Merged branch 'dev_native' into lm_sla_supports_auto

Added igl library files

src/igl/lbs_matrix.h

@@ -0,0 +1,94 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 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_LBS_MATRIX_H
+#define IGL_LBS_MATRIX_H
+#include "igl_inline.h"
+
+#include <Eigen/Dense>
+#include <Eigen/Sparse>
+
+namespace igl
+{
+  // LBS_MATRIX Linear blend skinning can be expressed by V' = M * T where V' is
+  // a #V by dim matrix of deformed vertex positions (one vertex per row), M is a
+  // #V by (dim+1)*#T (composed of weights and rest positions) and T is a
+  // #T*(dim+1) by dim matrix of #T stacked transposed transformation matrices.
+  // See equations (1) and (2) in "Fast Automatic Skinning Transformations"
+  // [Jacobson et al 2012]
+  //
+  // Inputs:
+  //   V  #V by dim list of rest positions
+  //   W  #V+ by #T  list of weights
+  // Outputs:
+  //   M  #V by #T*(dim+1)
+  //
+  // In MATLAB:
+  //   kron(ones(1,size(W,2)),[V ones(size(V,1),1)]).*kron(W,ones(1,size(V,2)+1))
+  IGL_INLINE void lbs_matrix(
+    const Eigen::MatrixXd & V, 
+    const Eigen::MatrixXd & W,
+    Eigen::MatrixXd & M);
+  // LBS_MATRIX  construct a matrix that when multiplied against a column of
+  // affine transformation entries computes new coordinates of the vertices
+  //
+  // I'm not sure it makes since that the result is stored as a sparse matrix.
+  // The number of non-zeros per row *is* dependent on the number of mesh
+  // vertices and handles.
+  //
+  // Inputs:
+  //   V  #V by dim list of vertex rest positions
+  //   W  #V by #handles list of correspondence weights
+  // Output:
+  //   M  #V * dim by #handles * dim * (dim+1) matrix such that
+  //     new_V(:) = LBS(V,W,A) = reshape(M * A,size(V)), where A is a column
+  //     vectors formed by the entries in each handle's dim by dim+1 
+  //     transformation matrix. Specifcally, A =
+  //       reshape(permute(Astack,[3 1 2]),n*dim*(dim+1),1)
+  //     or A = [Lxx;Lyx;Lxy;Lyy;tx;ty], and likewise for other dim
+  //     if Astack(:,:,i) is the dim by (dim+1) transformation at handle i
+  IGL_INLINE void lbs_matrix_column(
+    const Eigen::MatrixXd & V, 
+    const Eigen::MatrixXd & W,
+    Eigen::SparseMatrix<double>& M);
+  IGL_INLINE void lbs_matrix_column(
+    const Eigen::MatrixXd & V, 
+    const Eigen::MatrixXd & W,
+    Eigen::MatrixXd & M);
+  // Same as LBS_MATRIX above but instead of giving W as a full matrix of weights
+  // (each vertex has #handles weights), a constant number of weights are given
+  // for each vertex.
+  // 
+  // Inputs:
+  //   V  #V by dim list of vertex rest positions
+  //   W  #V by k  list of k correspondence weights per vertex
+  //   WI  #V by k  list of k correspondence weight indices per vertex. Such that
+  //     W(j,WI(i)) gives the ith most significant correspondence weight on vertex j
+  // Output:
+  //   M  #V * dim by #handles * dim * (dim+1) matrix such that
+  //     new_V(:) = LBS(V,W,A) = reshape(M * A,size(V)), where A is a column
+  //     vectors formed by the entries in each handle's dim by dim+1 
+  //     transformation matrix. Specifcally, A =
+  //       reshape(permute(Astack,[3 1 2]),n*dim*(dim+1),1)
+  //     or A = [Lxx;Lyx;Lxy;Lyy;tx;ty], and likewise for other dim
+  //     if Astack(:,:,i) is the dim by (dim+1) transformation at handle i
+  //
+  IGL_INLINE void lbs_matrix_column(
+    const Eigen::MatrixXd & V, 
+    const Eigen::MatrixXd & W,
+    const Eigen::MatrixXi & WI,
+    Eigen::SparseMatrix<double>& M);
+  IGL_INLINE void lbs_matrix_column(
+    const Eigen::MatrixXd & V, 
+    const Eigen::MatrixXd & W,
+    const Eigen::MatrixXi & WI,
+    Eigen::MatrixXd & M);
+}
+#ifndef IGL_STATIC_LIBRARY
+#include "lbs_matrix.cpp"
+#endif
+#endif