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cgal/Skin_surface_3/include/CGAL/triangulate_mixed_complex_3.h

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// Copyright (c) 2005 Rijksuniversiteit Groningen (Netherlands)
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
//
// Author(s) : Nico Kruithof <Nico@cs.rug.nl>
#ifndef CGAL_TRIANGULATE_MIXED_COMPLEX_3
#define CGAL_TRIANGULATE_MIXED_COMPLEX_3
// #include <CGAL/Unique_hash_map.h>
#include <CGAL/Compute_anchor_3.h>
#include <CGAL/Triangulation_data_structure_3.h>
#include <CGAL/Triangulated_mixed_complex_observer_3.h>
#include <CGAL/Triangulation_incremental_builder_3.h>
// NGHK: move this one to SkinSurfaceTraits
#include <CGAL/Mixed_complex_traits_3.h>
CGAL_BEGIN_NAMESPACE
template <class RegularTriangulation_3>
class Combinatorial_mixed_complex_triangulator_3 {
public:
typedef RegularTriangulation_3 Regular;
typedef typename Regular::Geom_traits Regular_traits;
// NGHK: Make private again: private:
typedef typename Regular::Vertex_handle Rt_Vertex_handle;
typedef typename Regular::Edge Rt_Edge;
typedef typename Regular::Facet Rt_Facet;
typedef typename Regular::Cell_handle Rt_Cell_handle;
typedef typename Regular::Finite_vertices_iterator Rt_Finite_vertices_iterator;
typedef typename Regular::Finite_edges_iterator Rt_Finite_edges_iterator;
typedef typename Regular::Finite_facets_iterator Rt_Finite_facets_iterator;
typedef typename Regular::All_cells_iterator Rt_All_cells_iterator;
typedef typename Regular::Finite_cells_iterator Rt_Finite_cells_iterator;
typedef typename Regular::Cell_circulator Rt_Cell_circulator;
typedef Triangulation_simplex_3<Regular> Rt_Simplex;
typedef typename Regular::Bare_point Rt_Point;
typedef typename Regular_traits::FT Rt_FT;
typedef typename Regular::Weighted_point Rt_Weighted_point;
typedef Compute_anchor_3<Regular> Compute_anchor;
typedef std::pair<Rt_Simplex,Rt_Simplex> Symb_anchor;
typedef Symb_anchor Vertex;
class Cell {
public:
Cell(Symb_anchor vs[]) {
for (int i=0; i<4; i++) _vs[i] = vs[i];
}
Cell(const Symb_anchor &vh0,
const Symb_anchor &vh1,
const Symb_anchor &vh2,
const Symb_anchor &vh3)
{
_vs[0] = vh0;
_vs[1] = vh1;
_vs[2] = vh2;
_vs[3] = vh3;
}
Vertex operator[](int i) {
CGAL_assertion((0 <= i) && (i<4));
return _vs[i];
}
private:
Symb_anchor _vs[4];
};
// You might get type differences here:
// The map that maps a Rt_Simplex to an iterator of the map
// (used as union_find_structure)
struct Anchor_map_iterator_tmp;
typedef std::map<Rt_Simplex, Anchor_map_iterator_tmp> Anchor_map;
struct Anchor_map_iterator_tmp : Anchor_map::iterator {
Anchor_map_iterator_tmp()
: Anchor_map::iterator() {}
Anchor_map_iterator_tmp(typename Anchor_map::iterator const &it)
: Anchor_map::iterator(it) {}
};
typedef typename Anchor_map::iterator Anchor_map_iterator;
public:
Combinatorial_mixed_complex_triangulator_3(Regular const &regular,
Rt_FT const &shrink,
bool verbose)
: regular(regular), shrink(shrink), verbose(verbose),
compute_anchor_obj(regular) {
}
public:
template <class OutputIteratorVertices>
void construct_vertices(OutputIteratorVertices vertices);
template <class OutputIteratorCells>
void construct_0_cell(Rt_Vertex_handle rt_vh,
OutputIteratorCells out);
template <class OutputIteratorCells>
void construct_1_cell(const Rt_Finite_edges_iterator &eit,
OutputIteratorCells out);
template <class OutputIteratorCells>
void construct_2_cell(const Rt_Finite_facets_iterator &fit,
OutputIteratorCells out);
template <class OutputIteratorCells>
void construct_3_cell(Rt_Cell_handle rt_ch,
OutputIteratorCells out);
template <class MixedComplexTraits_3>
typename MixedComplexTraits_3::Bare_point
location(const Vertex &v,
const MixedComplexTraits_3 &traits) const {
typename MixedComplexTraits_3::Bare_point p_del =
orthocenter(v.first, traits);
typename MixedComplexTraits_3::Bare_point p_vor =
orthocenter(v.second, traits);
return traits.construct_anchor_point_3_object()(p_del, p_vor);
}
void location(const Vertex &v) const {
}
private:
template <class MixedComplexTraits_3>
typename MixedComplexTraits_3::Bare_point
orthocenter(const Rt_Simplex &s,
const MixedComplexTraits_3 &traits) const {
Weighted_converter_3
