libigl_Martin/include/igl/intrinsic_delaunay_triangulation.cpp

// This file is part of libigl, a simple c++ geometry processing library.
// 
// Copyright (C) 2018 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 "intrinsic_delaunay_triangulation.h"
#include "is_intrinsic_delaunay.h"
#include "tan_half_angle.h"
#include "unique_edge_map.h"
#include "flip_edge.h"
#include "EPS.h"
#include "matlab_format.h"
#include <iostream>
#include <queue>
#include <map>

template <
  typename Derivedl_in,
  typename DerivedF_in,
  typename Derivedl,
  typename DerivedF>
IGL_INLINE void igl::intrinsic_delaunay_triangulation(
  const Eigen::MatrixBase<Derivedl_in> & l_in,
  const Eigen::MatrixBase<DerivedF_in> & F_in,
  Eigen::PlainObjectBase<Derivedl> & l,
  Eigen::PlainObjectBase<DerivedF> & F)
{
  // We're going to work in place
  l = l_in;
  F = F_in;

  typedef Eigen::Matrix<typename DerivedF::Scalar,Eigen::Dynamic,2> MatrixX2I;
  typedef Eigen::Matrix<typename DerivedF::Scalar,Eigen::Dynamic,1> VectorXI;
  MatrixX2I E,uE;
  VectorXI EMAP;
  std::vector<std::vector<typename DerivedF::Scalar> > uE2E;
  igl::unique_edge_map(F, E, uE, EMAP, uE2E);
  typedef typename DerivedF::Scalar Index;
  typedef typename Derivedl::Scalar Scalar;
  const Index num_faces = F.rows();

  // Copied from delaunay_triangulation
  bool all_delaunay = false;
  // Dumb O(#E * #flips). Use queue and gather only edges that could have
  // changed to make this O(#E + #flips). 
  while(!all_delaunay) 
  {
    all_delaunay = true;
    for (size_t uei=0; uei<uE2E.size(); uei++) 
    {
      if (uE2E[uei].size() == 2) 
      {
        if(!is_intrinsic_delaunay(l,F,uE2E,uei)) 
        {
          // update l just before flipping edge
          //      .        //
          //     /|\       //
          //   a/ | \d     //
          //   /  e  \     //
          //  /   |   \    //
          // .----|-f--.   //
          //  \   |   /    //
          //   \  |  /     //
          //   b\α|δ/c     //
          //     \|/       //
          //      .        //
          // Annotated from flip_edge:
          // Edge to flip [v1,v2] --> [v3,v4]
          // Before:
          // F(f1,:) = [v1,v2,v4] // in some cyclic order
          // F(f2,:) = [v1,v3,v2] // in some cyclic order
          // After: 
          // F(f1,:) = [v1,v3,v4] // in *this* order 
          // F(f2,:) = [v2,v4,v3] // in *this* order
          //
          //          v1                 v1
          //          /|\                / \
          //        c/ | \b            c/f1 \b
          //     v3 /f2|f1\ v4  =>  v3 /__f__\ v4
          //        \  e  /            \ f2  /
          //        d\ | /a            d\   /a
          //          \|/                \ /
          //          v2                 v2
          //
          // Compute intrinsic length of oppposite edge
          assert(uE2E[uei].size() == 2 && "edge should have 2 incident faces");
          const Index f1 = uE2E[uei][0]%num_faces;
          const Index f2 = uE2E[uei][1]%num_faces;
          const Index c1 = uE2E[uei][0]/num_faces;
          const Index c2 = uE2E[uei][1]/num_faces;
          assert(c1 < 3);
          assert(c2 < 3);
          assert(f1 != f2);
          const Index v1 = F(f1, (c1+1)%3);
          const Index v2 = F(f1, (c1+2)%3);
          const Index v4 = F(f1, c1);
          const Index v3 = F(f2, c2);
          assert(F(f2, (c2+2)%3) == v1);
          assert(F(f2, (c2+1)%3) == v2);
          // From gptoolbox/mesh/flip_edge.m
          // "If edge-after-flip already  exists then this will create a non-manifold
          // edge"
          // Yes, this can happen: e.g., an edge of a tetrahedron."
          // "If two edges will be the same edge after flip then this will create a
          // non-manifold edge."
          // I dont' think this can happen if we flip one at a time. gptoolbox
          // flips in parallel.
          //
          // Does edge (a,b) exist in the edges of all faces incident on
          // existing unique edge uei.
          //
          // Inputs:
          //   a  1st end-point of query edge
          //   b  2nd end-point of query edge
          //   uei  index into uE/uE2E of unique edge
          //   uE2E  map from unique edges to half-edges (see unique_edge_map)
          //   E  #F*3 by 2 list of half-edges
          //
          const auto edge_exists_near = 
            [&](const Index & a,const Index & b,const Index & uei)->bool
          {
            assert(a!=b);
            // Not handling case where (a,b) is edge of face incident on uei
            // since this can't happen for edge-flipping.
            assert(a!=uE(uei,0));
            assert(a!=uE(uei,1));
            assert(b!=uE(uei,0));
            assert(b!=uE(uei,1));
            // starting with the (2) faces incident on e, consider all faces
            // incident on edges containing either a or b.
            //
            // face_queue  Queue containing faces incident on exactly one of a/b
            std::queue<Index> face_queue;
            const Index f1 = uE2E[uei][0]%num_faces;
            const Index f2 = uE2E[uei][1]%num_faces;
            std::map<Index,bool> pushed;
            face_queue.push(f1);
            pushed[f1] = true;
            face_queue.push(f2);
            pushed[f2] = true;
            while(!face_queue.empty())
            {
              const Index f = face_queue.front();
              face_queue.pop();
              pushed[f] = true;
              // consider each edge of this face
              for(int c = 0;c<3;c++)
              {
                // Unique edge id
                const Index uec = EMAP(c*num_faces+f);
                const Index s = uE(uec,0);
                const Index d = uE(uec,1);
                const bool ona = s == a || d == a;
                const bool onb = s == b || d == b;
                // Is this the edge we're looking for?
                if(ona && onb)
                {
                  return true;
                }
                // not incident on either?
                if(!ona && !onb)
                {
                  continue;
                }
                // loop over all incident half-edges
                for(const auto & he : uE2E[uec])
                {
                  // face of this he
                  const Index fhe = he%num_faces;
                  if(!pushed[fhe])
                  {
                    pushed[fhe] = true;
                    face_queue.push(fhe);
                  }
                }
              }
            }
            return false;
          };

