBase<DerivedW>& W);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "peel_winding_number_layers.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/piecewise_constant_winding_number.cpp

@@ -0,0 +1,27 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "piecewise_constant_winding_number.h"
+#include "../../piecewise_constant_winding_number.h"
+#include "remesh_self_intersections.h"
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <algorithm>
+
+template < typename DerivedV, typename DerivedF>
+IGL_INLINE bool igl::copyleft::cgal::piecewise_constant_winding_number(
+  const Eigen::PlainObjectBase<DerivedV> & V,
+  const Eigen::PlainObjectBase<DerivedF> & F)
+{
+  Eigen::Matrix<CGAL::Epeck::FT,Eigen::Dynamic,3> VV;
+  Eigen::Matrix<typename DerivedF::Scalar,Eigen::Dynamic,3> FF;
+  Eigen::Matrix<typename DerivedF::Index,Eigen::Dynamic,2> IF;
+  Eigen::Matrix<typename DerivedF::Index,Eigen::Dynamic,1> J;
+  Eigen::Matrix<typename DerivedV::Index,Eigen::Dynamic,1> UIM,IM;
+  // resolve intersections
+  remesh_self_intersections(V,F,{false,false,true},VV,FF,IF,J,IM);
+  return igl::piecewise_constant_winding_number(FF);
+}

src/igl/copyleft/cgal/piecewise_constant_winding_number.h

@@ -0,0 +1,41 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_PIECEWISE_CONSTANT_WINDING_NUMBER_H
+#define IGL_COPYLEFT_CGAL_PIECEWISE_CONSTANT_WINDING_NUMBER_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <vector>
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // PIECEWISE_CONSTANT_WINDING_NUMBER Determine if a given mesh induces a
+      // piecewise constant winding number field: Is this mesh valid input to
+      // solid set operations.
+      // 
+      // Inputs:
+      //   V  #V by 3 list of mesh vertex positions
+      //   F  #F by 3 list of triangle indices into V
+      // Returns true if the mesh _combinatorially_ induces a piecewise
+      // constant winding number field.
+      template <
+        typename DerivedV,
+        typename DerivedF>
+      IGL_INLINE bool piecewise_constant_winding_number(
+        const Eigen::PlainObjectBase<DerivedV> & V,
+        const Eigen::PlainObjectBase<DerivedF>& F);
+    }
+  }
+}
+#ifndef IGL_STATIC_LIBRARY
+#  include "piecewise_constant_winding_number.cpp"
+#endif
+#endif
+

src/igl/copyleft/cgal/point_areas.cpp

@@ -0,0 +1,181 @@
+#include "point_areas.h"
+#include "delaunay_triangulation.h"
+
+#include "../../colon.h"
+#include "../../slice.h"
+#include "../../slice_mask.h"
+#include "../../parallel_for.h"
+
+#include "CGAL/Exact_predicates_inexact_constructions_kernel.h"
+#include "CGAL/Triangulation_vertex_base_with_info_2.h"
+#include "CGAL/Triangulation_data_structure_2.h"
+#include "CGAL/Delaunay_triangulation_2.h"
+
+
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel           Kernel;
+typedef CGAL::Triangulation_vertex_base_with_info_2<unsigned int, Kernel> Vb;
+typedef CGAL::Triangulation_data_structure_2<Vb>                      Tds;
+typedef CGAL::Delaunay_triangulation_2<Kernel, Tds>                   Delaunay;
+typedef Kernel::Point_2                                               Point;
+
+namespace igl {
+  namespace copyleft{
+    namespace cgal{
+      
+      template <typename DerivedP, typename DerivedI, typename DerivedN,
+      typename DerivedA>
+      IGL_INLINE void point_areas(
+                                  const Eigen::MatrixBase<DerivedP>& P,
+                                  const Eigen::MatrixBase<DerivedI>& I,
+                                  const Eigen::MatrixBase<DerivedN>& N,
+                                  Eigen::PlainObjectBase<DerivedA> & A)
+      {
+        Eigen::MatrixXd T;
+        point_areas(P,I,N,A,T);
+      }
+      
+      
+      template <typename DerivedP, typename DerivedI, typename DerivedN,
+      typename DerivedA, typename DerivedT>
+      IGL_INLINE void point_areas(
+                                        const Eigen::MatrixBase<DerivedP>& P,
+                                        const Eigen::MatrixBase<DerivedI>& I,
+                                        const Eigen::MatrixBase<DerivedN>& N,
+                                        Eigen::PlainObjectBase<DerivedA> & A,
+                                        Eigen::PlainObjectBase<DerivedT> & T)
+      {
+        typedef typename DerivedP::Scalar real;
+        typedef typename DerivedN::Scalar scalarN;
+        typedef typename DerivedA::Scalar scalarA;
+        typedef Eigen::Matrix<real,1,3> RowVec3;
+        typedef Eigen::Matrix<real,1,2> RowVec2;
+        
+        typedef Eigen::Matrix<real, Eigen::Dynamic, Eigen::Dynamic> MatrixP;
+        typedef Eigen::Matrix<scalarN, Eigen::Dynamic, Eigen::Dynamic> MatrixN;
+        typedef Eigen::Matrix<typename DerivedN::Scalar,
+                  Eigen::Dynamic, Eigen::Dynamic> VecotorO;
+        typedef Eigen::Matrix<typename DerivedI::Scalar,
+                  Eigen::Dynamic, Eigen::Dynamic> MatrixI;
+        
+        
+        
+        const int n = P.rows();
+        
+        assert(P.cols() == 3 && "P must have exactly 3 columns");
+        assert(P.rows() == N.rows()
+               && "P and N must have the same number of rows");
+        assert(P.rows() == I.rows()
+               && "P and I must have the same number of rows");
+        
+        A.setZero(n,1);
+        T.setZero(n,3);
+        igl::parallel_for(P.rows(),[&](int i)
+        {
+          MatrixI neighbor_index = I.row(i);
+          MatrixP neighbors;
+          igl::slice(P,neighbor_index,1,neighbors);
+          if(N.rows() && neighbors.rows() > 1){
+            MatrixN neighbor_normals;
+            igl::slice(N,neighbor_index,1,neighbor_normals);
+            Eigen::Matrix<scalarN,1,3> poi_normal = neighbor_normals.row(0);
+            Eigen::Matrix<scalarN,Eigen::Dynamic,1> dotprod =
+                            poi_normal(0)*neighbor_normals.col(0)
+            + poi_normal(1)*neighbor_normals.col(1)
+            + poi_normal(2)*neighbor_normals.col(2);
+            Eigen::Array<bool,Eigen::Dynamic,1> keep = dotprod.array() > 0;
+            igl::slice_mask(Eigen::MatrixXd(neighbors),keep,1,neighbors);
+          }
+          if(neighbors.rows() <= 2){
+            A(i) = 0;
+          } else {
+            //subtract the mean from neighbors, then take svd,
+            //the scores will be U*S. This is our pca plane fitting
+            RowVec3 mean = neighbors.colwise().mean();
+            MatrixP mean_centered = neighbors.rowwise() - mean;
+            Eigen::JacobiSVD<MatrixP> svd(mean_centered,
+                                    Eigen::ComputeThinU | Eigen::ComputeThinV);
+            MatrixP scores = svd.matrixU() * svd.singularValues().asDiagonal();
+            
+            T.row(i) = svd.matrixV().col(2).transpose();
+            if(T.row(i).dot(N.row(i)) < 0){
+              T.row(i) *= -1;
+            }
+            
+            MatrixP plane;
+            igl::slice(scores,igl::colon<int>(0,scores.rows()-1),
+                     igl::colon<int>(0,1),plane);
+            
+            std::vector< std::pair<Point,unsigned> > points;
+            //This is where we obtain a delaunay triangulation of the points
+            for(unsigned iter = 0; iter < plane.rows(); iter++){
+              points.push_back( std::make_pair(
+                      Point(plane(iter,0),plane(iter,1)), iter ) );
+            }
+            Delaunay triangulation;
+            triangulation.insert(points.begin(),points.end());
+            Eigen::MatrixXi F(triangulation.number_of_faces(),3);
+            int f_row = 0;
+            for(Delaunay::Finite_faces_iterator fit =
+                triangulation.finite_faces_begin();
+                fit != triangulation.finite_faces_end(); ++fit) {
+              Delaunay::Face_handle face = fit;
+              F.row(f_row) = Eigen::RowVector3i((int)face->vertex(0)->info(),
+                                                (int)face->vertex(1)->info(),
+                                                (int)face->vertex(2)->info());
+              f_row++;
+            }
+            
+            //Here we calculate the voronoi area of the point
+            scalarA area_accumulator = 0;
+            for(int f = 0; f < F.rows(); f++){
+              int X = -1;
+              for(int face_iter = 0; face_iter < 3; face_iter++){
+                if(F(f,face_iter) == 0){
+                  X = face_iter;
+                }
+              }
+              if(X >= 0){
+              //Triangle XYZ with X being the point we want the area of
+                int Y = (X+1)%3;
+                int Z = (X+2)%3;
+                scalarA x = (plane.row(F(f,Y))-plane.row(F(f,Z))).norm();
+                scalarA y = (plane.row(F(f,X))-plane.row(F(f,Z))).norm();
+                scalarA z = (plane.row(F(f,Y))-plane.row(F(f,X))).norm();
+                scalarA cosX = (z*z + y*y - x*x)/(2*y*z);
+                scalarA cosY = (z*z + x*x - y*y)/(2*x*z);
+                scalarA cosZ = (x*x + y*y - z*z)/(2*y*x);
+                Eigen::Matrix<scalarA,1,3> barycentric;
+                barycentric << x*cosX, y*cosY, z*cosZ;
+                barycentric /= (barycentric(0)+barycentric(1)+barycentric(2));
+                
+                //TODO: to make numerically stable, reorder so that x≥y≥z:
+                scalarA full_area = 0.25*std::sqrt(
+                                    (x+(y+z))*(z-(x-y))*(z+(x-y))*(x+(y-z)));
+                Eigen::Matrix<scalarA,1,3> partial_area =
+                                                    barycentric * full_area;
+                if(cosX < 0){
+                  area_accumulator += 0.5*full_area;
+                } else if (cosY < 0 || cosZ < 0){
+                  area_accumulator += 0.25*full_area;
+                } else {
+                  area_accumulator += (partial_area(1) + partial_area(2))/2;
+                }
+              }
+            }
+            
+            if(std::isfinite(area_accumulator)){
+              A(i) = area_accumulator;
+            } else {
+              A(i) = 0;
+            }
+          }
+        },1000);
+      }
+    }
+  }
+}
+
+
+
+

