330 lines
9.3 KiB
C++
330 lines
9.3 KiB
C++
#include "outer_hull.h"
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#include "outer_facet.h"
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#include "facet_components.h"
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#include "winding_number.h"
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#include "triangle_triangle_adjacency.h"
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#include "unique_edge_map.h"
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#include "barycenter.h"
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#include "per_face_normals.h"
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#include "all_edges.h"
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#include "colon.h"
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#include "get_seconds.h"
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#include <Eigen/Geometry>
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#include <vector>
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#include <map>
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#include <queue>
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#include <iostream>
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//#define IGL_OUTER_HULL_DEBUG
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template <
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typename DerivedV,
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typename DerivedF,
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typename DerivedG,
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typename DerivedJ,
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typename Derivedflip>
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IGL_INLINE void igl::outer_hull(
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const Eigen::PlainObjectBase<DerivedV> & V,
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const Eigen::PlainObjectBase<DerivedF> & F,
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Eigen::PlainObjectBase<DerivedG> & G,
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Eigen::PlainObjectBase<DerivedJ> & J,
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Eigen::PlainObjectBase<Derivedflip> & flip)
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{
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using namespace Eigen;
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using namespace std;
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using namespace igl;
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typedef typename DerivedF::Index Index;
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Matrix<Index,DerivedF::RowsAtCompileTime,1> C;
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typedef Matrix<typename DerivedV::Scalar,Dynamic,DerivedV::ColsAtCompileTime> MatrixXV;
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typedef Matrix<typename DerivedF::Scalar,Dynamic,DerivedF::ColsAtCompileTime> MatrixXF;
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typedef Matrix<typename DerivedG::Scalar,Dynamic,DerivedG::ColsAtCompileTime> MatrixXG;
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typedef Matrix<typename DerivedJ::Scalar,Dynamic,DerivedJ::ColsAtCompileTime> MatrixXJ;
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const Index m = F.rows();
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#ifdef IGL_OUTER_HULL_DEBUG
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cout<<"outer hull..."<<endl;
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#endif
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#ifdef IGL_OUTER_HULL_DEBUG
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cout<<"edge map..."<<endl;
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#endif
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typedef Matrix<typename DerivedF::Scalar,Dynamic,2> MatrixX2I;
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typedef Matrix<typename DerivedF::Index,Dynamic,1> VectorXI;
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MatrixX2I E,uE;
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VectorXI EMAP;
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vector<vector<typename DerivedF::Index> > uE2E;
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unique_edge_map(F,E,uE,EMAP,uE2E);
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vector<vector<vector<Index > > > TT,_1;
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triangle_triangle_adjacency(E,EMAP,uE2E,false,TT,_1);
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VectorXI counts;
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#ifdef IGL_OUTER_HULL_DEBUG
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cout<<"facet components..."<<endl;
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#endif
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facet_components(TT,C,counts);
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assert(C.maxCoeff()+1 == counts.rows());
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const size_t ncc = counts.rows();
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G.resize(0,F.cols());
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J.resize(0,1);
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flip.setConstant(m,1,false);
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// precompute face normals
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typename Eigen::Matrix<
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typename DerivedV::Scalar,
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DerivedF::RowsAtCompileTime,
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3> N;
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#ifdef IGL_OUTER_HULL_DEBUG
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cout<<"normals..."<<endl;
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#endif
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per_face_normals(V,F,N);
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#ifdef IGL_OUTER_HULL_DEBUG
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cout<<"reindex..."<<endl;
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#endif
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// H contains list of faces on outer hull;
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vector<bool> FH(m,false);
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vector<bool> EH(3*m,false);
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vector<MatrixXG> vG(ncc);
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vector<MatrixXJ> vJ(ncc);
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vector<MatrixXJ> vIM(ncc);
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for(size_t id = 0;id<ncc;id++)
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{
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vIM[id].resize(counts[id],1);
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}
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// current index into each IM
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vector<size_t> g(ncc,0);
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// place order of each face in its respective component
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for(Index f = 0;f<m;f++)
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{
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vIM[C(f)](g[C(f)]++) = f;
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}
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#ifdef IGL_OUTER_HULL_DEBUG
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cout<<"barycenters..."<<endl;
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#endif
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// assumes that "resolve" has handled any coplanar cases correctly and nearly
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// coplanar cases can be sorted based on barycenter.