<Cartesian_converter<typename Regular_traits::Bare_point::R,
typename MixedComplexTraits_3::K> >
converter;
switch(s.dimension()) {
case 0:
{
Rt_Vertex_handle vh = s;
return converter(vh->point());
}
case 1:
{
Rt_Edge e = s;
return traits.construct_weighted_circumcenter_3_object()
(converter(e.first->vertex(e.second)->point()),
converter(e.first->vertex(e.third)->point()));
}
case 2:
{
Rt_Facet f = s;
return traits.construct_weighted_circumcenter_3_object()
(converter(f.first->vertex((f.second+1)&3)->point()),
converter(f.first->vertex((f.second+2)&3)->point()),
converter(f.first->vertex((f.second+3)&3)->point()));
}
case 3:
{
Rt_Cell_handle ch = s;
return traits.construct_weighted_circumcenter_3_object()
(converter(ch->vertex(0)->point()),
converter(ch->vertex(1)->point()),
converter(ch->vertex(2)->point()),
converter(ch->vertex(3)->point()));
}
}
CGAL_assertion(false);
return typename MixedComplexTraits_3::Weighted_point_3();
}
template <class OutputIteratorVertices>
Vertex add_vertex(Symb_anchor const &anchor,
OutputIteratorVertices vertices);
template <class OutputIteratorCells>
void add_cell(Vertex vh[],
int orient,
OutputIteratorCells cells);
Vertex &get_vertex(Rt_Simplex &sDel, Rt_Simplex &sVor);
void construct_anchor_del(Rt_Simplex const &sDel);
void construct_anchor_vor(Rt_Simplex const &sVor);
void construct_anchors();
Rt_Simplex get_anchor_del(Rt_Simplex const &sDel) {
return find_anchor(anchor_del2, sDel)->first;
}
Rt_Simplex get_anchor_vor(Rt_Simplex const &sVor) {
return find_anchor(anchor_vor2, sVor)->first;
}
Anchor_map_iterator find_anchor(Anchor_map &a_map, Rt_Simplex const&s) {
return find_anchor(a_map, a_map.find(s));
}
Anchor_map_iterator find_anchor(Anchor_map &a_map,
Anchor_map_iterator const&it) {
CGAL_assertion(it != a_map.end());
Anchor_map_iterator it2 = it->second;
while (it2 != it2->second) {
it->second = it2->second;
// NGHK: changed the type for the map-iterator-hack
it2->second = it;
it2 = it->second;
}
return it2;
}
private:
Regular const &regular;
Rt_FT const &shrink;
bool verbose;
Compute_anchor_3<Regular> compute_anchor_obj;
Anchor_map anchor_del2, anchor_vor2;
std::map<Symb_anchor, Vertex> anchors;
};
template <class RegularTriangulation_3>
void
Combinatorial_mixed_complex_triangulator_3<RegularTriangulation_3>::
construct_anchor_del(Rt_Simplex const &sDel) {
Rt_Simplex s = compute_anchor_obj.anchor_del(sDel);
anchor_del2[sDel] = Anchor_map_iterator();
Anchor_map_iterator it = anchor_del2.find(sDel);
Anchor_map_iterator it2 = anchor_del2.find(s);
CGAL_assertion(it != anchor_del2.end());
CGAL_assertion(it2 != anchor_del2.end());
it->second = it2;
// degenerate simplices:
if (compute_anchor_obj.is_degenerate()) {
it = find_anchor(anchor_del2, it);
typename Compute_anchor::Simplex_iterator degenerate_it;
for (degenerate_it = compute_anchor_obj.equivalent_anchors_begin();
degenerate_it != compute_anchor_obj.equivalent_anchors_end();
degenerate_it++) {
Anchor_map_iterator tmp;
it2 = anchor_del2.find(*degenerate_it);
CGAL_assertion(it2 != anchor_del2.end());
// Merge sets:
while (it2 != it2->second) {
tmp = it2->second;
it2->second = it->second;
it2 = tmp;
CGAL_assertion(it2 != anchor_del2.end());
}
it2->second = it->second;
}
}
}
template <class RegularTriangulation_3>
void
Combinatorial_mixed_complex_triangulator_3<RegularTriangulation_3>::
construct_anchor_vor(Rt_Simplex const &sVor) {
Rt_Simplex s = compute_anchor_obj.anchor_vor(sVor);
anchor_vor2[sVor] = Anchor_map_iterator();
Anchor_map_iterator it = anchor_vor2.find(sVor);
Anchor_map_iterator it2 = anchor_vor2.find(s);
CGAL_assertion(it != anchor_vor2.end());
CGAL_assertion(it2 != anchor_vor2.end());
it->second = it2;
// degenerate simplices:
if (compute_anchor_obj.is_degenerate()) {
it = find_anchor(anchor_vor2, it);
typename Compute_anchor::Simplex_iterator degenerate_it;
for (degenerate_it = compute_anchor_obj.equivalent_anchors_begin();
degenerate_it != compute_anchor_obj.equivalent_anchors_end();
degenerate_it++) {
Anchor_map_iterator tmp;
it2 = anchor_vor2.find(*degenerate_it);
// Possibly not found for 2 Voronoi vertices with the same center,
// If the first vertex is inserted and the second is already found.
