199 lines
8.6 KiB
C++
199 lines
8.6 KiB
C++
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// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2018 Alec Jacobson <alecjacobson@gmail.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 "intrinsic_delaunay_triangulation.h"
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#include "is_intrinsic_delaunay.h"
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#include "tan_half_angle.h"
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#include "unique_edge_map.h"
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#include "flip_edge.h"
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#include "EPS.h"
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#include <iostream>
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#include <queue>
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#include <map>
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template <
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typename Derivedl_in,
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typename DerivedF_in,
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typename Derivedl,
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typename DerivedF>
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IGL_INLINE void igl::intrinsic_delaunay_triangulation(
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const Eigen::MatrixBase<Derivedl_in> & l_in,
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const Eigen::MatrixBase<DerivedF_in> & F_in,
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Eigen::PlainObjectBase<Derivedl> & l,
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Eigen::PlainObjectBase<DerivedF> & F)
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{
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typedef Eigen::Matrix<typename DerivedF::Scalar,Eigen::Dynamic,2> MatrixX2I;
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typedef Eigen::Matrix<typename DerivedF::Scalar,Eigen::Dynamic,1> VectorXI;
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MatrixX2I E,uE;
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VectorXI EMAP;
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std::vector<std::vector<typename DerivedF::Scalar> > uE2E;
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return intrinsic_delaunay_triangulation(l_in,F_in,l,F,E,uE,EMAP,uE2E);
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}
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template <
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typename Derivedl_in,
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typename DerivedF_in,
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typename Derivedl,
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typename DerivedF,
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typename DerivedE,
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typename DeriveduE,
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typename DerivedEMAP,
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typename uE2EType>
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IGL_INLINE void igl::intrinsic_delaunay_triangulation(
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const Eigen::MatrixBase<Derivedl_in> & l_in,
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const Eigen::MatrixBase<DerivedF_in> & F_in,
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Eigen::PlainObjectBase<Derivedl> & l,
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Eigen::PlainObjectBase<DerivedF> & F,
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Eigen::PlainObjectBase<DerivedE> & E,
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Eigen::PlainObjectBase<DeriveduE> & uE,
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Eigen::PlainObjectBase<DerivedEMAP> & EMAP,
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std::vector<std::vector<uE2EType> > & uE2E)
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{
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igl::unique_edge_map(F_in, E, uE, EMAP, uE2E);
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// We're going to work in place
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l = l_in;
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F = F_in;
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typedef typename DerivedF::Scalar Index;
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typedef typename Derivedl::Scalar Scalar;
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const Index num_faces = F.rows();
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// Vector is faster than queue...
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std::vector<Index> Q;
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Q.reserve(uE2E.size());
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for (size_t uei=0; uei<uE2E.size(); uei++)
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{
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Q.push_back(uei);
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}
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// I tried using a "delaunay_since = iter" flag to avoid duplicates, but there
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// was no speed up.