src/igl/copyleft/cgal/point_areas.h

@@ -0,0 +1,78 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2018 Gavin Barill <gavinpcb@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/
+
+#ifndef IGL_POINT_AREAS_H
+#define IGL_POINT_AREAS_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+    // Given a 3D set of points P, each with a list of k-nearest-neighbours,
+    // estimate the geodesic voronoi area associated with each point.
+    //
+    // The k nearest neighbours may be known from running igl::knn_octree on
+    // the output data from igl::octree. We reccomend using a k value
+    // between 15 and 20 inclusive for accurate area estimation.
+    //
+    // N is used filter the neighbours, to ensure area estimation only occurs
+    // using neighbors that are on the same side of the surface (ie for thin
+    // sheets), as well as to solve the orientation ambiguity of the tangent
+    // plane normal.
+    //
+    // Note: This function *should* be implemented by pre-filtering I, rather
+    // than filtering in this function using N. In this case, the function
+    // would only take P and I as input.
+    //
+    // Inputs:
+    //   P  #P by 3 list of point locations
+    //   I  #P by k list of k-nearest-neighbor indices into P
+    //   N  #P by 3 list of point normals
+    // Outputs:
+    //   A  #P list of estimated areas
+    template <typename DerivedP, typename DerivedI, typename DerivedN,
+      typename DerivedA>
+    IGL_INLINE void point_areas(
+                                        const Eigen::MatrixBase<DerivedP>& P,
+                                        const Eigen::MatrixBase<DerivedI>& I,
+                                        const Eigen::MatrixBase<DerivedN>& N,
+                                        Eigen::PlainObjectBase<DerivedA> & A);
+      
+    // This version can be used to output the tangent plane normal at each
+    // point. Since we area already fitting a plane to each point's neighbour
+    // set, the tangent plane normals come "for free"
+    //
+    // Inputs:
+    //   P  #P by 3 list of point locations
+    //   I  #P by k list of k-nearest-neighbor indices into P
+    //   N  #P by 3 list of point normals
+    // Outputs:
+    //   A  #P list of estimated areas
+    //   T  #P by 3 list of tangent plane normals for each point
+    template <typename DerivedP, typename DerivedI, typename DerivedN,
+    typename DerivedA, typename DerivedT>
+    IGL_INLINE void point_areas(
+                                const Eigen::MatrixBase<DerivedP>& P,
+                                const Eigen::MatrixBase<DerivedI>& I,
+                                const Eigen::MatrixBase<DerivedN>& N,
+                                Eigen::PlainObjectBase<DerivedA> & A,
+                                Eigen::PlainObjectBase<DerivedT> & T);
+      
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "point_areas.cpp"
+#endif
+
+#endif
+

src/igl/copyleft/cgal/point_mesh_squared_distance.cpp

@@ -0,0 +1,138 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "point_mesh_squared_distance.h"
+#include "mesh_to_cgal_triangle_list.h"
+#include "assign_scalar.h"
+
+template <
+  typename Kernel,
+  typename DerivedP,
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedsqrD,
+  typename DerivedI,
+  typename DerivedC>
+IGL_INLINE void igl::copyleft::cgal::point_mesh_squared_distance(
+  const Eigen::PlainObjectBase<DerivedP> & P,
+  const Eigen::PlainObjectBase<DerivedV> & V,
+  const Eigen::PlainObjectBase<DerivedF> & F,
+        Eigen::PlainObjectBase<DerivedsqrD> & sqrD,
+        Eigen::PlainObjectBase<DerivedI> & I,
+        Eigen::PlainObjectBase<DerivedC> & C)
+{
+  using namespace std;
+  typedef CGAL::Triangle_3<Kernel> Triangle_3; 
+  typedef typename std::vector<Triangle_3>::iterator Iterator;
+  typedef CGAL::AABB_triangle_primitive<Kernel, Iterator> Primitive;
+  typedef CGAL::AABB_traits<Kernel, Primitive> AABB_triangle_traits;
+  typedef CGAL::AABB_tree<AABB_triangle_traits> Tree;
+  Tree tree;
+  vector<Triangle_3> T;
+  point_mesh_squared_distance_precompute(V,F,tree,T);
+  return point_mesh_squared_distance(P,tree,T,sqrD,I,C);
+}
+
+template <typename Kernel, typename DerivedV, typename DerivedF>
+IGL_INLINE void igl::copyleft::cgal::point_mesh_squared_distance_precompute(
+  const Eigen::PlainObjectBase<DerivedV> & V,
+  const Eigen::PlainObjectBase<DerivedF> & F,
+  CGAL::AABB_tree<
+    CGAL::AABB_traits<Kernel, 
+      CGAL::AABB_triangle_primitive<Kernel, 
+        typename std::vector<CGAL::Triangle_3<Kernel> >::iterator
+      >
+    >
+  > & tree,
+  std::vector<CGAL::Triangle_3<Kernel> > & T)
+{
+  using namespace std;
+
+  typedef CGAL::Triangle_3<Kernel> Triangle_3; 
+  typedef CGAL::Point_3<Kernel> Point_3; 
+  typedef typename std::vector<Triangle_3>::iterator Iterator;
+  typedef CGAL::AABB_triangle_primitive<Kernel, Iterator> Primitive;
+  typedef CGAL::AABB_traits<Kernel, Primitive> AABB_triangle_traits;
+  typedef CGAL::AABB_tree<AABB_triangle_traits> Tree;
+
+  // Must be 3D
+  assert(V.cols() == 3);
+  // Must be triangles
+  assert(F.cols() == 3);
+
+  // WTF ALERT!!!! 
+  //
+  // There's a bug in clang probably or at least in cgal. Without calling this
+  // line (I guess invoking some compilation from <vector>), clang will vomit
+  // errors inside CGAL.
+  //
+  // http://stackoverflow.com/questions/27748442/is-clangs-c11-support-reliable
+  T.reserve(0);
+
+  // Make list of cgal triangles
+  mesh_to_cgal_triangle_list(V,F,T);
+  tree.clear();
+  tree.insert(T.begin(),T.end());
+  tree.accelerate_distance_queries();
+  // accelerate_distance_queries doesn't seem actually to do _all_ of the
+  // precomputation. the tree (despite being const) will still do more
+  // precomputation and reorganizing on the first call of `closest_point` or
+  // `closest_point_and_primitive`. Therefore, call it once here.
+  tree.closest_point_and_primitive(Point_3(0,0,0));
+}
+
+template <
+  typename Kernel,
+  typename DerivedP,
+  typename DerivedsqrD,
+  typename DerivedI,
+  typename DerivedC>
+IGL_INLINE void igl::copyleft::cgal::point_mesh_squared_distance(
+  const Eigen::PlainObjectBase<DerivedP> & P,
+  const CGAL::AABB_tree<
+    CGAL::AABB_traits<Kernel, 
+      CGAL::AABB_triangle_primitive<Kernel, 
+        typename std::vector<CGAL::Triangle_3<Kernel> >::iterator
+      >
+    >
+  > & tree,
+  const std::vector<CGAL::Triangle_3<Kernel> > & T,
+  Eigen::PlainObjectBase<DerivedsqrD> & sqrD,
+  Eigen::PlainObjectBase<DerivedI> & I,
+  Eigen::PlainObjectBase<DerivedC> & C)
+{
+  typedef CGAL::Triangle_3<Kernel> Triangle_3; 
+  typedef typename std::vector<Triangle_3>::iterator Iterator;
+  typedef CGAL::AABB_triangle_primitive<Kernel, Iterator> Primitive;
+  typedef CGAL::AABB_traits<Kernel, Primitive> AABB_triangle_traits;
+  typedef CGAL::AABB_tree<AABB_triangle_traits> Tree;
+  typedef typename Tree::Point_and_primitive_id Point_and_primitive_id;
+  typedef CGAL::Point_3<Kernel>    Point_3;
+  assert(P.cols() == 3);
+  const int n = P.rows();
+  sqrD.resize(n,1);
+  I.resize(n,1);
+  C.resize(n,P.cols());
+  for(int p = 0;p < n;p++)
+  {
+    Point_3 query(P(p,0),P(p,1),P(p,2));
+    // Find closest point and primitive id
+    Point_and_primitive_id pp = tree.closest_point_and_primitive(query);
+    Point_3 closest_point = pp.first;
+    assign_scalar(closest_point[0],C(p,0));
+    assign_scalar(closest_point[1],C(p,1));
+    assign_scalar(closest_point[2],C(p,2));
+    assign_scalar((closest_point-query).squared_length(),sqrD(p));
+    I(p) = pp.second - T.begin();
+  }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template void igl::copyleft::cgal::point_mesh_squared_distance<CGAL::Epeck, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+template void igl::copyleft::cgal::point_mesh_squared_distance<CGAL::Epeck,   Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>,   Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1,   -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 1, 0, -1, 1>,   Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>   >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3,   0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0,   -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1>   > const&,   Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 1,   0, -1, 1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&,   Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+#endif

src/igl/copyleft/cgal/point_mesh_squared_distance.h

@@ -0,0 +1,104 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_POINT_MESH_SQUARED_DISTANCE_H
+#define IGL_COPYLEFT_CGAL_POINT_MESH_SQUARED_DISTANCE_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <vector>
+#include "CGAL_includes.hpp"
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Compute distances from a set of points P to a triangle mesh (V,F)
+      //
+      // Templates:
+      //   Kernal  CGAL computation and construction kernel (e.g.
+      //     CGAL::Simple_cartesian<double>)
+      // Inputs:
+      //   P  #P by 3 list of query point positions
+      //   V  #V by 3 list of vertex positions
+      //   F  #F by 3 list of triangle indices
+      // Outputs:
+      //   sqrD  #P list of smallest squared distances
+      //   I  #P list of facet indices corresponding to smallest distances
+      //   C  #P by 3 list of closest points
+      //
+      // Known bugs: This only computes distances to triangles. So unreferenced
+      // vertices and degenerate triangles (segments) are ignored.
+      template <
+        typename Kernel,
+        typename DerivedP,
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedsqrD,
+        typename DerivedI,
+        typename DerivedC>
+      IGL_INLINE void point_mesh_squared_distance(
+        const Eigen::PlainObjectBase<DerivedP> & P,
+        const Eigen::PlainObjectBase<DerivedV> & V,
+        const Eigen::PlainObjectBase<DerivedF> & F,
+              Eigen::PlainObjectBase<DerivedsqrD> & sqrD,
+              Eigen::PlainObjectBase<DerivedI> & I,
+              Eigen::PlainObjectBase<DerivedC> & C);
+      // Probably can do this in a way that we don't pass around `tree` and `T`
+      //
+      // Outputs:
+      //   tree  CGAL's AABB tree
+      //   T  list of CGAL triangles in order of F (for determining which was found
+      //     in computation)
+      template <
+        typename Kernel,
+        typename DerivedV,
+        typename DerivedF
+        >
+      IGL_INLINE void point_mesh_squared_distance_precompute(
+        const Eigen::PlainObjectBase<DerivedV> & V,
+        const Eigen::PlainObjectBase<DerivedF> & F,
+        CGAL::AABB_tree<
+          CGAL::AABB_traits<Kernel, 
+            CGAL::AABB_triangle_primitive<Kernel, 
+              typename std::vector<CGAL::Triangle_3<Kernel> >::iterator
+            >
+          >
+        > & tree,
+        std::vector<CGAL::Triangle_3<Kernel> > & T);
+      // Inputs:
+      //  see above
+      // Outputs:
+      //  see above
+      template <
+        typename Kernel,
+        typename DerivedP,
+        typename DerivedsqrD,
+        typename DerivedI,
+        typename DerivedC>
+      IGL_INLINE void point_mesh_squared_distance(
+        const Eigen::PlainObjectBase<DerivedP> & P,
+        const CGAL::AABB_tree<
+          CGAL::AABB_traits<Kernel, 
+            CGAL::AABB_triangle_primitive<Kernel, 
+              typename std::vector<CGAL::Triangle_3<Kernel> >::iterator
+            >
+          >
+        > & tree,
+        const std::vector<CGAL::Triangle_3<Kernel> > & T,
+        Eigen::PlainObjectBase<DerivedsqrD> & sqrD,
+        Eigen::PlainObjectBase<DerivedI> & I,
+        Eigen::PlainObjectBase<DerivedC> & C);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "point_mesh_squared_distance.cpp"
+#endif
+
+#endif