// see compute_anchor_obj.anchor_vor(Cell_handle)
if (it2 != anchor_vor2.end()) {
CGAL_assertion(it2 != anchor_vor2.end());
// Merge sets:
while (it2 != it2->second) {
tmp = it2->second;
it2->second = it->second;
it2 = tmp;
CGAL_assertion(it2 != anchor_vor2.end());
}
it2->second = it->second;
}
}
}
}
template <class RegularTriangulation_3>
void
Combinatorial_mixed_complex_triangulator_3<RegularTriangulation_3>::
construct_anchors() {
Rt_Finite_vertices_iterator vit;
Rt_Finite_edges_iterator eit;
Rt_Finite_facets_iterator fit;
Rt_Finite_cells_iterator cit;
Rt_Simplex s;
// Compute anchor points:
for (vit=regular.finite_vertices_begin();
vit!=regular.finite_vertices_end(); vit++) {
construct_anchor_del(Rt_Simplex(vit));
}
for (eit=regular.finite_edges_begin();
eit!=regular.finite_edges_end(); eit++) {
s = Rt_Simplex(*eit);
construct_anchor_del(s);
CGAL_assertion(s.dimension() == 1);
}
for (fit=regular.finite_facets_begin();
fit!=regular.finite_facets_end(); fit++) {
s = Rt_Simplex(*fit);
construct_anchor_del(s);
CGAL_assertion(s.dimension() == 2);
}
for (cit=regular.finite_cells_begin();
cit!=regular.finite_cells_end(); cit++) {
s = Rt_Simplex(cit);
construct_anchor_del(s);
construct_anchor_vor(s);
CGAL_assertion(s.dimension() == 3);
}
for (fit=regular.finite_facets_begin();
fit!=regular.finite_facets_end(); fit++) {
s = Rt_Simplex(*fit);
construct_anchor_vor(s);
CGAL_assertion(s.dimension() == 2);
}
for (eit=regular.finite_edges_begin();
eit!=regular.finite_edges_end(); eit++) {
s = Rt_Simplex(*eit);
construct_anchor_vor(s);
CGAL_assertion(s.dimension() == 1);
}
for (vit=regular.finite_vertices_begin();
vit!=regular.finite_vertices_end(); vit++) {
CGAL_assertion(vit->cell() != Rt_Cell_handle());
s = Rt_Simplex(vit);
construct_anchor_vor(s);
CGAL_assertion(s.dimension() == 0);
}
}
// Constructs the vertices of the simplicial complex
template <class RegularTriangulation_3>
template <class OutputIteratorVertices>
void
Combinatorial_mixed_complex_triangulator_3<RegularTriangulation_3>::
construct_vertices(OutputIteratorVertices vertices)
{
Rt_All_cells_iterator acit;
Rt_Finite_cells_iterator cit;
Rt_Finite_facets_iterator fit;
Rt_Finite_edges_iterator eit;
Rt_Finite_vertices_iterator vit;
Rt_Cell_circulator ccir, cstart;
Rt_Vertex_handle v1, v2, v3;
Rt_Edge e;
Rt_Cell_handle c1, c2;
Rt_Simplex sDel, sVor;
Vertex vh;
if (verbose) std::cout << "construct_anchors" << std::endl;
construct_anchors();
if (verbose) std::cout << "9 ";
// anchor dimDel=0, dimVor=3
for (cit=regular.finite_cells_begin();
cit!=regular.finite_cells_end(); cit++) {
sVor = get_anchor_vor(Rt_Simplex(cit));
for (int i=0; i<4; i++) {
sDel = get_anchor_del(Rt_Simplex(cit->vertex(i)));
if (anchors.find(Symb_anchor(sDel,sVor)) == anchors.end()) {
vh = add_vertex(Symb_anchor(sDel,sVor), vertices);
anchors[Symb_anchor(sDel,sVor)] = vh;
CGAL_assertion(vh == get_vertex(sDel, sVor));
}
}
}
if (verbose) std::cout << "8 ";
// anchor dimDel=1, dimVor=3
for (cit=regular.finite_cells_begin(); cit!=regular.finite_cells_end(); cit++) {
sVor = get_anchor_vor(Rt_Simplex(cit));
for (int i=0; i<3; i++) {
for (int j=i+1; j<4; j++) {
sDel = get_anchor_del(Rt_Simplex(Rt_Edge(cit,i,j)));
if (anchors.find(Symb_anchor(sDel,sVor)) == anchors.end()) {
vh = add_vertex(Symb_anchor(sDel,sVor), vertices);
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
}
}
}
if (verbose) std::cout << "7 ";
// anchor dimDel=2, dimVor=3 and dimDel=0, dimVor=2
for (fit=regular.finite_facets_begin(); fit!=regular.finite_facets_end(); fit++) {
// anchor dimDel=2, dimVor=3
c1 = fit->first;
c2 = c1->neighbor(fit->second);
sDel = get_anchor_del(*fit);
if (!regular.is_infinite(c1)) {