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while(!Q.empty())
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{
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#ifdef IGL_INTRINSIC_DELAUNAY_TRIANGULATION_DEBUG
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// Expensive sanity check
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{
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Eigen::Matrix<bool,Eigen::Dynamic,1> inQ(uE2E.size(),1);
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inQ.setConstant(false);
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for(const auto uei : Q)
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{
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inQ(uei) = true;
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}
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for (Index uei=0; uei<uE2E.size(); uei++)
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{
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if(!inQ(uei) && !is_intrinsic_delaunay(l,uE2E,num_faces,uei))
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{
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std::cout<<" "<<uei<<" might never be fixed!"<<std::endl;
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}
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}
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}
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#endif
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const Index uei = Q.back();
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Q.pop_back();
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if (uE2E[uei].size() == 2)
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{
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if(!is_intrinsic_delaunay(l,uE2E,num_faces,uei))
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{
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// update l just before flipping edge
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// . //
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// /|\ //
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// a/ | \d //
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// / e \ //
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// / | \ //
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// .----|-f--. //
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// \ | / //
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// \ | / //
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// b\α|δ/c //
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// \|/ //
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// . //
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// Annotated from flip_edge:
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// Edge to flip [v1,v2] --> [v3,v4]
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// Before:
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// F(f1,:) = [v1,v2,v4] // in some cyclic order
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// F(f2,:) = [v1,v3,v2] // in some cyclic order
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// After:
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// F(f1,:) = [v1,v3,v4] // in *this* order
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// F(f2,:) = [v2,v4,v3] // in *this* order
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//
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// v1 v1
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// /|\ / \
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// c/ | \b c/f1 \b
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// v3 /f2|f1\ v4 => v3 /__f__\ v4
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// \ e / \ f2 /
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// d\ | /a d\ /a
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// \|/ \ /
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// v2 v2
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//
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// Compute intrinsic length of oppposite edge
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assert(uE2E[uei].size() == 2 && "edge should have 2 incident faces");
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const Index f1 = uE2E[uei][0]%num_faces;
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const Index f2 = uE2E[uei][1]%num_faces;
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const Index c1 = uE2E[uei][0]/num_faces;
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const Index c2 = uE2E[uei][1]/num_faces;
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assert(c1 < 3);
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assert(c2 < 3);
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assert(f1 != f2);
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const Index v1 = F(f1, (c1+1)%3);
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const Index v2 = F(f1, (c1+2)%3);
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const Index v4 = F(f1, c1);
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const Index v3 = F(f2, c2);
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assert(F(f2, (c2+2)%3) == v1);
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assert(F(f2, (c2+1)%3) == v2);
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assert( std::abs(l(f1,c1)-l(f2,c2)) < igl::EPS<Scalar>() );
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const Scalar e = l(f1,c1);
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const Scalar a = l(f1,(c1+1)%3);
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const Scalar b = l(f1,(c1+2)%3);
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const Scalar c = l(f2,(c2+1)%3);
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const Scalar d = l(f2,(c2+2)%3);
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// tan(α/2)
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const Scalar tan_a_2= tan_half_angle(a,b,e);
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// tan(δ/2)
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const Scalar tan_d_2 = tan_half_angle(d,e,c);
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// tan((α+δ)/2)
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const Scalar tan_a_d_2 = (tan_a_2 + tan_d_2)/(1.0-tan_a_2*tan_d_2);
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// cos(α+δ)
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const Scalar cos_a_d =
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(1.0 - tan_a_d_2*tan_a_d_2)/(1.0+tan_a_d_2*tan_a_d_2);
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const Scalar f = sqrt(b*b + c*c - 2.0*b*c*cos_a_d);
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l(f1,0) = f;
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l(f1,1) = b;
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l(f1,2) = c;
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l(f2,0) = f;
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l(f2,1) = d;
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l(f2,2) = a;
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// Important to grab these indices _before_ calling flip_edges (they
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// will be correct after)
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const size_t e_24 = f1 + ((c1 + 1) % 3) * num_faces;
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const size_t e_41 = f1 + ((c1 + 2) % 3) * num_faces;
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const size_t e_13 = f2 + ((c2 + 1) % 3) * num_faces;
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const size_t e_32 = f2 + ((c2 + 2) % 3) * num_faces;
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const size_t ue_24 = EMAP(e_24);
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const size_t ue_41 = EMAP(e_41);
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const size_t ue_13 = EMAP(e_13);
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const size_t ue_32 = EMAP(e_32);
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flip_edge(F, E, uE, EMAP, uE2E, uei);
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Q.push_back(ue_24);
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Q.push_back(ue_41);
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Q.push_back(ue_13);
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Q.push_back(ue_32);
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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 instantiation
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// generated by autoexplicit.sh
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template void igl::intrinsic_delaunay_triangulation<Eigen::Matrix<double, -1, 3, 0, -1, 3>, 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, 3, 0, -1, 3> > 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> >&);
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// generated by autoexplicit.sh
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template void igl::intrinsic_delaunay_triangulation<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
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// generated by autoexplicit.sh
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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::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, int>(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> >&, 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> >&, std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > >&);
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// generated by autoexplicit.sh
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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> >&);
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#endif
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