src/igl/copyleft/cgal/point_segment_squared_distance.cpp

@@ -0,0 +1,41 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "point_segment_squared_distance.h"
+
+template < typename Kernel>
+IGL_INLINE void igl::copyleft::cgal::point_segment_squared_distance(
+  const CGAL::Point_3<Kernel> & P1,
+  const CGAL::Segment_3<Kernel> & S2,
+  CGAL::Point_3<Kernel> & P2,
+  typename Kernel::FT & d)
+{
+  if(S2.is_degenerate())
+  {
+    P2 = S2.source();
+    d = (P1-P2).squared_length();
+    return;
+  }
+  // http://stackoverflow.com/a/1501725/148668
+  const auto sqr_len = S2.squared_length();
+  assert(sqr_len != 0);
+  const auto & V = S2.source();
+  const auto & W = S2.target();
+  const auto t = (P1-V).dot(W-V)/sqr_len;
+  if(t<0)
+  {
+    P2 = V;
+  }else if(t>1)
+  {
+    P2 = W;
+  }else
+  {
+    P2 = V  + t*(W-V);
+  }
+  d = (P1-P2).squared_length();
+}
+

src/igl/copyleft/cgal/point_segment_squared_distance.h

@@ -0,0 +1,44 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_POINT_SEGMENT_SQUARED_DISTANCE_H
+#define IGL_COPYLEFT_CGAL_POINT_SEGMENT_SQUARED_DISTANCE_H
+#include "../../igl_inline.h"
+#include <CGAL/Segment_3.h>
+#include <CGAL/Point_3.h>
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Given a point P1 and segment S2 find the points on each of closest
+      // approach and the squared distance thereof.
+      // 
+      // Inputs:
+      //   P1  point
+      //   S2  segment
+      // Outputs:
+      //   P2  point on S2 closest to P1
+      //   d  distance betwee P1 and S2
+      template < typename Kernel>
+      IGL_INLINE void point_segment_squared_distance(
+          const CGAL::Point_3<Kernel> & P1,
+          const CGAL::Segment_3<Kernel> & S2,
+          CGAL::Point_3<Kernel> & P2,
+          typename Kernel::FT & d
+          );
+
+    }
+  }
+}
+#ifndef IGL_STATIC_LIBRARY
+#  include "point_segment_squared_distance.cpp"
+#endif
+
+#endif
+

src/igl/copyleft/cgal/point_solid_signed_squared_distance.cpp

@@ -0,0 +1,56 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "point_solid_signed_squared_distance.h"
+#include "points_inside_component.h"
+#include "point_mesh_squared_distance.h"
+#include "../../list_to_matrix.h"
+#include "../../slice_mask.h"
+#include <vector>
+#include <Eigen/Core>
+
+template <
+  typename DerivedQ,
+  typename DerivedVB,
+  typename DerivedFB,
+  typename DerivedD>
+IGL_INLINE void igl::copyleft::cgal::point_solid_signed_squared_distance(
+  const Eigen::PlainObjectBase<DerivedQ> & Q,
+  const Eigen::PlainObjectBase<DerivedVB> & VB,
+  const Eigen::PlainObjectBase<DerivedFB> & FB,
+  Eigen::PlainObjectBase<DerivedD> & D)
+{
+  // compute unsigned distances
+  Eigen::VectorXi I;
+  DerivedVB C;
+  point_mesh_squared_distance<CGAL::Epeck>(Q,VB,FB,D,I,C);
+  // Collect queries that have non-zero distance
+  Eigen::Array<bool,Eigen::Dynamic,1> NZ = D.array()!=0;
+  // Compute sign for non-zero distance queries
+  DerivedQ QNZ;
+  slice_mask(Q,NZ,1,QNZ);
+  Eigen::Array<bool,Eigen::Dynamic,1> DNZ;
+  igl::copyleft::cgal::points_inside_component(VB,FB,QNZ,DNZ);
+  // Apply sign to distances
+  DerivedD S = DerivedD::Zero(Q.rows(),1);
+  {
+    int k = 0;
+    for(int q = 0;q<Q.rows();q++)
+    {
+      if(NZ(q))
+      {
+        D(q) *= DNZ(k++) ? -1. : 1.;
+      }
+    }
+  }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void   igl::copyleft::cgal::point_solid_signed_squared_distance<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>,   -1, 3, 0, -1, 3>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int,   -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 1, 0,   -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>,   -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1,   -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0,   -1, -1> > const&,   Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 1,   0, -1, 1> >&);
+#endif

src/igl/copyleft/cgal/point_solid_signed_squared_distance.h

@@ -0,0 +1,48 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_POINT_SOLID_SIGNED_SQUARED_DISTANCE_H
+#define IGL_COPYLEFT_CGAL_POINT_SOLID_SIGNED_SQUARED_DISTANCE_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // POINT_SOLID_SIGNED_SQUARED_DISTANCE Given a set of points (Q) and the
+      // boundary mesh (VB,FB) of a solid (as defined in [Zhou et al. 2016],
+      // determine the signed squared distance for each point q in Q so that d(q,B) is
+      // negative if inside and positive if outside.
+      //
+      // Inputs:
+      //   Q  #Q by 3 list of query point positions
+      //   VB  #VB by 3 list of mesh vertex positions of B
+      //   FB  #FB by 3 list of mesh triangle indices into VB
+      // Outputs:
+      //   D
+      template <
+        typename DerivedQ,
+        typename DerivedVB,
+        typename DerivedFB,
+        typename DerivedD>
+      IGL_INLINE void point_solid_signed_squared_distance(
+        const Eigen::PlainObjectBase<DerivedQ> & Q,
+        const Eigen::PlainObjectBase<DerivedVB> & VB,
+        const Eigen::PlainObjectBase<DerivedFB> & FB,
+        Eigen::PlainObjectBase<DerivedD> & D);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "point_solid_signed_squared_distance.cpp"
+#endif
+
+#endif

src/igl/copyleft/cgal/point_triangle_squared_distance.cpp

@@ -0,0 +1,47 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "point_triangle_squared_distance.h"
+#include <CGAL/Segment_3.h>
+template < typename Kernel>
+IGL_INLINE void point_triangle_squared_distance(
+  const CGAL::Point_3<Kernel> & P1,
+  const CGAL::Triangle_3<Kernel> & T2,
+  CGAL::Point_3<Kernel> & P2,
+  typename Kernel::FT & d)
+{
+  assert(!T2.is_degenerate());
+  if(T2.has_on(P1))
+  {
+    P2 = P1;
+    d = 0;
+    return;
+  }
+  const auto proj_1 = T2.supporting_plane().projection(P2);
+  if(T2.has_on(proj_1))
+  {
+    P2 = proj_1;
+    d = (proj_1-P1).squared_length();
+    return;
+  }
+  // closest point must be on the boundary
+  bool first = true;
+  // loop over edges
+  for(int i=0;i<3;i++)
+  {
+    CGAL::Point_3<Kernel> P2i;
+    typename Kernel::FT di;
+    const CGAL::Segment_3<Kernel> si( T2.vertex(i+1), T2.vertex(i+2));
+    point_segment_squared_distance(P1,si,P2i,di);
+    if(first || di < d)
+    {
+      first = false;
+      d = di;
+      P2 = P2i;
+    }
+  }
+}

src/igl/copyleft/cgal/point_triangle_squared_distance.h

@@ -0,0 +1,45 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_POINT_TRIANGLE_SQUARED_DISTANCE_H
+#define IGL_COPYLEFT_CGAL_POINT_TRIANGLE_SQUARED_DISTANCE_H
+#include "../../igl_inline.h"
+#include <CGAL/Triangle_3.h>
+#include <CGAL/Point_3.h>
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Given a point P1 and triangle T2 find the points on each of closest
+      // approach and the squared distance thereof.
+      // 
+      // Inputs:
+      //   P1  point
+      //   T2  triangle
+      // Outputs:
+      //   P2  point on T2 closest to P1
+      //   d  distance betwee P1 and T2
+      template < typename Kernel>
+      IGL_INLINE void point_triangle_squared_distance(
+        const CGAL::Point_3<Kernel> & P1,
+        const CGAL::Triangle_3<Kernel> & T2,
+        CGAL::Point_3<Kernel> & P2,
+        typename Kernel::FT & d
+        );
+
+    }
+  }
+}
+#ifndef IGL_STATIC_LIBRARY
+#  include "point_triangle_squared_distance.cpp"
+#endif
+
+#endif
+
+