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MatrixXV BC;
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barycenter(V,F,BC);
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#ifdef IGL_OUTER_HULL_DEBUG
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cout<<"loop over CCs..."<<endl;
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#endif
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for(Index id = 0;id<(Index)ncc;id++)
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{
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auto & IM = vIM[id];
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// starting face that's guaranteed to be on the outer hull and in this
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// component
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int f;
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bool f_flip;
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#ifdef IGL_OUTER_HULL_DEBUG
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cout<<"outer facet..."<<endl;
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#endif
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outer_facet(V,F,N,IM,f,f_flip);
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int FHcount = 0;
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// Q contains list of face edges to continue traversing upong
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queue<int> Q;
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Q.push(f+0*m);
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Q.push(f+1*m);
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Q.push(f+2*m);
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flip(f) = f_flip;
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#ifdef IGL_OUTER_HULL_DEBUG
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cout<<"BFS..."<<endl;
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#endif
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while(!Q.empty())
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{
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// face-edge
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const int e = Q.front();
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Q.pop();
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// face
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const int f = e%m;
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// corner
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const int c = e/m;
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// Should never see edge again...
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if(EH[e] == true)
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{
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continue;
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}
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EH[e] = true;
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// first time seeing face
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if(!FH[f])
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{
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FH[f] = true;
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FHcount++;
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}
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// find overlapping face-edges
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const auto & neighbors = uE2E[EMAP(e)];
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const auto & fN = (flip(f)?-1.:1.)*N.row(f);
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// source of edge according to f
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const int fs = flip(f)?F(f,(c+2)%3):F(f,(c+1)%3);
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// destination of edge according to f
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const int fd = flip(f)?F(f,(c+1)%3):F(f,(c+2)%3);
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const auto & eV = (V.row(fd)-V.row(fs)).normalized();
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// Loop over and find max dihedral angle
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typename DerivedV::Scalar max_di = -1;
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int max_ne = -1;
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typename Eigen::Matrix< typename DerivedV::Scalar, 1, 3> max_nN;
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for(const auto & ne : neighbors)
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{
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const int nf = ne%m;
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if(nf == f)
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{
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continue;
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}
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const int nc = ne/m;
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// are faces consistently oriented
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//const int ns = F(nf,(nc+1)%3);
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const int nd = F(nf,(nc+2)%3);
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const bool cons = (flip(f)?fd:fs) == nd;
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const auto & nN = (cons? (flip(f)?-1:1.) : (flip(f)?1.:-1.) )*N.row(nf);
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const auto & ndi = M_PI - atan2( fN.cross(nN).dot(eV), fN.dot(nN));
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if(ndi>=max_di)
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{
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max_ne = ne;
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max_di = ndi;
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max_nN = nN;
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}
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}
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if(max_ne>=0)
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{
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const int nf = max_ne%m;
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const int nc = max_ne/m;
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const int nd = F(nf,(nc+2)%3);
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const bool cons = (flip(f)?fd:fs) == nd;
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flip(nf) = (cons ? flip(f) : !flip(f));
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const int ne1 = nf+((nc+1)%3)*m;
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const int ne2 = nf+((nc+2)%3)*m;
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if(!EH[ne1])
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{
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Q.push(ne1);
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}
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if(!EH[ne2])
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{
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Q.push(ne2);
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}
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}
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}
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{
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vG[id].resize(FHcount,3);
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vJ[id].resize(FHcount,1);
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//nG += FHcount;
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size_t h = 0;
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assert(counts(id) == IM.rows());
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for(int i = 0;i<counts(id);i++)
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{
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const size_t f = IM(i);
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//if(f_flip)
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//{
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// flip(f) = !flip(f);
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//}
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if(FH[f])
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{
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vG[id].row(h) = (flip(f)?F.row(f).reverse().eval():F.row(f));
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vJ[id](h,0) = f;
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h++;
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}
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}
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assert((int)h == FHcount);
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}
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}
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// Is A inside B? Assuming A and B are consistently oriented but closed and
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// non-intersecting.