sVor = get_anchor_vor(c1);
if (anchors.find(Symb_anchor(sDel,sVor)) == anchors.end()) {
vh = add_vertex(Symb_anchor(sDel,sVor), vertices);
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
}
if (!regular.is_infinite(c2)) {
sVor = get_anchor_vor(c2);
if (anchors.find(Symb_anchor(sDel,sVor)) == anchors.end()) {
vh = add_vertex(Symb_anchor(sDel,sVor), vertices);
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
}
// anchor dimDel=0, dimVor=2
sVor = get_anchor_vor(*fit);
for (int i=1; i<4; i++) {
sDel = get_anchor_del(Rt_Simplex(c1->vertex((fit->second+i)&3)));
if (anchors.find(Symb_anchor(sDel,sVor)) == anchors.end()) {
vh = add_vertex(Symb_anchor(sDel,sVor), vertices);
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
} else {
vh = get_vertex(sDel, sVor);
}
}
}
if (verbose) std::cout << "6 ";
// anchor dimDel=0, dimVor=1
for (eit=regular.finite_edges_begin(); eit!=regular.finite_edges_end(); eit++) {
sVor = get_anchor_vor(*eit);
v1 = eit->first->vertex(eit->second);
v2 = eit->first->vertex(eit->third);
sDel = get_anchor_del(v1);
if (anchors.find(Symb_anchor(sDel,sVor)) == anchors.end()) {
vh = add_vertex(Symb_anchor(sDel,sVor), vertices);
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
sDel = get_anchor_del(v2);
if (anchors.find(Symb_anchor(sDel,sVor)) == anchors.end()) {
vh = add_vertex(Symb_anchor(sDel,sVor), vertices);
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
}
if (verbose) std::cout << "5 ";
// anchor dimDel=3, dimVor=3
for (cit=regular.finite_cells_begin(); cit!=regular.finite_cells_end(); cit++) {
sDel = get_anchor_del(Rt_Simplex(cit));
sVor = get_anchor_vor(Rt_Simplex(cit));
if (anchors.find(Symb_anchor(sDel,sVor)) == anchors.end()) {
vh = add_vertex(Symb_anchor(sDel,sVor), vertices);
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
}
if (verbose) std::cout << "4 ";
// anchor dimDel=0, dimVor=0
for (vit=regular.finite_vertices_begin(); vit!=regular.finite_vertices_end(); vit++) {
sDel = get_anchor_del(Rt_Simplex(vit));
sVor = get_anchor_vor(Rt_Simplex(vit));
if (anchors.find(Symb_anchor(sDel,sVor)) == anchors.end()) {
vh = add_vertex(Symb_anchor(sDel,sVor), vertices);
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
}
if (verbose) std::cout << "3 ";
// anchor dimDel=1, dimVor=2
for (fit=regular.finite_facets_begin(); fit!=regular.finite_facets_end(); fit++) {
c1 = fit->first;
c2 = c1->neighbor(fit->second);
sVor = get_anchor_vor(Rt_Simplex(*fit));
for (int i=1; i<3; i++) {
for (int j=i+1; j<4; j++) {
e.first = c1;
e.second = (fit->second+i)&3;
e.third = (fit->second+j)&3;
sDel = get_anchor_del(Rt_Simplex(e));
if (anchors.find(Symb_anchor(sDel,sVor)) == anchors.end()) {
vh = add_vertex(Symb_anchor(sDel,sVor), vertices);
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
}
}
}
if (verbose) std::cout << "2 ";
// anchor dimDel=2, dimVor=2
for (fit=regular.finite_facets_begin(); fit!=regular.finite_facets_end(); fit++) {
c1 = fit->first;
c2 = c1->neighbor(fit->second);
sVor = get_anchor_vor(Rt_Simplex(*fit));
sDel = get_anchor_del(Rt_Simplex(*fit));
if (anchors.find(Symb_anchor(sDel,sVor)) == anchors.end()) {
vh = add_vertex(Symb_anchor(sDel,sVor), vertices);
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
}
if (verbose) std::cout << "1" << std::endl;
// anchor dimDel=1, dimVor=1
for (eit=regular.finite_edges_begin(); eit!=regular.finite_edges_end(); eit++) {
v1 = eit->first->vertex(eit->second);
v2 = eit->first->vertex(eit->third);
sVor = get_anchor_vor(Rt_Simplex(*eit));
sDel = get_anchor_del(Rt_Simplex(*eit));
if (anchors.find(Symb_anchor(sDel,sVor)) == anchors.end()) {
vh = add_vertex(Symb_anchor(sDel,sVor), vertices);