src/igl/copyleft/cgal/points_inside_component.cpp

@@ -0,0 +1,350 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "points_inside_component.h"
+#include "../../LinSpaced.h"
+#include "order_facets_around_edge.h"
+#include "assign_scalar.h"
+
+#include <CGAL/AABB_tree.h>
+#include <CGAL/AABB_traits.h>
+#include <CGAL/AABB_triangle_primitive.h>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+
+#include <cassert>
+#include <list>
+#include <limits>
+#include <vector>
+
+
+namespace igl {
+  namespace copyleft 
+  {
+    namespace cgal {
+        namespace points_inside_component_helper {
+            typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
+            typedef Kernel::Ray_3 Ray_3;
+            typedef Kernel::Point_3 Point_3;
+            typedef Kernel::Vector_3 Vector_3;
+            typedef Kernel::Triangle_3 Triangle;
+            typedef Kernel::Plane_3 Plane_3;
+            typedef std::vector<Triangle>::iterator Iterator;
+            typedef CGAL::AABB_triangle_primitive<Kernel, Iterator> Primitive;
+            typedef CGAL::AABB_traits<Kernel, Primitive> AABB_triangle_traits;
+            typedef CGAL::AABB_tree<AABB_triangle_traits> Tree;
+
+            template<typename DerivedF, typename DerivedI>
+            void extract_adj_faces(
+                    const Eigen::PlainObjectBase<DerivedF>& F,
+                    const Eigen::PlainObjectBase<DerivedI>& I,
+                    const size_t s, const size_t d,
+                    std::vector<int>& adj_faces) {
+                const size_t num_faces = I.rows();
+                for (size_t i=0; i<num_faces; i++) {
+                    Eigen::Vector3i f = F.row(I(i, 0));
+                    if (((size_t)f[0] == s && (size_t)f[1] == d) ||
+                        ((size_t)f[1] == s && (size_t)f[2] == d) ||
+                        ((size_t)f[2] == s && (size_t)f[0] == d)) {
+                        adj_faces.push_back((I(i, 0)+1) * -1);
+                        continue;
+                    }
+                    if (((size_t)f[0] == d && (size_t)f[1] == s) ||
+                        ((size_t)f[1] == d && (size_t)f[2] == s) ||
+                        ((size_t)f[2] == d && (size_t)f[0] == s)) {
+                        adj_faces.push_back(I(i, 0)+1);
+                        continue;
+                    }
+                }
+            }
+
+            template<typename DerivedF, typename DerivedI>
+            void extract_adj_vertices(
+                    const Eigen::PlainObjectBase<DerivedF>& F,
+                    const Eigen::PlainObjectBase<DerivedI>& I,
+                    const size_t v, std::vector<int>& adj_vertices) {
+                std::set<size_t> unique_adj_vertices;
+                const size_t num_faces = I.rows();
+                for (size_t i=0; i<num_faces; i++) {
+                    Eigen::Vector3i f = F.row(I(i, 0));
+                    if ((size_t)f[0] == v) {
+                        unique_adj_vertices.insert(f[1]);
+                        unique_adj_vertices.insert(f[2]);
+                    } else if ((size_t)f[1] == v) {
+                        unique_adj_vertices.insert(f[0]);
+                        unique_adj_vertices.insert(f[2]);
+                    } else if ((size_t)f[2] == v) {
+                        unique_adj_vertices.insert(f[0]);
+                        unique_adj_vertices.insert(f[1]);
+                    }
+                }
+                adj_vertices.resize(unique_adj_vertices.size());
+                std::copy(unique_adj_vertices.begin(),
+                        unique_adj_vertices.end(),
+                        adj_vertices.begin());
+            }
+
+            template<typename DerivedV, typename DerivedF, typename DerivedI>
+            bool determine_point_edge_orientation(
+                    const Eigen::PlainObjectBase<DerivedV>& V,
+                    const Eigen::PlainObjectBase<DerivedF>& F,
+                    const Eigen::PlainObjectBase<DerivedI>& I,
+                    const Point_3& query, size_t s, size_t d) {
+                // Algorithm:
+                //
+                // Order the adj faces around the edge (s,d) clockwise using
+                // query point as pivot.  (i.e. The first face of the ordering
+                // is directly after the pivot point, and the last face is
+                // directly before the pivot.)
+                //
+                // The point is outside if the first and last faces of the
+                // ordering forms a convex angle.  This check can be done
+                // without any construction by looking at the orientation of the
+                // faces.  The angle is convex iff the first face contains (s,d)
+                // as an edge and the last face contains (d,s) as an edge.
+                //
+                // The point is inside if the first and last faces of the
+                // ordering forms a concave angle.  That is the first face
+                // contains (d,s) as an edge and the last face contains (s,d) as
+                // an edge.
+                //
+                // In the special case of duplicated faces. I.e. multiple faces
+                // sharing the same 3 corners, but not necessarily the same
+                // orientation.  The ordering will always rank faces containing
+                // edge (s,d) before faces containing edge (d,s).
+                //
+                // Therefore, if there are any duplicates of the first faces,
+                // the ordering will always choose the one with edge (s,d) if
+                // possible.  The same for the last face.
+                //
+                // In the very degenerated case where the first and last face
+                // are duplicates, but with different orientations, it is
+                // equally valid to think the angle formed by them is either 0
+                // or 360 degrees.  By default, 0 degree is used, and thus the
+                // query point is outside.
+
+                std::vector<int> adj_faces;
+                extract_adj_faces(F, I, s, d, adj_faces);
+                const size_t num_adj_faces = adj_faces.size();
+                assert(num_adj_faces > 0);
+
+                DerivedV pivot_point(1, 3);
+                igl::copyleft::cgal::assign_scalar(query.x(), pivot_point(0, 0));
+                igl::copyleft::cgal::assign_scalar(query.y(), pivot_point(0, 1));
+                igl::copyleft::cgal::assign_scalar(query.z(), pivot_point(0, 2));
+                Eigen::VectorXi order;
+                order_facets_around_edge(V, F, s, d,
+                        adj_faces, pivot_point, order);
+                assert((size_t)order.size() == num_adj_faces);
+                if (adj_faces[order[0]] > 0 &&
+                    adj_faces[order[num_adj_faces-1] < 0]) {
+                    return true;
+                } else if (adj_faces[order[0]] < 0 &&
+                    adj_faces[order[num_adj_faces-1] > 0]) {
+                    return false;
+                } else {
+                    throw "The input mesh does not represent a valid volume";
+                }
+                throw "The input mesh does not represent a valid volume";
+                return false;
+            }
+
+            template<typename DerivedV, typename DerivedF, typename DerivedI>
+            bool determine_point_vertex_orientation(
+                    const Eigen::PlainObjectBase<DerivedV>& V,
+                    const Eigen::PlainObjectBase<DerivedF>& F,
+                    const Eigen::PlainObjectBase<DerivedI>& I,
+                    const Point_3& query, size_t s) {
+                std::vector<int> adj_vertices;
+                extract_adj_vertices(F, I, s, adj_vertices);
+                const size_t num_adj_vertices = adj_vertices.size();
+
+                std::vector<Point_3> adj_points;
+                for (size_t i=0; i<num_adj_vertices; i++) {
+                    const size_t vi = adj_vertices[i];
+                    adj_points.emplace_back(V(vi,0), V(vi,1), V(vi,2));
+                }
+
+                // A plane is on the exterior if all adj_points lies on or to
+                // one side of the plane.
+                auto is_on_exterior = [&](const Plane_3& separator) -> bool{
+                    size_t positive=0;
+                    size_t negative=0;
+                    size_t coplanar=0;
+                    for (const auto& point : adj_points) {
+                        switch(separator.oriented_side(point)) {
+                            case CGAL::ON_POSITIVE_SIDE:
+                                positive++;
+                                break;
+                            case CGAL::ON_NEGATIVE_SIDE:
+                                negative++;
+                                break;
+                            case CGAL::ON_ORIENTED_BOUNDARY:
+                                coplanar++;
+                                break;
+                            default:
+                                throw "Unknown plane-point orientation";
+                        }
+                    }
+                    auto query_orientation = separator.oriented_side(query);
+                    bool r =
+                        (positive == 0 && query_orientation == CGAL::POSITIVE)
+                        ||
+                        (negative == 0 && query_orientation == CGAL::NEGATIVE);
+                    return r;
+                };
+
+                size_t d = std::numeric_limits<size_t>::max();
+                Point_3 p(V(s,0), V(s,1), V(s,2));
+                for (size_t i=0; i<num_adj_vertices; i++) {
+                    const size_t vi = adj_vertices[i];
+                    for (size_t j=i+1; j<num_adj_vertices; j++) {
+                        Plane_3 separator(p, adj_points[i], adj_points[j]);
+                        if (separator.is_degenerate()) {
+                            throw "Input mesh contains degenerated faces";
+                        }
+                        if (is_on_exterior(separator)) {
+                            d = vi;
+                            assert(!CGAL::collinear(p, adj_points[i], query));
+                            break;
+                        }
+                    }
+                    if (d < (size_t)V.rows()) break;
+                }
+                if (d > (size_t)V.rows()) {
+                    // All adj faces are coplanar, use the first edge.
+                    d = adj_vertices[0];
+                }
+                return determine_point_edge_orientation(V, F, I, query, s, d);
+            }
+
+            template<typename DerivedV, typename DerivedF, typename DerivedI>
+            bool determine_point_face_orientation(
+                    const Eigen::PlainObjectBase<DerivedV>& V,
+                    const Eigen::PlainObjectBase<DerivedF>& F,
+                    const Eigen::PlainObjectBase<DerivedI>& I,
+                    const Point_3& query, size_t fid) {
+                // Algorithm: A point is on the inside of a face if the
+                // tetrahedron formed by them is negatively oriented.
+
+                Eigen::Vector3i f = F.row(I(fid, 0));
+                const Point_3 v0(V(f[0], 0), V(f[0], 1), V(f[0], 2));
+                const Point_3 v1(V(f[1], 0), V(f[1], 1), V(f[1], 2));
+                const Point_3 v2(V(f[2], 0), V(f[2], 1), V(f[2], 2));
+                auto result = CGAL::orientation(v0, v1, v2, query);
+                if (result == CGAL::COPLANAR) {
+                    throw "Cannot determine inside/outside because query point lies exactly on the input surface.";
+                }
+                return result == CGAL::NEGATIVE;
+            }
+        }
+    }
+  }
+}
+
+template<typename DerivedV, typename DerivedF, typename DerivedI,
+    typename DerivedP, typename DerivedB>
+IGL_INLINE void igl::copyleft::cgal::points_inside_component(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        const Eigen::PlainObjectBase<DerivedI>& I,
+        const Eigen::PlainObjectBase<DerivedP>& P,
+        Eigen::PlainObjectBase<DerivedB>& inside) {
+    using namespace igl::copyleft::cgal::points_inside_component_helper;
+    if (F.rows() <= 0 || I.rows() <= 0) {
+        throw "Inside check cannot be done on empty facet component.";
+    }
+
+    const size_t num_faces = I.rows();
+    std::vector<Triangle> triangles;
+    for (size_t i=0; i<num_faces; i++) {
+        const Eigen::Vector3i f = F.row(I(i, 0));
+        triangles.emplace_back(
+                Point_3(V(f[0], 0), V(f[0], 1), V(f[0], 2)),
+                Point_3(V(f[1], 0), V(f[1], 1), V(f[1], 2)),
+                Point_3(V(f[2], 0), V(f[2], 1), V(f[2], 2)));
+        if (triangles.back().is_degenerate()) {
+            throw "Input facet components contains degenerated triangles";
+        }
+    }
+    Tree tree(triangles.begin(), triangles.end());
+    tree.accelerate_distance_queries();
+
+    enum ElementType { VERTEX, EDGE, FACE };
+    auto determine_element_type = [&](
+            size_t fid, const Point_3& p, size_t& element_index) -> ElementType{
+        const Eigen::Vector3i f = F.row(I(fid, 0));
+        const Point_3 p0(V(f[0], 0), V(f[0], 1), V(f[0], 2));
+        const Point_3 p1(V(f[1], 0), V(f[1], 1), V(f[1], 2));
+        const Point_3 p2(V(f[2], 0), V(f[2], 1), V(f[2], 2));
+
+        if (p == p0) { element_index = 0; return VERTEX; }
+        if (p == p1) { element_index = 1; return VERTEX; }
+        if (p == p2) { element_index = 2; return VERTEX; }
+        if (CGAL::collinear(p0, p1, p)) { element_index = 2; return EDGE; }
+        if (CGAL::collinear(p1, p2, p)) { element_index = 0; return EDGE; }
+        if (CGAL::collinear(p2, p0, p)) { element_index = 1; return EDGE; }
+
+        element_index = 0;
+        return FACE;
+    };
+
+    const size_t num_queries = P.rows();
+    inside.resize(num_queries, 1);
+    for (size_t i=0; i<num_queries; i++) {
+        const Point_3 query(P(i,0), P(i,1), P(i,2));
+        auto projection = tree.closest_point_and_primitive(query);
+        auto closest_point = projection.first;
+        size_t fid = projection.second - triangles.begin();
+
+        size_t element_index;
+        switch (determine_element_type(fid, closest_point, element_index)) {
+            case VERTEX:
+                {
+                    const size_t s = F(I(fid, 0), element_index);
+                    inside(i,0) = determine_point_vertex_orientation(
+                            V, F, I, query, s);
+                }
+                break;
+            case EDGE:
+                {
+                    const size_t s = F(I(fid, 0), (element_index+1)%3);
+                    const size_t d = F(I(fid, 0), (element_index+2)%3);
+                    inside(i,0) = determine_point_edge_orientation(
+                            V, F, I, query, s, d);
+                }
+                break;
+            case FACE:
+                inside(i,0) = determine_point_face_orientation(V, F, I, query, fid);
+                break;
+            default:
+                throw "Unknown closest element type!";
+        }
+    }
+}
+
+template<typename DerivedV, typename DerivedF, typename DerivedP,
+    typename DerivedB>
+IGL_INLINE void igl::copyleft::cgal::points_inside_component(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        const Eigen::PlainObjectBase<DerivedP>& P,
+        Eigen::PlainObjectBase<DerivedB>& inside) {
+    Eigen::VectorXi I = igl::LinSpaced<Eigen::VectorXi>(F.rows(), 0, F.rows()-1);
+    igl::copyleft::cgal::points_inside_component(V, F, I, P, inside);
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::points_inside_component<Eigen::Matrix<double, -1,   -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>,   Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>,   Eigen::Array<bool, -1, 1, 0, -1, 1>   >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&,   Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&,   Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3,   0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Array<bool, -1, 1, 0, -1, 1>   >&);
+template void igl::copyleft::cgal::points_inside_component< Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<   int, -1, -1, 0, -1, -1>, Eigen::Matrix<   int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<   int, -1, -1, 0, -1, -1> > ( Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<   int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<   int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<   int, -1, -1, 0, -1, -1> >&);
+template void igl::copyleft::cgal::points_inside_component< Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<   int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<   int, -1, -1, 0, -1, -1> > ( Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix< int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<   int, -1, -1, 0, -1, -1> >&);
+template void igl::copyleft::cgal::points_inside_component<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::points_inside_component<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::points_inside_component<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+template void igl::copyleft::cgal::points_inside_component<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+#endif