          bool flippable = !edge_exists_near(v3,v4,uei);
          if(flippable)
          {
            all_delaunay = false;

            assert( std::abs(l(f1,c1)-l(f2,c2)) < igl::EPS<Scalar>() );
            const Scalar e = l(f1,c1);
            const Scalar a = l(f1,(c1+1)%3);
            const Scalar b = l(f1,(c1+2)%3);
            const Scalar c = l(f2,(c2+1)%3);
            const Scalar d = l(f2,(c2+2)%3);
            // tan(α/2)
            const Scalar tan_a_2= tan_half_angle(a,b,e);
            // tan(δ/2)
            const Scalar tan_d_2 = tan_half_angle(d,e,c);
            // tan((α+δ)/2)
            const Scalar tan_a_d_2 = (tan_a_2 + tan_d_2)/(1.0-tan_a_2*tan_d_2);
            // cos(α+δ)
            const Scalar cos_a_d = 
              (1.0 - tan_a_d_2*tan_a_d_2)/(1.0+tan_a_d_2*tan_a_d_2);
            const Scalar f = sqrt(b*b + c*c - 2.0*b*c*cos_a_d);
            l(f1,0) = f;
            l(f1,1) = b;
            l(f1,2) = c;
            l(f2,0) = f;
            l(f2,1) = d;
            l(f2,2) = a;
            flip_edge(F, E, uE, EMAP, uE2E, uei);
          }
        }
      }
    }
  }
}

#ifdef IGL_STATIC_LIBRARY
// Explicit template instantiation
// generated by autoexplicit.sh
template void igl::intrinsic_delaunay_triangulation<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::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
#endif