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
}
}
// Constructs the cells of the mixed complex corresponding
// to Regular vertices
template <class RegularTriangulation_3>
template <class OutputIteratorCells>
void
Combinatorial_mixed_complex_triangulator_3<RegularTriangulation_3>::
construct_0_cell(Rt_Vertex_handle rt_vh, OutputIteratorCells cells)
{
Rt_Simplex sDel_v, sVor_v, sVor_e, sVor_f, sVor_c;
Vertex vh[4];
Rt_Simplex simplex(rt_vh);
sDel_v = get_anchor_del(Rt_Simplex(rt_vh));
sVor_v = get_anchor_vor(Rt_Simplex(rt_vh));
vh[0] = get_vertex(sDel_v,sVor_v);
std::list<Rt_Cell_handle> adj_cells;
typename std::list<Rt_Cell_handle>::iterator adj_cell;
regular.incident_cells(rt_vh, std::back_inserter(adj_cells));
// Construct cells:
for (adj_cell = adj_cells.begin();
adj_cell != adj_cells.end();
adj_cell ++) {
if (!regular.is_infinite(*adj_cell)) {
sVor_c = get_anchor_vor(Rt_Simplex(*adj_cell));
vh[3] = get_vertex(sDel_v,sVor_c);
int index = (*adj_cell)->index(rt_vh);
for (int i=1; i<4; i++) {
sVor_f = get_anchor_vor(Rt_Simplex(Rt_Facet(*adj_cell,(index+i)&3)));
vh[2] = get_vertex(sDel_v,sVor_f);
for (int j=1; j<4; j++) {
if (j!=i) {
sVor_e = get_anchor_vor(
Rt_Simplex(Rt_Edge(*adj_cell,index,(index+j)&3)));
vh[1] = get_vertex(sDel_v,sVor_e);
if ((vh[0] != vh[1]) && (vh[1] != vh[2]) && (vh[2] != vh[3])) {
CGAL_assertion(sVor_v != sVor_e);
CGAL_assertion(sVor_e != sVor_f);
CGAL_assertion(sVor_f != sVor_c);
add_cell(vh,(index + (j==(i%3+1)? 1:0))&1, cells);
}
}
}
}
}
}
}
// Constructs 1-cells of the mixed complex corresponding to edges
// of the regular triangulation
template <class RegularTriangulation_3>
template <class OutputIteratorCells>
void
Combinatorial_mixed_complex_triangulator_3<RegularTriangulation_3>::
construct_1_cell(const Rt_Finite_edges_iterator &e,
OutputIteratorCells cells) {
Rt_Simplex sDel_v, sDel_e, sVor_e, sVor_f, sVor_c;
Vertex vh[4];
Rt_Vertex_handle v[2];
Rt_Simplex mixed_cell_simplex(*e);
sDel_e = get_anchor_del(Rt_Simplex(*e));
sVor_e = get_anchor_vor(Rt_Simplex(*e));
v[0] = e->first->vertex(e->second);
v[1] = e->first->vertex(e->third);
// Construct cells on the side of v[vi]:
for (int vi=0; vi<2; vi++) {
sDel_v = get_anchor_del(Rt_Simplex(v[vi]));
if (!(sDel_v == sDel_e)) {
Rt_Cell_circulator ccir, cstart;
ccir = cstart = regular.incident_cells(*e);
do {
if (!regular.is_infinite(ccir)) {
int index0 = ccir->index(v[vi]);
int index1 = ccir->index(v[1-vi]);
sVor_c = get_anchor_vor(Rt_Simplex(ccir));
for (int fi=1; fi<4; fi++) {
if (((index0+fi)&3) != index1) {
sVor_f =
get_anchor_vor(Rt_Simplex(Rt_Facet(ccir,(index0+fi)&3)));
if ((sVor_c != sVor_f) && (sVor_f != sVor_e)) {
vh[0] = get_vertex(sDel_v, sVor_e);
vh[1] = get_vertex(sDel_e, sVor_e);
vh[2] = get_vertex(sDel_e, sVor_f);
vh[3] = get_vertex(sDel_e, sVor_c);
int orient;
if (((4+index1-index0)&3) == 1) {
orient = (index1 + (fi==2))&1;
} else {
orient = (index1 + (fi==1))&1;
}
// vh: dimension are (01,11,12,13)
add_cell(vh,orient,cells);
vh[1] = get_vertex(sDel_v, sVor_f);
// vh: dimension are (01,02,12,13)
add_cell(vh,1-orient,cells);
vh[2] = get_vertex(sDel_v, sVor_c);
// vh: dimension are (01,02,03,13)
add_cell(vh,orient,cells);
}
}
}
}
ccir ++;
} while (ccir != cstart);
}
}
}
// Constructs 2-cells of the mixed complex corresponding to facets
// of the regular triangulation
template <class RegularTriangulation_3>
template <class OutputIteratorCells>
void
Combinatorial_mixed_complex_triangulator_3<RegularTriangulation_3>::
construct_2_cell(const Rt_Finite_facets_iterator &fit,
OutputIteratorCells cells) {
Rt_Simplex sDel_v, sDel_e, sDel_f, sVor_f, sVor_c;
Vertex vh[4]; // Implicit function over vLabels is increasing ...