src/igl/copyleft/cgal/points_inside_component.h

@@ -0,0 +1,71 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_POINTS_INSIDE_COMPONENTS
+#define IGL_COPYLEFT_CGAL_POINTS_INSIDE_COMPONENTS
+
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <vector>
+
+namespace igl 
+{
+  namespace copyleft
+  {
+    namespace cgal {
+
+      // Determine if queries points P are inside of connected facet component
+      // (V, F, I), where I indicates a subset of facets that forms the
+      // component.
+      //
+      // Precondition:
+      // The input mesh must be a closed, self-intersection free,
+      // non-degenerated surface.  Queries points must be either inside or
+      // outside of the mesh (i.e. not on the surface of the mesh).
+      //
+      // Inputs:
+      //   V  #V by 3 array of vertex positions.
+      //   F  #F by 3 array of triangles.
+      //   I  #I list of triangle indices to consider.
+      //   P  #P by 3 array of query points.
+      //
+      // Outputs:
+      //   inside  #P list of booleans that is true iff the corresponding
+      //           query point is inside of the mesh.
+      template<
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedI,
+        typename DerivedP,
+        typename DerivedB>
+      IGL_INLINE void points_inside_component(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        const Eigen::PlainObjectBase<DerivedI>& I,
+        const Eigen::PlainObjectBase<DerivedP>& P,
+        Eigen::PlainObjectBase<DerivedB>& inside);
+
+      // Determine if query points P is inside of the mesh (V, F).
+      // See above for precondition and I/O specs.
+      template<
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedP,
+        typename DerivedB>
+      IGL_INLINE void points_inside_component(
+          const Eigen::PlainObjectBase<DerivedV>& V,
+          const Eigen::PlainObjectBase<DerivedF>& F,
+          const Eigen::PlainObjectBase<DerivedP>& P,
+          Eigen::PlainObjectBase<DerivedB>& inside);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#include "points_inside_component.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/polyhedron_to_mesh.cpp

@@ -0,0 +1,69 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "polyhedron_to_mesh.h"
+#include <CGAL/Polyhedron_3.h>
+
+template <
+  typename Polyhedron,
+  typename DerivedV,
+  typename DerivedF>
+IGL_INLINE void igl::copyleft::cgal::polyhedron_to_mesh(
+  const Polyhedron & poly,
+  Eigen::PlainObjectBase<DerivedV> & V,
+  Eigen::PlainObjectBase<DerivedF> & F)
+{
+  using namespace std;
+  V.resize(poly.size_of_vertices(),3);
+  F.resize(poly.size_of_facets(),3);
+  typedef typename Polyhedron::Vertex_const_iterator Vertex_iterator;
+  std::map<Vertex_iterator,size_t> vertex_to_index;
+  {
+    size_t v = 0;
+    for(
+      typename Polyhedron::Vertex_const_iterator p = poly.vertices_begin();
+      p != poly.vertices_end();
+      p++)
+    {
+      V(v,0) = p->point().x();
+      V(v,1) = p->point().y();
+      V(v,2) = p->point().z();
+      vertex_to_index[p] = v;
+      v++;
+    }
+  }
+  {
+    size_t f = 0;
+    for(
+      typename Polyhedron::Facet_const_iterator facet = poly.facets_begin();
+      facet != poly.facets_end();
+      ++facet)
+    {
+      typename Polyhedron::Halfedge_around_facet_const_circulator he = 
+        facet->facet_begin();
+      // Facets in polyhedral surfaces are at least triangles.
+      assert(CGAL::circulator_size(he) == 3 && "Facets should be triangles");
+      size_t c = 0;
+      do {
+        //// This is stooopidly slow
+        // F(f,c) = std::distance(poly.vertices_begin(), he->vertex());
+        F(f,c) = vertex_to_index[he->vertex()];
+        c++;
+      } while ( ++he != facet->facet_begin());
+      f++;
+    }
+  }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+#include <CGAL/Simple_cartesian.h>
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Polyhedron_items_with_id_3.h>
+template void igl::copyleft::cgal::polyhedron_to_mesh<CGAL::Polyhedron_3<CGAL::Epick, CGAL::Polyhedron_items_3, CGAL::HalfedgeDS_default, std::allocator<int> >, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(CGAL::Polyhedron_3<CGAL::Epick, CGAL::Polyhedron_items_3, CGAL::HalfedgeDS_default, std::allocator<int> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+template void igl::copyleft::cgal::polyhedron_to_mesh<CGAL::Polyhedron_3<CGAL::Simple_cartesian<double>,CGAL::Polyhedron_items_with_id_3, CGAL::HalfedgeDS_default, std::allocator<int> >, Eigen::Matrix<double, -1, -1, 0,-1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(CGAL::Polyhedron_3<CGAL::Simple_cartesian<double>,CGAL::Polyhedron_items_with_id_3, CGAL::HalfedgeDS_default, std::allocator<int> > const&,Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0,-1, -1> >&);
+#endif

src/igl/copyleft/cgal/polyhedron_to_mesh.h

@@ -0,0 +1,43 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_POLYHEDRON_TO_MESH_H
+#define IGL_COPYLEFT_CGAL_POLYHEDRON_TO_MESH_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Convert a CGAL Polyhedron to a mesh (V,F)
+      //
+      // Templates:
+      //   Polyhedron  CGAL Polyhedron type (e.g. Polyhedron_3)
+      // Inputs:
+      //   poly  cgal polyhedron
+      // Outputs:
+      //   V  #V by 3 list of vertex positions
+      //   F  #F by 3 list of triangle indices
+      template <
+        typename Polyhedron,
+        typename DerivedV,
+        typename DerivedF>
+      IGL_INLINE void polyhedron_to_mesh(
+        const Polyhedron & poly,
+        Eigen::PlainObjectBase<DerivedV> & V,
+        Eigen::PlainObjectBase<DerivedF> & F);
+    }
+  }
+}
+#ifndef IGL_STATIC_LIBRARY
+#  include "polyhedron_to_mesh.cpp"
+#endif
+
+#endif

src/igl/copyleft/cgal/projected_cdt.cpp

@@ -0,0 +1,82 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2016 Alec Jacobson
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "projected_cdt.h"
+#include "insert_into_cdt.h"
+#include "assign_scalar.h"
+#include "../../list_to_matrix.h"
+template <typename Kernel, typename Index>
+IGL_INLINE void igl::copyleft::cgal::projected_cdt(
+  const std::vector<CGAL::Object> & objects,
+  const CGAL::Plane_3<Kernel> & P,
+  std::vector<CGAL::Point_3<Kernel> >& vertices,
+  std::vector<std::vector<Index> >& faces)
+{
+  typedef CGAL::Triangulation_vertex_base_2<Kernel>  TVB_2;
+  typedef CGAL::Constrained_triangulation_face_base_2<Kernel> CTFB_2;
+  typedef CGAL::Triangulation_data_structure_2<TVB_2,CTFB_2> TDS_2;
+  typedef CGAL::Exact_intersections_tag Itag;
+  typedef CGAL::Constrained_Delaunay_triangulation_2<Kernel,TDS_2,Itag> CDT_2;
+  typedef CGAL::Constrained_triangulation_plus_2<CDT_2> CDT_plus_2;
+  CDT_plus_2 cdt;
+  for(const auto & obj : objects) insert_into_cdt(obj,P,cdt);
+  // Read off vertices of the cdt, remembering index
+  std::map<typename CDT_plus_2::Vertex_handle,Index> v2i;
+  size_t count=0;
+  for (
+    auto itr = cdt.finite_vertices_begin();
+    itr != cdt.finite_vertices_end();
+    itr++)
+  {
+    vertices.push_back(P.to_3d(itr->point()));
+    v2i[itr] = count;
+    count++;
+  }
+  // Read off faces and store index triples
+  for (
+    auto itr = cdt.finite_faces_begin();
+    itr != cdt.finite_faces_end();
+    itr++)
+  {
+    faces.push_back(
+      { v2i[itr->vertex(0)], v2i[itr->vertex(1)], v2i[itr->vertex(2)] });
+  }
+}
+
+template < typename Kernel, typename DerivedV, typename DerivedF>
+IGL_INLINE void igl::copyleft::cgal::projected_cdt(
+  const std::vector<CGAL::Object> & objects,
+  const CGAL::Plane_3<Kernel> & P,
+  Eigen::PlainObjectBase<DerivedV> & V,
+  Eigen::PlainObjectBase<DerivedF> & F)
+{
+  std::vector<CGAL::Point_3<Kernel> > vertices;
+  std::vector<std::vector<typename DerivedF::Scalar> > faces;
+  projected_cdt(objects,P,vertices,faces);
+  V.resize(vertices.size(),3);
+  for(int v = 0;v<vertices.size();v++)
+  {
+    for(int d = 0;d<3;d++)
+    {
+      assign_scalar(vertices[v][d], V(v,d));
+    }
+  }
+  list_to_matrix(faces,F);
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::projected_cdt<CGAL::Epick, long>(std::vector<CGAL::Object, std::allocator<CGAL::Object> > const&, CGAL::Plane_3<CGAL::Epick> const&, std::vector<CGAL::Point_3<CGAL::Epick>, std::allocator<CGAL::Point_3<CGAL::Epick> > >&, std::vector<std::vector<long, std::allocator<long> >, std::allocator<std::vector<long, std::allocator<long> > > >&);
+// generated by autoexplicit.sh
+template void igl::copyleft::cgal::projected_cdt<CGAL::Epeck, long>(std::vector<CGAL::Object, std::allocator<CGAL::Object> > const&, CGAL::Plane_3<CGAL::Epeck> const&, std::vector<CGAL::Point_3<CGAL::Epeck>, std::allocator<CGAL::Point_3<CGAL::Epeck> > >&, std::vector<std::vector<long, std::allocator<long> >, std::allocator<std::vector<long, std::allocator<long> > > >&);
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#ifdef WIN32
+template void igl::copyleft::cgal::projected_cdt<class CGAL::Epeck, __int64>(class std::vector<class CGAL::Object, class std::allocator<class CGAL::Object>> const &, class CGAL::Plane_3<class CGAL::Epeck> const &, class std::vector<class CGAL::Point_3<class CGAL::Epeck>, class std::allocator<class CGAL::Point_3<class CGAL::Epeck>>> &, class std::vector<class std::vector<__int64, class std::allocator<__int64>>, class std::allocator<class std::vector<__int64, class std::allocator<__int64>>>> &);
+template void igl::copyleft::cgal::projected_cdt<class CGAL::Epick, __int64>(class std::vector<class CGAL::Object, class std::allocator<class CGAL::Object>> const &, class CGAL::Plane_3<class CGAL::Epick> const &, class std::vector<class CGAL::Point_3<class CGAL::Epick>, class std::allocator<class CGAL::Point_3<class CGAL::Epick>>> &, class std::vector<class std::vector<__int64, class std::allocator<__int64>>, class std::allocator<class std::vector<__int64, class std::allocator<__int64>>>> &);
+#endif
+#endif

