vendor/libigl/include/igl/predicates/ear_clipping.cpp

// This file is part of libigl, a simple c++ geometry processing library.
//
// Copyright (C) 2019 Hanxiao Shen <hanxiao@cs.nyu.edu>
//
// 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 <igl/slice.h>
#include "ear_clipping.h"
#include "point_inside_convex_polygon.h"
#include "predicates.h"

template <typename DerivedP, typename DerivedRT,
          typename DerivedF, typename DerivedI>
IGL_INLINE void igl::predicates::ear_clipping(
  const Eigen::MatrixBase<DerivedP>& P,
  const Eigen::MatrixBase<DerivedRT>& RT,
  Eigen::PlainObjectBase<DerivedI>& I,
  Eigen::PlainObjectBase<DerivedF>& eF,
  Eigen::PlainObjectBase<DerivedP>& nP
){
  typedef typename DerivedF::Scalar Index;
  typedef typename DerivedP::Scalar Scalar;
  static_assert(std::is_same<typename DerivedI::Scalar,
                             typename DerivedF::Scalar>::value,
                "index type should be consistent");
  
  // check whether vertex i is an ear
  auto is_ear = [](
    const Eigen::MatrixBase<DerivedP>& P,
    const Eigen::MatrixBase<DerivedRT>& RT,
    const Eigen::Matrix<Index,Eigen::Dynamic,1>& L,
    const Eigen::Matrix<Index,Eigen::Dynamic,1>& R,
    const Index i
  ){
    
    Index a = L(i), b = R(i);
    if(RT(i) != 0 || RT(a) != 0 || RT(b) != 0) return false;
    Eigen::Matrix<Scalar,1,2> pa = P.row(a);
    Eigen::Matrix<Scalar,1,2> pb = P.row(b);
    Eigen::Matrix<Scalar,1,2> pi = P.row(i);
    auto r = igl::predicates::orient2d(pa,pi,pb);
    if(r == igl::predicates::Orientation::NEGATIVE || 
       r == igl::predicates::Orientation::COLLINEAR) return false;
    
    // check if any vertex is lying inside triangle (a,b,i);
    Index k=R(b);
    while(k!=a){
      Eigen::Matrix<Scalar,-1,2> T(3,2);
      T<<P.row(a),P.row(i),P.row(b);
      Eigen::Matrix<Scalar,1,2> q=P.row(k);
      if(igl::predicates::point_inside_convex_polygon(T,q))
        return false;
      k=R(k);
    }
    return true;
  };

  Eigen::Matrix<Index,Eigen::Dynamic,1> L(P.rows());
  Eigen::Matrix<Index,Eigen::Dynamic,1> R(P.rows());
  for(int i=0;i<P.rows();i++){
    L(i) = Index((i-1+P.rows())%P.rows());
    R(i) = Index((i+1)%P.rows());
  }

  Eigen::Matrix<Index,Eigen::Dynamic,1> ears; // mark ears
  Eigen::Matrix<Index,Eigen::Dynamic,1> X; // clipped vertices
  ears.setZero(P.rows());
  X.setZero(P.rows());

  // initialize ears
  for(int i=0;i<P.rows();i++){
    ears(i) = is_ear(P,RT,L,R,i);
  }

  // clip ears until none left
  while(ears.maxCoeff()==1){
    
    // find the first ear
    Index e = 0;
    while(e<ears.rows()&&ears(e)!=1) e++;
    
    // find valid neighbors
    Index a = L(e), b = R(e);
    if(a == b) break;

    // clip ear and store face
    eF.conservativeResize(eF.rows()+1,3);
    eF.bottomRows(1)<<a,e,b;
    L(b) = a;
    L(e) = -1;
    R(a) = b;
    R(e) = -1;
    ears(e) = 0; // mark vertex e as non-ear

    // update neighbor's ear status
    ears(a) = is_ear(P,RT,L,R,a);
    ears(b) = is_ear(P,RT,L,R,b);
    X(e) = 1;

    // when only one edge left
    // mark the endpoints as clipped
    if(L(a)==b && R(b)==a){
      X(a) = 1;
      X(b) = 1;
    }
  }
  
  // collect remaining vertices if theres any
  for(int i=0;i<X.rows();i++)
    X(i) = 1-X(i);
  I.resize(X.sum());
  Index j=0;
  for(Index i=0;i<X.rows();i++)
    if(X(i)==1){
      I(j++) = i;
    }
  igl::slice(P,I,1,nP);
}

#ifdef IGL_STATIC_LIBRARY
template void igl::predicates::ear_clipping<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::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<int, -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