Rt_Cell_handle rt_ch;
int index;
rt_ch = fit->first;
index = fit->second;
Rt_Simplex simplex(*fit);
sDel_f = get_anchor_del(Rt_Simplex(*fit));
sVor_f = get_anchor_vor(Rt_Simplex(*fit));
for (int i=0; i<2; i++) { // Do this twice
if (!regular.is_infinite(rt_ch)) {
sVor_c = get_anchor_vor(Rt_Simplex(rt_ch));
vh[3] = get_vertex(sDel_f, sVor_c);
Vertex vh2 = get_vertex(sDel_f, sVor_f);
if (vh2 != vh[3]) {
// Facet and cell do not coincide ..
for (int vi=1; vi<4; vi++) {
sDel_v = get_anchor_del(Rt_Simplex(rt_ch->vertex((index+vi)&3)));
//index_02[rt_ch].V[index][(index+vi)&3];
vh[0] = get_vertex(sDel_v, sVor_f);
for (int ei=1; ei<4; ei++) {
if (vi != ei) {
vh[2] = vh2;
int index0 = (index+vi)&3;
int index1 = (index+ei)&3;
int fi = (6+index-vi-ei)&3;//6-index-index0-index1;
sDel_e =
get_anchor_del(Rt_Simplex(Rt_Edge(rt_ch, index0, index1)));
vh[1] = get_vertex(sDel_e, sVor_f);
//index_12[rt_ch].V[index][(6+index-vi-ei)&3];
if ((vh[0] != vh[1]) && (vh[1] != vh[2])) {
// index0: v0
// index1: v1
// index0+fi&3 == facet
int orient;
if (((4+index1-index0)&3) == 3) {
orient = (index1 + (((4+index0-fi)&3)==2))&1;
} else {
orient = (index1 + (((4+index0-fi)&3)==1))&1;
}
add_cell(vh,orient,cells);
vh[2] = get_vertex(sDel_e, sVor_c);
add_cell(vh,1-orient,cells);
vh[1] = get_vertex(sDel_v, sVor_c);
add_cell(vh,orient,cells);
}
}
}
}
}
}
// swap to the other cell
Rt_Cell_handle ch_old = rt_ch;
rt_ch = rt_ch->neighbor(index);
index = rt_ch->index(ch_old);
}
CGAL_assertion(rt_ch == fit->first);
CGAL_assertion(index == fit->second);
}
// Constructs 3-cells of the mixed complex corresponding to cells
// of the regular triangulation
template <class RegularTriangulation_3>
template <class OutputIteratorCells>
void
Combinatorial_mixed_complex_triangulator_3<RegularTriangulation_3>::
construct_3_cell(Rt_Cell_handle rt_ch,
OutputIteratorCells cells) {
Rt_Simplex sDel_v, sDel_e, sDel_f, sDel_c, sVor_c;
Vertex vh[4];
// construct the tetrahedron:
// C[ch], C[Facet(ch,fi)], C[Edge(ch,ei,vi)], C[ch->vertex(vi)]
sDel_c = get_anchor_del(Rt_Simplex(rt_ch));
sVor_c = get_anchor_vor(Rt_Simplex(rt_ch));
Rt_Simplex simplex = Rt_Simplex(rt_ch);
vh[0] = get_vertex(sDel_c, sVor_c);
for (int fi=0; fi<4; fi++) {
sDel_f = get_anchor_del(Rt_Simplex(Rt_Facet(rt_ch, fi)));
vh[1] = get_vertex(sDel_f, sVor_c);
if (vh[0] != vh[1]) {
for (int vi=1; vi<4; vi++) {
int index0 = (fi+vi)&3;
sDel_v = get_anchor_del(Rt_Simplex(rt_ch->vertex(index0)));
for (int ei=1; ei<4; ei++) {
int index1 = (fi+ei)&3;
if (vi != ei) {
sDel_e = get_anchor_del(Rt_Simplex(Rt_Edge(rt_ch, index0, index1)));
vh[2] = get_vertex(sDel_e, sVor_c);
// index_13[rt_ch].V[edge_index[index0][index1]];
vh[3] = get_vertex(sDel_v, sVor_c);
// index_03[rt_cit].V[index0];
if ((vh[1] != vh[2]) && (vh[2] != vh[3])) {
int orient;
if (((4+index1-index0)&3) == 1) {
orient = (index1 + (vi==2))&1;
} else {
orient = (index1 + (vi==3))&1;
}
add_cell(vh, orient, cells);
}
}
}
}
}
}
}
// Adds a vertex to the simplicial complex
template <class RegularTriangulation_3>
template <class OutputIteratorVertices>
typename Combinatorial_mixed_complex_triangulator_3<RegularTriangulation_3>::
Vertex
Combinatorial_mixed_complex_triangulator_3<RegularTriangulation_3>::
add_vertex (Symb_anchor const &anchor,
OutputIteratorVertices vertices)
{
*vertices++ = anchor;
return anchor;
}
// Gets a vertex from the simplicial complex based on the anchors
template <class RegularTriangulation_3>
typename Combinatorial_mixed_complex_triangulator_3<RegularTriangulation_3>::
Vertex &
Combinatorial_mixed_complex_triangulator_3<RegularTriangulation_3>::