src/igl/copyleft/cgal/projected_cdt.h

@@ -0,0 +1,61 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2016 Alec Jacobson
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_PROJECTED_CDT_H
+#define IGL_COPYLEFT_CGAL_PROJECTED_CDT_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <CGAL/Plane_3.h>
+#include <CGAL/Point_3.h>
+#include <CGAL/Object.h>
+#include <vector>
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Given a list of objects (e.g., resulting from intersecting a triangle
+      // with many other triangles), construct a constrained Delaunay
+      // triangulation on a given plane (P), by inersting constraints for each
+      // object projected onto that plane.
+      //
+      // Inputs:
+      //   objects  list of objects. This should lie on the given plane (P),
+      //     otherwise they are added to the cdt _after_ their non-trivial
+      //     projection
+      //   P  plane upon which all objects lie and upon which the CDT is
+      //     conducted
+      // Outputs:
+      //   vertices  list of vertices of the CDT mesh _back on the 3D plane_
+      //   faces  list of list of triangle indices into vertices
+      //
+      template <typename Kernel, typename Index>
+      IGL_INLINE void projected_cdt(
+        const std::vector<CGAL::Object> & objects,
+        const CGAL::Plane_3<Kernel> & P,
+        std::vector<CGAL::Point_3<Kernel> >& vertices,
+        std::vector<std::vector<Index> >& faces);
+      // Outputs:
+      //   V  #V by 3 list of vertices of the CDT mesh _back on the 3D plane_,
+      //     **cast** from the number type of Kernel to the number type of
+      //     DerivedV
+      //   F  #F by 3 list of triangle indices into V
+      template < typename Kernel, typename DerivedV, typename DerivedF>
+      IGL_INLINE void projected_cdt(
+        const std::vector<CGAL::Object> & objects,
+        const CGAL::Plane_3<Kernel> & P,
+        Eigen::PlainObjectBase<DerivedV> & V,
+        Eigen::PlainObjectBase<DerivedF> & F);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "projected_cdt.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/projected_delaunay.cpp

@@ -0,0 +1,106 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "projected_delaunay.h"
+#include "../../REDRUM.h"
+#include <iostream>
+#include <cassert>
+
+#if CGAL_VERSION_NR < 1040611000
+#  warning "CGAL Version < 4.6.1 may result in crashes. Please upgrade CGAL"
+#endif
+
+template <typename Kernel>
+IGL_INLINE void igl::copyleft::cgal::projected_delaunay(
+  const CGAL::Triangle_3<Kernel> & A,
+  const std::vector<CGAL::Object> & A_objects_3,
+  CGAL::Constrained_triangulation_plus_2<
+    CGAL::Constrained_Delaunay_triangulation_2<
+      Kernel,
+      CGAL::Triangulation_data_structure_2<
+        CGAL::Triangulation_vertex_base_2<Kernel>,
+        CGAL::Constrained_triangulation_face_base_2<Kernel> >,
+      CGAL::Exact_intersections_tag> > & cdt)
+{
+  using namespace std;
+  // 3D Primitives
+  typedef CGAL::Point_3<Kernel>    Point_3;
+  typedef CGAL::Segment_3<Kernel>  Segment_3; 
+  typedef CGAL::Triangle_3<Kernel> Triangle_3; 
+  typedef CGAL::Plane_3<Kernel>    Plane_3;
+  //typedef CGAL::Tetrahedron_3<Kernel> Tetrahedron_3; 
+  typedef CGAL::Point_2<Kernel>    Point_2;
+  //typedef CGAL::Segment_2<Kernel>  Segment_2; 
+  //typedef CGAL::Triangle_2<Kernel> Triangle_2; 
+  typedef CGAL::Triangulation_vertex_base_2<Kernel>  TVB_2;
+  typedef CGAL::Constrained_triangulation_face_base_2<Kernel> CTFB_2;
+  typedef CGAL::Triangulation_data_structure_2<TVB_2,CTFB_2> TDS_2;
+  typedef CGAL::Exact_intersections_tag Itag;
+  typedef CGAL::Constrained_Delaunay_triangulation_2<Kernel,TDS_2,Itag> 
+    CDT_2;
+  typedef CGAL::Constrained_triangulation_plus_2<CDT_2> CDT_plus_2;
+
+  // http://www.cgal.org/Manual/3.2/doc_html/cgal_manual/Triangulation_2/Chapter_main.html#Section_2D_Triangulations_Constrained_Plus
+  // Plane of triangle A
+  Plane_3 P(A.vertex(0),A.vertex(1),A.vertex(2));
+  // Insert triangle into vertices
+  typename CDT_plus_2::Vertex_handle corners[3];
+  typedef size_t Index;
+  for(Index i = 0;i<3;i++)
+  {
+    const Point_3 & p3 = A.vertex(i);
+    const Point_2 & p2 = P.to_2d(p3);
+    typename CDT_plus_2::Vertex_handle corner = cdt.insert(p2);
+    corners[i] = corner;
+  }
+  // Insert triangle edges as constraints
+  for(Index i = 0;i<3;i++)
+  {
+    cdt.insert_constraint( corners[(i+1)%3], corners[(i+2)%3]);
+  }
+  // Insert constraints for intersection objects
+  for( const auto & obj : A_objects_3)
+  {
+    if(const Segment_3 *iseg = CGAL::object_cast<Segment_3 >(&obj))
+    {
+      // Add segment constraint
+      cdt.insert_constraint(P.to_2d(iseg->vertex(0)),P.to_2d(iseg->vertex(1)));
+    }else if(const Point_3 *ipoint = CGAL::object_cast<Point_3 >(&obj))
+    {
+      // Add point
+      cdt.insert(P.to_2d(*ipoint));
+    } else if(const Triangle_3 *itri = CGAL::object_cast<Triangle_3 >(&obj))
+    {
+      // Add 3 segment constraints
+      cdt.insert_constraint(P.to_2d(itri->vertex(0)),P.to_2d(itri->vertex(1)));
+      cdt.insert_constraint(P.to_2d(itri->vertex(1)),P.to_2d(itri->vertex(2)));
+      cdt.insert_constraint(P.to_2d(itri->vertex(2)),P.to_2d(itri->vertex(0)));
+    } else if(const std::vector<Point_3 > *polyp = 
+        CGAL::object_cast< std::vector<Point_3 > >(&obj))
+    {
+      //cerr<<REDRUM("Poly...")<<endl;
+      const std::vector<Point_3 > & poly = *polyp;
+      const Index m = poly.size();
+      assert(m>=2);
+      for(Index p = 0;p<m;p++)
+      {
+        const Index np = (p+1)%m;
+        cdt.insert_constraint(P.to_2d(poly[p]),P.to_2d(poly[np]));
+      }
+    }else
+    {
+      cerr<<REDRUM("What is this object?!")<<endl;
+      assert(false);
+    }
+  }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template void igl::copyleft::cgal::projected_delaunay<CGAL::Epeck>(CGAL::Triangle_3<CGAL::Epeck> const&, std::vector<CGAL::Object, std::allocator<CGAL::Object> > const&, CGAL::Constrained_triangulation_plus_2<CGAL::Constrained_Delaunay_triangulation_2<CGAL::Epeck, CGAL::Triangulation_data_structure_2<CGAL::Triangulation_vertex_base_2<CGAL::Epeck, CGAL::Triangulation_ds_vertex_base_2<void> >, CGAL::Constrained_triangulation_face_base_2<CGAL::Epeck, CGAL::Triangulation_face_base_2<CGAL::Epeck, CGAL::Triangulation_ds_face_base_2<void> > > >, CGAL::Exact_intersections_tag> >&);
+template void igl::copyleft::cgal::projected_delaunay<CGAL::Epick>(CGAL::Triangle_3<CGAL::Epick> const&, std::vector<CGAL::Object, std::allocator<CGAL::Object> > const&, CGAL::Constrained_triangulation_plus_2<CGAL::Constrained_Delaunay_triangulation_2<CGAL::Epick, CGAL::Triangulation_data_structure_2<CGAL::Triangulation_vertex_base_2<CGAL::Epick, CGAL::Triangulation_ds_vertex_base_2<void> >, CGAL::Constrained_triangulation_face_base_2<CGAL::Epick, CGAL::Triangulation_face_base_2<CGAL::Epick, CGAL::Triangulation_ds_face_base_2<void> > > >, CGAL::Exact_intersections_tag> >&);
+#endif

src/igl/copyleft/cgal/projected_delaunay.h

@@ -0,0 +1,46 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_PROJECTED_DELAUNAY_H
+#define IGL_COPYLEFT_CGAL_PROJECTED_DELAUNAY_H
+#include "../../igl_inline.h"
+#include "CGAL_includes.hpp"
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Compute 2D delaunay triangulation of a given 3d triangle and a list of
+      // intersection objects (points,segments,triangles). CGAL uses an affine
+      // projection rather than an isometric projection, so we're not guaranteed
+      // that the 2D delaunay triangulation here will be a delaunay triangulation
+      // in 3D.
+      //
+      // Inputs:
+      //   A  triangle in 3D
+      //   A_objects_3  updated list of intersection objects for A
+      // Outputs:
+      //   cdt  Contrained delaunay triangulation in projected 2D plane
+      template <typename Kernel>
+      IGL_INLINE void projected_delaunay(
+        const CGAL::Triangle_3<Kernel> & A,
+        const std::vector<CGAL::Object> & A_objects_3,
+        CGAL::Constrained_triangulation_plus_2<
+          CGAL::Constrained_Delaunay_triangulation_2<
+            Kernel,
+            CGAL::Triangulation_data_structure_2<
+              CGAL::Triangulation_vertex_base_2<Kernel>,
+              CGAL::Constrained_triangulation_face_base_2<Kernel> >,
+            CGAL::Exact_intersections_tag> > & cdt);
+    }
+  }
+}
+#ifndef IGL_STATIC_LIBRARY
+#  include "projected_delaunay.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/propagate_winding_numbers.cpp

