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211 lines
9.1 KiB
C++
211 lines
9.1 KiB
C++
// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2016 Yotam Gingold <yotam@yotamgingold.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla Public License
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// v. 2.0. If a copy of the MPL was not distributed with this file, You can
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// obtain one at http://mozilla.org/MPL/2.0/.
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#include "seam_edges.h"
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#include <unordered_map>
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#include <unordered_set>
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#include <cassert>
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// Yotam has verified that this function produces the exact same output as
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// `find_seam_fast.py` for `cow_triangled.obj`.
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template <
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typename DerivedV,
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typename DerivedTC,
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typename DerivedF,
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typename DerivedFTC,
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typename Derivedseams,
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typename Derivedboundaries,
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typename Derivedfoldovers>
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IGL_INLINE void igl::seam_edges(
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const Eigen::PlainObjectBase<DerivedV>& V,
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const Eigen::PlainObjectBase<DerivedTC>& TC,
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const Eigen::PlainObjectBase<DerivedF>& F,
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const Eigen::PlainObjectBase<DerivedFTC>& FTC,
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Eigen::PlainObjectBase<Derivedseams>& seams,
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Eigen::PlainObjectBase<Derivedboundaries>& boundaries,
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Eigen::PlainObjectBase<Derivedfoldovers>& foldovers)
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{
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// Assume triangles.
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assert( F.cols() == 3 );
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assert( F.cols() == FTC.cols() );
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assert( F.rows() == FTC.rows() );
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// Assume 2D texture coordinates (foldovers tests).
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assert( TC.cols() == 2 );
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typedef Eigen::Matrix< typename DerivedTC::Scalar, 2, 1 > Vector2S;
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// Computes the orientation of `c` relative to the line between `a` and `b`.
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// Assumes 2D vector input.
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// Based on: https://www.cs.cmu.edu/~quake/robust.html
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const auto& Orientation = [](
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const Vector2S& a,
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const Vector2S& b,
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const Vector2S& c ) -> typename DerivedTC::Scalar
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{
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const Vector2S row0 = a - c;
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const Vector2S row1 = b - c;
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return row0(0)*row1(1) - row1(0)*row0(1);
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};
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seams .setZero( 3*F.rows(), 4 );
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boundaries.setZero( 3*F.rows(), 2 );
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foldovers .setZero( 3*F.rows(), 4 );
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int num_seams = 0;
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int num_boundaries = 0;
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int num_foldovers = 0;
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// A map from a pair of vertex indices to the index (face and endpoints)
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// into face_position_indices.
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// The following should be true for every key, value pair:
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// key == face_position_indices[ value ]
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// This gives us a "reverse map" so that we can look up other face
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// attributes based on position edges.
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// The value are written in the format returned by numpy.where(),
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// which stores multi-dimensional indices such as array[a0,b0], array[a1,b1]
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// as ( (a0,a1), (b0,b1) ).
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// We need to make a hash function for our directed edges.
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// We'll use i*V.rows() + j.
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typedef std::pair< typename DerivedF::Scalar, typename DerivedF::Scalar >
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directed_edge;
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const int numV = V.rows();
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const int numF = F.rows();
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const auto& edge_hasher =
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[numV]( directed_edge const& e ) { return e.first*numV + e.second; };
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// When we pass a hash function object, we also need to specify the number of
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// buckets. The Euler characteristic says that the number of undirected edges
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// is numV + numF -2*genus.
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std::unordered_map<directed_edge,std::pair<int,int>,decltype(edge_hasher) >
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directed_position_edge2face_position_index(2*( numV + numF ), edge_hasher);
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for( int fi = 0; fi < F.rows(); ++fi )
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{
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for( int i = 0; i < 3; ++i )
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{
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const int j = ( i+1 ) % 3;
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directed_position_edge2face_position_index[
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std::make_pair( F(fi,i), F(fi,j) ) ] = std::make_pair( fi, i );
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}
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}
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// First find all undirected position edges (collect a canonical orientation
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// of the directed edges).
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std::unordered_set< directed_edge, decltype( edge_hasher ) >
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undirected_position_edges( numV + numF, edge_hasher );
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for( const auto& el : directed_position_edge2face_position_index )
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{
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// The canonical orientation is the one where the smaller of
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// the two vertex indices is first.
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undirected_position_edges.insert( std::make_pair(
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std::min( el.first.first, el.first.second ),
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std::max( el.first.first, el.first.second ) ) );
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}
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// Now we will iterate over all position edges.
