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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/Compute_anchor_3.h>
#include <CGAL/Union_find.h>
CGAL_BEGIN_NAMESPACE
template <
class RegularTriangulation_3,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3 =
Triangulated_mixed_complex_observer_3<TriangulatedMixedComplex_3,
RegularTriangulation_3> >
class Mixed_complex_triangulator_3 {
public:
typedef typename RegularTriangulation_3::Geom_traits
Regular_traits;
typedef typename TriangulatedMixedComplex_3::Geom_traits
Triangulated_mixed_complex_traits;
typedef RegularTriangulation_3 Regular;
typedef TriangulatedMixedComplex_3 Triangulated_mixed_complex;
typedef TriangulatedMixedComplexObserver_3
Triangulated_mixed_complex_observer;
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 typename Triangulated_mixed_complex::Vertex_handle Tmc_Vertex_handle;
typedef typename Triangulated_mixed_complex::Edge Tmc_Edge;
typedef typename Triangulated_mixed_complex::Facet Tmc_Facet;
typedef typename Triangulated_mixed_complex::Cell_handle Tmc_Cell_handle;
typedef typename Triangulated_mixed_complex::Finite_vertices_iterator
Tmc_Finite_vertices_iterator;
typedef typename Triangulated_mixed_complex::Finite_edges_iterator
Tmc_Finite_edges_iterator;
typedef typename Triangulated_mixed_complex::Finite_facets_iterator
Tmc_Finite_facets_iterator;
typedef typename Triangulated_mixed_complex::All_cells_iterator
Tmc_All_cells_iterator;
typedef typename Triangulated_mixed_complex::Finite_cells_iterator
Tmc_Finite_cells_iterator;
typedef typename Triangulated_mixed_complex::Cell_circulator
Tmc_Cell_circulator;
typedef typename TriangulatedMixedComplex_3::Geom_traits::Point_3 Tmc_Point;
typedef typename Triangulated_mixed_complex::Geom_traits::RT Tmc_RT;
typedef Triangulation_incremental_builder_3<Triangulated_mixed_complex>
Triangulation_incremental_builder;
typedef Compute_anchor_3<Regular> Compute_anchor;
typedef std::pair<Rt_Simplex,Rt_Simplex> Symb_anchor;
public:
Mixed_complex_triangulator_3(
Regular const &regular,
Rt_FT const &shrink,
Triangulated_mixed_complex &triangulated_mixed_complex)
: regular(regular),
shrink(shrink),
triangulated_mixed_complex(triangulated_mixed_complex),
triangulation_incr_builder(triangulated_mixed_complex),
compute_anchor_obj(regular) {
build();
}
Mixed_complex_triangulator_3(
Regular &regular,
Rt_FT const &shrink,
Triangulated_mixed_complex &triangulated_mixed_complex,
Triangulated_mixed_complex_observer &observer)
: regular(regular),
shrink(shrink),
triangulated_mixed_complex(triangulated_mixed_complex),
observer(observer),
triangulation_incr_builder(triangulated_mixed_complex),
compute_anchor_obj(regular) {
build();
}
private:
void build() {
triangulation_incr_builder.begin_triangulation(3);
construct_vertices();
construct_0_cells(); // mixed cells corresponding to regular vertices
construct_1_cells(); // mixed cells corresponding to regular edges
construct_2_cells(); // mixed cells corresponding to regular facets
construct_3_cells(); // mixed cells corresponding to regular cells
triangulation_incr_builder.end_triangulation();
}
Tmc_Vertex_handle add_vertex(Symb_anchor const &anchor);
Tmc_Cell_handle add_cell(Tmc_Vertex_handle vh[], int orient, Rt_Simplex s);
Tmc_Vertex_handle 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 *anchor_del.find(map_del[sDel]);
}
Rt_Simplex get_anchor_vor(Rt_Simplex const &sVor) {
return *anchor_vor.find(map_vor[sVor]);
}
void construct_vertices();
Tmc_Point get_orthocenter(Rt_Simplex const &s);
Tmc_Point get_anchor(Rt_Simplex const &sDel, Rt_Simplex const &sVor);
template <class Point>
Point construct_anchor_point(const Point &center_del,
const Point &center_vor) {
return center_del + shrink*(center_vor - center_del);
}
void construct_0_cells();
void construct_1_cells();
void construct_2_cells();
void construct_3_cells();
private:
Regular const &regular;
Rt_FT const &shrink;
Triangulated_mixed_complex &triangulated_mixed_complex;
Triangulated_mixed_complex_observer &observer;
Triangulation_incremental_builder triangulation_incr_builder;
Construct_weighted_circumcenter_3<
Regular_triangulation_euclidean_traits_3<
Triangulated_mixed_complex_traits> > orthocenter_obj;
Compute_squared_radius_smallest_orthogonal_sphere_3<
Regular_triangulation_euclidean_traits_3<
Triangulated_mixed_complex_traits> > orthoweight_obj;
Compute_anchor_3<Regular> compute_anchor_obj;
Weighted_converter_3<
Cartesian_converter<typename Regular_traits::Bare_point::R,
Triangulated_mixed_complex_traits > >
r2t_converter_object;
const static int edge_index[4][4];
struct Index_c4 { Tmc_Vertex_handle V[4]; };
struct Index_c6 { Tmc_Vertex_handle V[6]; };
struct Index_c44 { Tmc_Vertex_handle V[4][4]; };
struct Index_v {
Unique_hash_map < Rt_Vertex_handle, Tmc_Vertex_handle > V;
};
// Facets on the border of the simplicial complex:
// name is given by (dim del,dim vor)
// index to vertex
Unique_hash_map < Rt_Cell_handle, Index_c4 > index_03;
typedef Union_find<Rt_Simplex> Union_find_anchor;
typedef typename Union_find_anchor::handle Union_find_anchor_handle;
typedef typename Union_find_anchor::iterator Union_find_anchor_iterator;
Union_find_anchor anchor_del, anchor_vor;
std::map<Rt_Simplex, Union_find_anchor_handle> map_del, map_vor;
std::map<Symb_anchor, Tmc_Vertex_handle> anchors;
};
template <
class RegularTriangulation_3,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3>
const int Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3>::
edge_index[4][4] = {{-1,0,1,2},{0,-1,3,4},{1,3,-1,5},{2,4,5,-1}};
template <