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const auto & is_component_inside_other = [](
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const Eigen::PlainObjectBase<DerivedV> & V,
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const MatrixXV & BC,
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const MatrixXG & A,
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const MatrixXJ & AJ,
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const MatrixXG & B)->bool
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{
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const auto & bounding_box = [](
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const Eigen::PlainObjectBase<DerivedV> & V,
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const MatrixXG & F)->
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MatrixXV
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{
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MatrixXV BB(2,3);
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BB<<
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1e26,1e26,1e26,
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-1e26,-1e26,-1e26;
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const size_t m = F.rows();
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for(size_t f = 0;f<m;f++)
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{
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for(size_t c = 0;c<3;c++)
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{
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const auto & vfc = V.row(F(f,c));
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BB.row(0) = BB.row(0).array().min(vfc.array()).eval();
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BB.row(1) = BB.row(1).array().max(vfc.array()).eval();
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}
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}
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return BB;
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};
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// A lot of the time we're dealing with unrelated, distant components: cull
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// them.
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MatrixXV ABB = bounding_box(V,A);
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MatrixXV BBB = bounding_box(V,B);
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if( (BBB.row(0)-ABB.row(1)).maxCoeff()>0 ||
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(ABB.row(0)-BBB.row(1)).maxCoeff()>0 )
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{
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// bounding boxes do not overlap
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return false;
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}
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////////////////////////////////////////////////////////////////////////
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// POTENTIAL ROBUSTNESS WEAK AREA
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////////////////////////////////////////////////////////////////////////
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//
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// q could be so close (<~1e-16) to B that the winding number is not a robust way to
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// determine inside/outsideness. We could try to find a _better_ q which is
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// farther away, but couldn't they all be bad?
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MatrixXV q = BC.row(AJ(0));
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// In a perfect world, it's enough to test a single point.
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double w;
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winding_number_3(
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V.data(),V.rows(),
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B.data(),B.rows(),
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q.data(),1,&w);
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return fabs(w)>0.5;
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};
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// Reject components which are completely inside other components
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vector<bool> keep(ncc,true);
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size_t nG = 0;
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// This is O( ncc * ncc * m)
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for(size_t id = 0;id<ncc;id++)
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{
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for(size_t oid = 0;oid<ncc;oid++)
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{
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if(id == oid)
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{
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continue;
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}
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keep[id] = keep[id] &&
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!is_component_inside_other(V,BC,vG[id],vJ[id],vG[oid]);
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}
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if(keep[id])
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{
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nG += vJ[id].rows();
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}
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}
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// collect G and J across components
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G.resize(nG,3);
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J.resize(nG,1);
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{
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size_t off = 0;
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for(Index id = 0;id<(Index)ncc;id++)
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{
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if(keep[id])
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{
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assert(vG[id].rows() == vJ[id].rows());
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G.block(off,0,vG[id].rows(),vG[id].cols()) = vG[id];
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J.block(off,0,vJ[id].rows(),vJ[id].cols()) = vJ[id];
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off += vG[id].rows();
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}
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}
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}
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}
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#ifdef IGL_STATIC_LIBRARY
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// Explicit template specialization
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template void igl::outer_hull<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<long, -1, 1, 0, -1, 1>, Eigen::Matrix<bool, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<long, -1, 1, 0, -1, 1> >&, Eigen::PlainObjectBase<Eigen::Matrix<bool, -1, 1, 0, -1, 1> >&);
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#endif
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