@@ -0,0 +1,324 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+//
+#include "propagate_winding_numbers.h"
+#include "../../extract_manifold_patches.h"
+#include "../../extract_non_manifold_edge_curves.h"
+#include "../../facet_components.h"
+#include "../../unique_edge_map.h"
+#include "../../piecewise_constant_winding_number.h"
+#include "../../writeOBJ.h"
+#include "../../writePLY.h"
+#include "../../get_seconds.h"
+#include "../../LinSpaced.h"
+#include "order_facets_around_edge.h"
+#include "outer_facet.h"
+#include "closest_facet.h"
+#include "assign.h"
+#include "extract_cells.h"
+#include "cell_adjacency.h"
+
+#include <stdexcept>
+#include <limits>
+#include <vector>
+#include <tuple>
+#include <queue>
+
+//#define PROPAGATE_WINDING_NUMBER_TIMING
+
+template<
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedL,
+  typename DerivedW>
+IGL_INLINE bool igl::copyleft::cgal::propagate_winding_numbers(
+    const Eigen::PlainObjectBase<DerivedV>& V,
+    const Eigen::PlainObjectBase<DerivedF>& F,
+    const Eigen::PlainObjectBase<DerivedL>& labels,
+    Eigen::PlainObjectBase<DerivedW>& W) 
+{
+#ifdef PROPAGATE_WINDING_NUMBER_TIMING
+  const auto & tictoc = []() -> double
+  {
+    static double t_start = igl::get_seconds();
+    double diff = igl::get_seconds()-t_start;
+    t_start += diff;
+    return diff;
+  };
+  const auto log_time = [&](const std::string& label) -> void {
+    std::cout << "propagate_winding_num." << label << ": "
+      << tictoc() << std::endl;
+  };
+  tictoc();
+#endif
+
+  Eigen::MatrixXi E, uE;
+  Eigen::VectorXi EMAP;
+  std::vector<std::vector<size_t> > uE2E;
+  igl::unique_edge_map(F, E, uE, EMAP, uE2E);
+
+  Eigen::VectorXi P;
+  const size_t num_patches = igl::extract_manifold_patches(F, EMAP, uE2E, P);
+
+  DerivedW per_patch_cells;
+  const size_t num_cells =
+    igl::copyleft::cgal::extract_cells(
+        V, F, P, E, uE, uE2E, EMAP, per_patch_cells);
+#ifdef PROPAGATE_WINDING_NUMBER_TIMING
+  log_time("cell_extraction");
+#endif
+
+  return propagate_winding_numbers(V, F,
+          uE, uE2E,
+          num_patches, P,
+          num_cells, per_patch_cells,
+          labels, W);
+}
+
+
+template<
+  typename DerivedV,
+  typename DerivedF,
+  typename DeriveduE,
+  typename uE2EType,
+  typename DerivedP,
+  typename DerivedC,
+  typename DerivedL,
+  typename DerivedW>
+IGL_INLINE bool igl::copyleft::cgal::propagate_winding_numbers(
+    const Eigen::PlainObjectBase<DerivedV>& V,
+    const Eigen::PlainObjectBase<DerivedF>& F,
+    const Eigen::PlainObjectBase<DeriveduE>& uE,
+    const std::vector<std::vector<uE2EType> >& uE2E,
+    const size_t num_patches,
+    const Eigen::PlainObjectBase<DerivedP>& P,
+    const size_t num_cells,
+    const Eigen::PlainObjectBase<DerivedC>& C,
+    const Eigen::PlainObjectBase<DerivedL>& labels,
+    Eigen::PlainObjectBase<DerivedW>& W)
+{
+#ifdef PROPAGATE_WINDING_NUMBER_TIMING
+  const auto & tictoc = []() -> double
+  {
+    static double t_start = igl::get_seconds();
+    double diff = igl::get_seconds()-t_start;
+    t_start += diff;
+    return diff;
+  };
+  const auto log_time = [&](const std::string& label) -> void {
+    std::cout << "propagate_winding_num." << label << ": "
+      << tictoc() << std::endl;
+  };
+  tictoc();
+#endif
+
+  bool valid = true;
+  // https://github.com/libigl/libigl/issues/674
+  if (!igl::piecewise_constant_winding_number(F, uE, uE2E)) 
+  {
+    assert(false && "Input mesh is not PWN");
+    std::cerr << "Input mesh is not PWN!" << std::endl;
+    valid = false;
+  }
+
+  const size_t num_faces = F.rows();
+  typedef std::tuple<typename DerivedC::Scalar, bool, size_t> CellConnection;
+  std::vector<std::set<CellConnection> > cell_adj;
+  igl::copyleft::cgal::cell_adjacency(C, num_cells, cell_adj);
+#ifdef PROPAGATE_WINDING_NUMBER_TIMING
+  log_time("cell_connectivity");
+#endif
+
+  auto save_cell = [&](const std::string& filename, size_t cell_id) -> void{
+    std::vector<size_t> faces;
+    for (size_t i=0; i<num_patches; i++) {
+      if ((C.row(i).array() == cell_id).any()) {
+        for (size_t j=0; j<num_faces; j++) {
+          if ((size_t)P[j] == i) {
+            faces.push_back(j);
+          }
+        }
+      }
+    }
+    Eigen::MatrixXi cell_faces(faces.size(), 3);
+    for (size_t i=0; i<faces.size(); i++) {
+      cell_faces.row(i) = F.row(faces[i]);
+    }
+    Eigen::MatrixXd vertices;
+    assign(V,vertices);
+    writePLY(filename, vertices, cell_faces);
+  };
+
+#ifndef NDEBUG
+  {
+    // Check for odd cycle.
+    Eigen::VectorXi cell_labels(num_cells);
+    cell_labels.setZero();
+    Eigen::VectorXi parents(num_cells);
+    parents.setConstant(-1);
+    auto trace_parents = [&](size_t idx) -> std::list<size_t> {
+      std::list<size_t> path;
+      path.push_back(idx);
+      while ((size_t)parents[path.back()] != path.back()) {
+        path.push_back(parents[path.back()]);
+      }
+      return path;
+    };
+    for (size_t i=0; i<num_cells; i++) {
+      if (cell_labels[i] == 0) {
+        cell_labels[i] = 1;
+        std::queue<size_t> Q;
+        Q.push(i);
+        parents[i] = i;
+        while (!Q.empty()) {
+          size_t curr_idx = Q.front();
+          Q.pop();
+          int curr_label = cell_labels[curr_idx];
+          for (const auto& neighbor : cell_adj[curr_idx]) {
+            if (cell_labels[std::get<0>(neighbor)] == 0) 
+            {
+              cell_labels[std::get<0>(neighbor)] = curr_label * -1;
+              Q.push(std::get<0>(neighbor));
+              parents[std::get<0>(neighbor)] = curr_idx;
+            } else 
+            {
+              if (cell_labels[std::get<0>(neighbor)] != curr_label * -1) 
+              {
+                std::cerr << "Odd cell cycle detected!" << std::endl;
+                auto path = trace_parents(curr_idx);
+                path.reverse();
+                auto path2 = trace_parents(std::get<0>(neighbor));
+                path.insert(path.end(), path2.begin(), path2.end());
+                for (auto cell_id : path) 
+                {
+                  std::cout << cell_id << " ";
+                  std::stringstream filename;
+                  filename << "cell_" << cell_id << ".ply";
+                  save_cell(filename.str(), cell_id);
+                }
+                std::cout << std::endl;
+                valid = false;
+              }
+              // Do not fail when odd cycle is detected because the resulting
+              // integer winding number field, although inconsistent, may still
+              // be used if the problem region is local and embedded within a
+              // valid volume.
+              //assert(cell_labels[std::get<0>(neighbor)] == curr_label * -1);
+            }
+          }
+        }
+      }
+    }
+#ifdef PROPAGATE_WINDING_NUMBER_TIMING
+    log_time("odd_cycle_check");
+#endif
+  }
+#endif
+
+  size_t outer_facet;
+  bool flipped;
+  Eigen::VectorXi I = igl::LinSpaced<Eigen::VectorXi>(num_faces, 0, num_faces-1);
+  igl::copyleft::cgal::outer_facet(V, F, I, outer_facet, flipped);
+#ifdef PROPAGATE_WINDING_NUMBER_TIMING
+  log_time("outer_facet");
+#endif
+
+  const size_t outer_patch = P[outer_facet];
+  const size_t infinity_cell = C(outer_patch, flipped?1:0);
+
+  Eigen::VectorXi patch_labels(num_patches);
+  const int INVALID = std::numeric_limits<int>::max();
+  patch_labels.setConstant(INVALID);
+  for (size_t i=0; i<num_faces; i++) {
+    if (patch_labels[P[i]] == INVALID) {
+      patch_labels[P[i]] = labels[i];
+    } else {
+      assert(patch_labels[P[i]] == labels[i]);
+    }
+  }
+  assert((patch_labels.array() != INVALID).all());
+  const size_t num_labels = patch_labels.maxCoeff()+1;
+
+  Eigen::MatrixXi per_cell_W(num_cells, num_labels);
+  per_cell_W.setConstant(INVALID);
+  per_cell_W.row(infinity_cell).setZero();
+  std::queue<size_t> Q;
+  Q.push(infinity_cell);
+  while (!Q.empty()) {
+    size_t curr_cell = Q.front();
+    Q.pop();
+    for (const auto& neighbor : cell_adj[curr_cell]) {
+      size_t neighbor_cell, patch_idx;
+      bool direction;
+      std::tie(neighbor_cell, direction, patch_idx) = neighbor;
+      if ((per_cell_W.row(neighbor_cell).array() == INVALID).any()) {
+        per_cell_W.row(neighbor_cell) = per_cell_W.row(curr_cell);
+        for (size_t i=0; i<num_labels; i++) {
+          int inc = (patch_labels[patch_idx] == (int)i) ?
+            (direction ? -1:1) :0;
+          per_cell_W(neighbor_cell, i) =
+            per_cell_W(curr_cell, i) + inc;
+        }
+        Q.push(neighbor_cell);
+      } else {
+#ifndef NDEBUG
+        // Checking for winding number consistency.
+        // This check would inevitably fail for meshes that contain open
+        // boundary or non-orientable.  However, the inconsistent winding number
+        // field would still be useful in some cases such as when problem region
+        // is local and embedded within the volume.  This, unfortunately, is the
+        // best we can do because the problem of computing integer winding
+        // number is ill-defined for open and non-orientable surfaces.
+        for (size_t i=0; i<num_labels; i++) {
+          if ((int)i == patch_labels[patch_idx]) {
+            int inc = direction ? -1:1;
+            //assert(per_cell_W(neighbor_cell, i) ==
+            //    per_cell_W(curr_cell, i) + inc);
+          } else {
+            //assert(per_cell_W(neighbor_cell, i) ==
+            //    per_cell_W(curr_cell, i));
+          }
+        }
+#endif
+      }
+    }
+  }
+#ifdef PROPAGATE_WINDING_NUMBER_TIMING
+  log_time("propagate_winding_number");
+#endif
+
+  W.resize(num_faces, num_labels*2);
+  for (size_t i=0; i<num_faces; i++) 
+  {
+    const size_t patch = P[i];
+    const size_t positive_cell = C(patch, 0);
+    const size_t negative_cell = C(patch, 1);
+    for (size_t j=0; j<num_labels; j++) {
+      W(i,j*2  ) = per_cell_W(positive_cell, j);
+      W(i,j*2+1) = per_cell_W(negative_cell, j);
+    }
+  }
+#ifdef PROPAGATE_WINDING_NUMBER_TIMING
+  log_time("store_result");
+#endif
+  return valid;
+}
+
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template bool igl::copyleft::cgal::propagate_winding_numbers<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, unsigned long, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<std::vector<unsigned long, std::allocator<unsigned long> >, std::allocator<std::vector<unsigned long, std::allocator<unsigned long> > > > const&, unsigned long, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, unsigned long, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+// generated by autoexplicit.sh
+template bool igl::copyleft::cgal::propagate_winding_numbers<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, unsigned long, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 1, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<std::vector<unsigned long, std::allocator<unsigned long> >, std::allocator<std::vector<unsigned long, std::allocator<unsigned long> > > > const&, unsigned long, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, unsigned long, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+template bool igl::copyleft::cgal::propagate_winding_numbers<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<CGAL::Lazy_exact_nt<CGAL::Gmpq>, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+#ifdef WIN32
+template bool igl::copyleft::cgal::propagate_winding_numbers<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, unsigned __int64, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class std::vector<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>, class std::allocator<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>>> const &, unsigned __int64, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, unsigned __int64, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> &);
+template bool igl::copyleft::cgal::propagate_winding_numbers<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>, class Eigen::Matrix<int, -1, 3, 1, -1, 3>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, unsigned __int64, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>, class Eigen::Matrix<int, -1, 1, 0, -1, 1>, class Eigen::Matrix<int, -1, -1, 0, -1, -1>>(class Eigen::PlainObjectBase<class Eigen::Matrix<class CGAL::Lazy_exact_nt<class CGAL::Gmpq>, -1, -1, 1, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 3, 1, -1, 3>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class std::vector<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>, class std::allocator<class std::vector<unsigned __int64, class std::allocator<unsigned __int64>>>> const &, unsigned __int64, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, unsigned __int64, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, 1, 0, -1, 1>> const &, class Eigen::PlainObjectBase<class Eigen::Matrix<int, -1, -1, 0, -1, -1>> &);
+#endif
+#endif