get_vertex (Rt_Simplex &sDel, Rt_Simplex &sVor)
{
Rt_Simplex sDel2 = get_anchor_del(sDel);
Rt_Simplex sVor2 = get_anchor_vor(sVor);
CGAL_assertion(sDel == sDel2);
CGAL_assertion(sVor == sVor2);
Vertex &vh = anchors[Symb_anchor(sDel2,sVor2)];
CGAL_assertion(vh != Vertex());
return vh;
}
// Adds a cell to the simplicial complex
template <class RegularTriangulation_3>
template <class OutputIteratorCells>
void
Combinatorial_mixed_complex_triangulator_3<RegularTriangulation_3>::
add_cell(Vertex vh[], int orient, OutputIteratorCells cells) {
assert((orient==0) || (orient==1));
assert(vh[0] != Vertex()); assert(vh[1] != Vertex());
assert(vh[2] != Vertex()); assert(vh[3] != Vertex());
assert(vh[0] != vh[1]); assert(vh[0] != vh[2]); assert(vh[0] != vh[3]);
assert(vh[1] != vh[2]); assert(vh[1] != vh[3]); assert(vh[2] != vh[3]);
if (orient) {
*cells++ = Cell(vh[0], vh[1], vh[2], vh[3]);
} else {
*cells++ = Cell(vh[0], vh[1], vh[3], vh[2]);
}
}
template <class RegularTriangulation_3,
class OutputTriangulation_3,
class TriangulatedMixedComplexObserver_3>
void
triangulate_mixed_complex_3(RegularTriangulation_3 &rt,
typename RegularTriangulation_3::Geom_traits::FT
const & shrink_factor,
OutputTriangulation_3 &tmc,
TriangulatedMixedComplexObserver_3 &observer,
bool verbose)
{
typedef RegularTriangulation_3 Regular;
typedef typename Regular::Finite_vertices_iterator Rt_Vertices_iterator;
typedef typename Regular::Finite_edges_iterator Rt_Edges_iterator;
typedef typename Regular::Finite_facets_iterator Rt_Facets_iterator;
typedef typename Regular::Finite_cells_iterator Rt_Cells_iterator;
typedef Triangulation_simplex_3<Regular> Rt_Simplex;
typedef Combinatorial_mixed_complex_triangulator_3<RegularTriangulation_3>
CMCT;
typedef typename CMCT::Vertex Cmct_Vertex;
typedef typename CMCT::Cell Cmct_Cell;
typedef Triangulation_incremental_builder_3<OutputTriangulation_3>
Triangulation_incremental_builder;
typedef Mixed_complex_traits_3<typename OutputTriangulation_3::Geom_traits>
Mc_traits;
typedef typename OutputTriangulation_3::Vertex_handle Out_Vertex_handle;
typedef typename OutputTriangulation_3::Cell_handle Out_Cell_handle;
CMCT mc_triangulator(rt, shrink_factor, verbose);
Triangulation_incremental_builder triangulation_incr_builder(tmc);
std::map <Cmct_Vertex, Out_Vertex_handle> vertex_map;
triangulation_incr_builder.begin_triangulation(3);
{ // Vertices
if (verbose) std::cout << "Construct vertices" << std::endl;
std::list<Cmct_Vertex> vertices;
mc_triangulator.construct_vertices(std::back_inserter(vertices));
for (typename std::list<Cmct_Vertex>::iterator vit = vertices.begin();
vit != vertices.end(); vit++) {
Out_Vertex_handle vh = triangulation_incr_builder.add_vertex();
vh->point() = mc_triangulator.location(*vit, Mc_traits(shrink_factor));
vertex_map[*vit] = vh;
observer.after_vertex_insertion(vit->first, vit->second, vh);
}
}
{ // Cells
std::vector<Cmct_Cell> cells;
// mixed cells corresponding to regular vertices
if (verbose) std::cout << "Construct 0 cells" << std::endl;
for (Rt_Vertices_iterator vit = rt.finite_vertices_begin();
vit != rt.finite_vertices_end(); vit ++) {
mc_triangulator.construct_0_cell(vit, std::back_inserter(cells));
Rt_Simplex s(vit);
for (typename std::vector<Cmct_Cell>::iterator it = cells.begin();
it != cells.end(); it++) {
Out_Cell_handle ch =
triangulation_incr_builder.add_cell(vertex_map[((*it)[0])],
vertex_map[((*it)[1])],
vertex_map[((*it)[2])],
vertex_map[((*it)[3])]);
observer.after_cell_insertion(s, ch);
}
cells.clear();
}
// mixed cells corresponding to regular edges
if (verbose) std::cout << "Construct 1 cells" << std::endl;