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// Seam edges are the edges whose two opposite directed edges have different
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// texcoord indices (or one doesn't exist at all in the case of a mesh
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// boundary).
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for( const auto& vp_edge : undirected_position_edges )
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{
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// We should only see canonical edges,
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// where the first vertex index is smaller.
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assert( vp_edge.first < vp_edge.second );
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const auto vp_edge_reverse = std::make_pair(vp_edge.second, vp_edge.first);
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// If it and its opposite exist as directed edges, check if their
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// texture coordinate indices match.
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if( directed_position_edge2face_position_index.count( vp_edge ) &&
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directed_position_edge2face_position_index.count( vp_edge_reverse ) )
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{
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const auto forwards =
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directed_position_edge2face_position_index[ vp_edge ];
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const auto backwards =
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directed_position_edge2face_position_index[ vp_edge_reverse ];
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// NOTE: They should never be equal.
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assert( forwards != backwards );
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// If the texcoord indices match (are similarly flipped),
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// this edge is not a seam. It could be a foldover.
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if(
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std::make_pair(
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FTC( forwards.first, forwards.second ),
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FTC( forwards.first, ( forwards.second+1 ) % 3 ) )
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==
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std::make_pair(
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FTC( backwards.first, ( backwards.second+1 ) % 3 ),
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FTC( backwards.first, backwards.second ) ))
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{
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// Check for foldovers in UV space.
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// Get the edge (a,b) and the two opposite vertices's texture
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// coordinates.
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const Vector2S a = TC.row( FTC( forwards.first, forwards.second ) );
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const Vector2S b =
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TC.row( FTC( forwards.first, (forwards.second+1) % 3 ) );
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const Vector2S c_forwards =
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TC.row( FTC( forwards .first, (forwards .second+2) % 3 ) );
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const Vector2S c_backwards =
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TC.row( FTC( backwards.first, (backwards.second+2) % 3 ) );
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// If the opposite vertices' texture coordinates fall on the same side
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// of the edge, we have a UV-space foldover.
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const auto orientation_forwards = Orientation( a, b, c_forwards );
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const auto orientation_backwards = Orientation( a, b, c_backwards );
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if( ( orientation_forwards > 0 && orientation_backwards > 0 ) ||
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( orientation_forwards < 0 && orientation_backwards < 0 )
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) {
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foldovers( num_foldovers, 0 ) = forwards.first;
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foldovers( num_foldovers, 1 ) = forwards.second;
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foldovers( num_foldovers, 2 ) = backwards.first;
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foldovers( num_foldovers, 3 ) = backwards.second;
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num_foldovers += 1;
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}
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}
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// Otherwise, we have a non-matching seam edge.
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else
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{
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seams( num_seams, 0 ) = forwards.first;
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seams( num_seams, 1 ) = forwards.second;
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seams( num_seams, 2 ) = backwards.first;
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seams( num_seams, 3 ) = backwards.second;
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num_seams += 1;
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}
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}
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// Otherwise, the edge and its opposite aren't both in the directed edges.
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// One of them should be.
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else if( directed_position_edge2face_position_index.count( vp_edge ) )
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{
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const auto forwards = directed_position_edge2face_position_index[vp_edge];
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boundaries( num_boundaries, 0 ) = forwards.first;
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boundaries( num_boundaries, 1 ) = forwards.second;
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num_boundaries += 1;
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} else if(
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directed_position_edge2face_position_index.count( vp_edge_reverse ) )
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{
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const auto backwards =
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directed_position_edge2face_position_index[ vp_edge_reverse ];
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boundaries( num_boundaries, 0 ) = backwards.first;
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boundaries( num_boundaries, 1 ) = backwards.second;
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num_boundaries += 1;
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} else {
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// This should never happen! One of these two must have been seen.
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assert(
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directed_position_edge2face_position_index.count( vp_edge ) ||
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directed_position_edge2face_position_index.count( vp_edge_reverse )
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);
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}
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}
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seams .conservativeResize( num_seams, Eigen::NoChange_t() );
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boundaries.conservativeResize( num_boundaries, Eigen::NoChange_t() );
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foldovers .conservativeResize( num_foldovers, Eigen::NoChange_t() );
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}
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#ifdef IGL_STATIC_LIBRARY
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// Explicit template instantiation
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// generated by autoexplicit.sh
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template void igl::seam_edges<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<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<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<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> >&);
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#endif
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