src/igl/copyleft/cgal/propagate_winding_numbers.h

@@ -0,0 +1,103 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+//
+#ifndef IGL_COPYLEFT_CGAL_PROPAGATE_WINDING_NUMBERS_H
+#define IGL_COPYLEFT_CGAL_PROPAGATE_WINDING_NUMBERS_H
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <vector>
+
+// The following methods compute the winding number on each side of each facet
+// or patch of a 3D mesh.  The input mesh is valid if it splits the ambient
+// space, R^3, into subspaces with constant integer winding numbers.  That is
+// the input mesh should be closed and for each directed edge the number of
+// clockwise facing facets should equal the number of counterclockwise facing
+// facets.
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // TODO: This shouldn't need to be in igl::copyleft::cgal, it should
+      // instead take as input an index of the ambient cell and the winding
+      // number vector there.
+      //
+      // Compute winding number on each side of the face.  The input mesh
+      // could contain multiple connected components.  The input mesh must
+      // represent the boundary of a valid 3D volume, which means it is
+      // closed, consistently oriented and induces integer winding numbers.
+      //
+      // Inputs:
+      //   V  #V by 3 list of vertex positions.
+      //   F  #F by 3 list of triangle indices into V.
+      //   labels  #F list of facet labels ranging from 0 to k-1.
+      // Output:
+      //   W  #F by k*2 list of winding numbers.  ``W(i,j*2)`` is the winding
+      //      number on the positive side of facet ``i`` with respect to the
+      //      facets labeled ``j``.  Similarly, ``W(i,j*2+1)`` is the winding
+      //      number on the negative side of facet ``i`` with respect to the
+      //      facets labeled ``j``.
+      // Returns true iff the input induces a piecewise-constant winding number
+      //   field.
+      template<
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedL,
+        typename DerivedW>
+      IGL_INLINE bool propagate_winding_numbers(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        const Eigen::PlainObjectBase<DerivedL>& labels,
+        Eigen::PlainObjectBase<DerivedW>& W);
+
+      // Inputs:
+      //   V  #V by 3 list of vertex positions.
+      //   F  #F by 3 list of triangle indices into V.
+      //   uE    #uE by 2 list of vertex_indices, represents undirected edges.
+      //   uE2E  #uE list of lists that maps uE to E. (a one-to-many map)
+      //   num_patches  number of patches
+      //   P  #F list of patch ids.
+      //   num_cells    number of cells
+      //   C  #P by 2 list of cell ids on each side of each patch.
+      //   labels  #F list of facet labels ranging from 0 to k-1.
+      // Output:
+      //   W  #F by k*2 list of winding numbers.  ``W(i,j*2)`` is the winding
+      //      number on the positive side of facet ``i`` with respect to the
+      //      facets labeled ``j``.  Similarly, ``W(i,j*2+1)`` is the winding
+      //      number on the negative side of facet ``i`` with respect to the
+      //      facets labeled ``j``.
+      template<
+        typename DerivedV,
+        typename DerivedF,
+        typename DeriveduE,
+        typename uE2EType,
+        typename DerivedP,
+        typename DerivedC,
+        typename DerivedL,
+        typename DerivedW>
+      IGL_INLINE bool propagate_winding_numbers(
+        const Eigen::PlainObjectBase<DerivedV>& V,
+        const Eigen::PlainObjectBase<DerivedF>& F,
+        const Eigen::PlainObjectBase<DeriveduE>& uE,
+        const std::vector<std::vector<uE2EType> >& uE2E,
+        const size_t num_patches,
+        const Eigen::PlainObjectBase<DerivedP>& P,
+        const size_t num_cells,
+        const Eigen::PlainObjectBase<DerivedC>& C,
+        const Eigen::PlainObjectBase<DerivedL>& labels,
+        Eigen::PlainObjectBase<DerivedW>& W);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "propagate_winding_numbers.cpp"
+#endif
+#endif

src/igl/copyleft/cgal/read_triangle_mesh.cpp

@@ -0,0 +1,26 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "read_triangle_mesh.h"
+#include "assign.h"
+#include "../../read_triangle_mesh.h"
+
+template <typename DerivedV, typename DerivedF>
+IGL_INLINE bool igl::copyleft::cgal::read_triangle_mesh(
+  const std::string str,
+  Eigen::PlainObjectBase<DerivedV>& V,
+  Eigen::PlainObjectBase<DerivedF>& F)
+{
+  Eigen::MatrixXd Vd;
+  bool ret = igl::read_triangle_mesh(str,Vd,F);
+  if(ret)
+  {
+    assign(Vd,V);
+  }
+  return ret;
+}

src/igl/copyleft/cgal/read_triangle_mesh.h

@@ -0,0 +1,42 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_COPYLEFT_CGAL_READ_TRIANGLE_MESH_H
+#define IGL_COPYLEFT_CGAL_READ_TRIANGLE_MESH_H
+#include "../../igl_inline.h"
+
+#include <Eigen/Core>
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Simple wrapper, reads floating point precision but assigns to
+      // DerivedV::Scalar which may be a CGAL type
+      //
+      // Inputs:
+      //   str  path to file
+      // Outputs:
+      //   V  eigen double matrix #V by 3
+      //   F  eigen int matrix #F by 3
+      // Returns true iff success
+      template <typename DerivedV, typename DerivedF>
+      IGL_INLINE bool read_triangle_mesh(
+        const std::string str,
+        Eigen::PlainObjectBase<DerivedV>& V,
+        Eigen::PlainObjectBase<DerivedF>& F);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "read_triangle_mesh.cpp"
+#endif
+
+#endif
+

src/igl/copyleft/cgal/relabel_small_immersed_cells.cpp

@@ -0,0 +1,117 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+//
+
+#include "relabel_small_immersed_cells.h"
+#include "../../centroid.h"
+#include "assign.h"
+#include "cell_adjacency.h"
+
+#include <vector>
+
+template<
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedP,
+  typename DerivedC,
+  typename FT,
+  typename DerivedW>
+IGL_INLINE void igl::copyleft::cgal::relabel_small_immersed_cells(
+    const Eigen::PlainObjectBase<DerivedV>& V,
+    const Eigen::PlainObjectBase<DerivedF>& F,
+    const size_t num_patches,
+    const Eigen::PlainObjectBase<DerivedP>& P,
+    const size_t num_cells,
+    const Eigen::PlainObjectBase<DerivedC>& C,
+    const FT vol_threashold,
+    Eigen::PlainObjectBase<DerivedW>& W)
+{
+  const size_t num_vertices = V.rows();
+  const size_t num_faces = F.rows();
+  typedef std::tuple<typename DerivedC::Scalar, bool, size_t> CellConnection;
+  std::vector<std::set<CellConnection> > cell_adj;
+  igl::copyleft::cgal::cell_adjacency(C, num_cells, cell_adj);
+
+  Eigen::MatrixXd VV;
+  assign(V,VV);
+
+  auto compute_cell_volume = [&](size_t cell_id) {
+    std::vector<short> is_involved(num_patches, 0);
+    for (size_t i=0; i<num_patches; i++) {
+      if (C(i,0) == cell_id) {
+        // cell is on positive side of patch i.
+        is_involved[i] = 1;
+      }
+      if (C(i,1) == cell_id) {
+        // cell is on negative side of patch i.
+        is_involved[i] = -1;
+      }
+    }
+
+    std::vector<size_t> involved_positive_faces;
+    std::vector<size_t> involved_negative_faces;
+    for (size_t i=0; i<num_faces; i++) {
+      switch (is_involved[P[i]]) {
+        case 1:
+          involved_negative_faces.push_back(i);
+          break;
+        case -1:
+          involved_positive_faces.push_back(i);
+          break;
+      }
+    }
+
+    const size_t num_positive_faces = involved_positive_faces.size();
+    const size_t num_negative_faces = involved_negative_faces.size();
+    DerivedF selected_faces(num_positive_faces + num_negative_faces, 3);
+    for (size_t i=0; i<num_positive_faces; i++) {
+      selected_faces.row(i) = F.row(involved_positive_faces[i]);
+    }
+    for (size_t i=0; i<num_negative_faces; i++) {
+      selected_faces.row(num_positive_faces+i) =
+        F.row(involved_negative_faces[i]).reverse();
+    }
+
+    Eigen::VectorXd c(3);
+    double vol;
+    igl::centroid(VV, selected_faces, c, vol);
+    return vol;
+  };
+
+  std::vector<typename DerivedV::Scalar> cell_volumes(num_cells);
+  for (size_t i=0; i<num_cells; i++) {
+    cell_volumes[i] = compute_cell_volume(i);
+  }
+
+  std::vector<typename DerivedW::Scalar> cell_values(num_cells);
+  for (size_t i=0; i<num_faces; i++) {
+    cell_values[C(P[i], 0)] = W(i, 0);
+    cell_values[C(P[i], 1)] = W(i, 1);
+  }
+
+  for (size_t i=1; i<num_cells; i++) {
+    std::cout << cell_volumes[i] << std::endl;
+    if (cell_volumes[i] >= vol_threashold) continue;
+    std::set<typename DerivedW::Scalar> neighbor_values;
+    const auto neighbors = cell_adj[i];
+    for (const auto& entry : neighbors) {
+      const auto& j = std::get<0>(entry);
+      neighbor_values.insert(cell_values[j]);
+    }
+    // If cell i is immersed, assign its value to be the immersed value.
+    if (neighbor_values.size() == 1) {
+      cell_values[i] = *neighbor_values.begin();
+    }
+  }
+
+  for (size_t i=0; i<num_faces; i++) {
+    W(i,0) = cell_values[C(P[i], 0)];
+    W(i,1) = cell_values[C(P[i], 1)];
+  }
+}
+

src/igl/copyleft/cgal/relabel_small_immersed_cells.h

@@ -0,0 +1,59 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Qingnan Zhou <qnzhou@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+//
+#ifndef IGL_RELABEL_SMALL_IMMERSED_CELLS
+#define IGL_RELABEL_SMALL_IMMERSED_CELLS
+
+#include "../../igl_inline.h"
+#include <Eigen/Core>
+#include <vector>
+
+namespace igl
+{
+  namespace copyleft
+  {
+    namespace cgal
+    {
+      // Inputs:
+      //   V  #V by 3 list of vertex positions.
+      //   F  #F by 3 list of triangle indices into V.
+      //   num_patches  number of patches
+      //   P  #F list of patch ids.
+      //   num_cells    number of cells
+      //   C  #P by 2 list of cell ids on each side of each patch.
+      //   vol_threshold  Volume threshold, cells smaller than this
+      //                  and is completely immersed will be relabeled.
+      //
+      // In/Output:
+      //   W  #F by 2 cell labels.  W(i,0) is the label on the positive side of
+      //      face i, W(i,1) is the label on the negative side of face i.  W
+      //      will be modified in place by this method.
+      template<
+        typename DerivedV,
+        typename DerivedF,
+        typename DerivedP,
+        typename DerivedC,
+        typename FT,
+        typename DerivedW>
+      IGL_INLINE void relabel_small_immersed_cells(
+          const Eigen::PlainObjectBase<DerivedV>& V,
+          const Eigen::PlainObjectBase<DerivedF>& F,
+          const size_t num_patches,
+          const Eigen::PlainObjectBase<DerivedP>& P,
+          const size_t num_cells,
+          const Eigen::PlainObjectBase<DerivedC>& C,
+          const FT vol_threashold,
+          Eigen::PlainObjectBase<DerivedW>& W);
+    }
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "relabel_small_immersed_cells.cpp"
+#endif
+#endif