for (Rt_Edges_iterator eit = rt.finite_edges_begin();
eit != rt.finite_edges_end(); eit ++) {
mc_triangulator.construct_1_cell(eit, std::back_inserter(cells));
Rt_Simplex s(*eit);
for (typename std::vector<Cmct_Cell>::iterator it = cells.begin();
it != cells.end(); it++) {
Out_Cell_handle ch =
triangulation_incr_builder.add_cell(vertex_map[((*it)[0])],
vertex_map[((*it)[1])],
vertex_map[((*it)[2])],
vertex_map[((*it)[3])]);
observer.after_cell_insertion(s, ch);
}
cells.clear();
}
// mixed cells corresponding to regular facets
if (verbose) std::cout << "Construct 2 cells" << std::endl;
for (Rt_Facets_iterator fit = rt.finite_facets_begin();
fit != rt.finite_facets_end(); fit ++) {
mc_triangulator.construct_2_cell(fit, std::back_inserter(cells));
Rt_Simplex s(*fit);
for (typename std::vector<Cmct_Cell>::iterator it = cells.begin();
it != cells.end(); it++) {
Out_Cell_handle ch =
triangulation_incr_builder.add_cell(vertex_map[((*it)[0])],
vertex_map[((*it)[1])],
vertex_map[((*it)[2])],
vertex_map[((*it)[3])]);
observer.after_cell_insertion(s, ch);
}
cells.clear();
}
// mixed cells corresponding to regular cells
if (verbose) std::cout << "Construct 3 cells" << std::endl;
for (Rt_Cells_iterator cit = rt.finite_cells_begin();
cit != rt.finite_cells_end(); cit ++) {
mc_triangulator.construct_3_cell(cit, std::back_inserter(cells));
Rt_Simplex s(cit);
for (typename std::vector<Cmct_Cell>::iterator it = cells.begin();
it != cells.end(); it++) {
Out_Cell_handle ch =
triangulation_incr_builder.add_cell(vertex_map[((*it)[0])],
vertex_map[((*it)[1])],
vertex_map[((*it)[2])],
vertex_map[((*it)[3])]);
observer.after_cell_insertion(s, ch);
}
cells.clear();
}
}
triangulation_incr_builder.end_triangulation();
// // mixed cells corresponding to regular edges
// if (verbose) std::cout << "Construct 1 cells" << std::endl;
// for (Rt_Finite_edges_iterator eit = regular.finite_edges_begin();
// eit != regular.finite_edges_end(); eit ++) {
// construct_1_cell(eit, std::back_inserter(cells));
// }
// // mixed cells corresponding to regular facets
// if (verbose) std::cout << "Construct 2 cells" << std::endl;
// for (Rt_Finite_facets_iterator fit = regular.finite_facets_begin();
// fit != regular.finite_facets_end(); fit ++) {
// construct_2_cell(fit, std::back_inserter(cells));
// }
// // mixed cells corresponding to regular cells
// if (verbose) std::cout << "Construct 3 cells" << std::endl;
// for (Rt_Finite_cells_iterator cit = regular.finite_cells_begin();
// cit != regular.finite_cells_end();
// cit++) {
// construct_3_cell(cit, std::back_inserter(cells));
// }
// triangulation_incr_builder.end_triangulation();
// anchors.clear();
// //remove_small_edges();
// { // NGHK: debug code:
// CGAL_assertion(_tmc.is_valid());
// std::vector<Vertex> ch_vertices;
// _tmc.incident_vertices(_tmc.infinite_vertex(),
// std::back_inserter(ch_vertices));
// for (typename std::vector<Vertex>::iterator
// vit = ch_vertices.begin(); vit != ch_vertices.end(); vit++) {
// CGAL_assertion((*vit)->sign() == POSITIVE);
// }
// }
}
template <
class RegularTriangulation_3,
class TriangulatedMixedComplex_3>
void
triangulate_mixed_complex_3(RegularTriangulation_3 const &regular,
typename RegularTriangulation_3::Geom_traits::FT
const &shrink_factor,
TriangulatedMixedComplex_3 &tmc,
bool verbose)
{
Triangulated_mixed_complex_observer_3<
TriangulatedMixedComplex_3, const RegularTriangulation_3>
observer(shrink_factor);
triangulate_mixed_complex_3(regular, shrink_factor, tmc, observer, verbose);
}
CGAL_END_NAMESPACE
#endif // CGAL_TRIANGULATE_MIXED_COMPLEX_H
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