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