class RegularTriangulation_3,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3>
void
Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3>::
construct_anchor_del(Rt_Simplex const &sDel) {
Rt_Simplex sim = sDel;
Union_find_anchor_handle handle = anchor_del.make_set(sDel);
map_del[sDel] = handle;
CGAL_assertion(sim == sDel);
Rt_Simplex s = compute_anchor_obj.anchor_del(sDel);
CGAL_assertion(sim == sDel);
if (sDel != s) {
CGAL_assertion(s != sim);
anchor_del.unify_sets(handle, map_del[s]);
}
// degenerate simplices:
if (compute_anchor_obj.is_degenerate()) {
typename Compute_anchor::Simplex_iterator it;
for (it = compute_anchor_obj.equivalent_anchors_begin();
it != compute_anchor_obj.equivalent_anchors_end(); it++) {
anchor_del.unify_sets(handle, map_del[*it]);
}
}
}
template <
class RegularTriangulation_3,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3>
void
Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3>::
construct_anchor_vor(Rt_Simplex const &sVor) {
Union_find_anchor_handle handle = anchor_vor.make_set(sVor);
map_vor[sVor] = handle;
Rt_Simplex s = compute_anchor_obj.anchor_vor(sVor);
if (sVor != s) {
anchor_vor.unify_sets(handle, map_vor[s]);
}
// degenerate simplices:
if (compute_anchor_obj.is_degenerate()) {
typename Compute_anchor::Simplex_iterator it;
for (it = compute_anchor_obj.equivalent_anchors_begin();
it != compute_anchor_obj.equivalent_anchors_end(); it++) {
typename std::map<Rt_Simplex, Union_find_anchor_handle>::iterator h_it;
h_it = map_vor.find(*it);
// Possibly not found for 2 Voronoi vertices with the same center,
// If the first vertex is inserted and the second is already found.
if (h_it != map_vor.end()) {
anchor_vor.unify_sets(handle, (*h_it).second);
} else {
CGAL_assertion(s.dimension() == 3);
}
}
}
}
template <
class RegularTriangulation_3,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3>
void
Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_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++) {
s = Rt_Simplex(vit);
construct_anchor_del(s);
CGAL_assertion(s.dimension() == 0);
}
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++) {
s = Rt_Simplex(vit);
construct_anchor_vor(s);
CGAL_assertion(s.dimension() == 0);
}
}
// Constructs the vertices of the simplicial complex
template <
class RegularTriangulation_3,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3>
void
Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3>::
construct_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;
Tmc_Vertex_handle vh;
construct_anchors();
// 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));
anchors[Symb_anchor(sDel,sVor)] = vh;
CGAL_assertion(vh == get_vertex(sDel, sVor));
}
}
}
// 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));
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
}
}
}
// 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));
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));
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));
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
} else {
vh = get_vertex(sDel, sVor);
}
}
}
// 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));
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));
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
}
// 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));
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
}
// 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));
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
}
// 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));
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
}
}
}
// 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));
anchors[Symb_anchor(sDel,sVor)] = vh;
assert(vh == get_vertex(sDel, sVor));
}
}
// 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));
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,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3>
void
Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3>::
construct_0_cells() {
Rt_Simplex sDel_v, sVor_v, sVor_e, sVor_f, sVor_c;
Tmc_Vertex_handle vh[4];
for (Rt_Finite_vertices_iterator vit=regular.finite_vertices_begin();
vit!=regular.finite_vertices_end(); vit++) {
Rt_Simplex simplex(vit);
sDel_v = get_anchor_del(Rt_Simplex(vit));
sVor_v = get_anchor_vor(Rt_Simplex(vit));
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(vit, 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(vit);
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);
Tmc_Cell_handle ch =
add_cell(vh,(index + (j==(i%3+1)? 1:0))&1,simplex);
}
}
}
}
}
}
}
}
// Constructs 1-cells of the mixed complex corresponding to edges
// of the regular triangulation
template <
class RegularTriangulation_3,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3>
void
Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3>::construct_1_cells() {
Rt_Simplex sDel_v, sDel_e, sVor_e, sVor_f, sVor_c;
Tmc_Vertex_handle vh[4];
Rt_Vertex_handle v[2];
Tmc_Cell_handle ch;
for (Rt_Finite_edges_iterator eit=regular.finite_edges_begin();
eit!=regular.finite_edges_end(); eit++) {
Rt_Simplex mixed_cell_simplex(*eit);
sDel_e = get_anchor_del(Rt_Simplex(*eit));
sVor_e = get_anchor_vor(Rt_Simplex(*eit));
v[0] = eit->first->vertex(eit->second);
v[1] = eit->first->vertex(eit->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(*eit);
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)
ch = add_cell(vh,orient,mixed_cell_simplex);
vh[1] = get_vertex(sDel_v, sVor_f);
// vh: dimension are (01,02,12,13)
ch = add_cell(vh,1-orient,mixed_cell_simplex);
vh[2] = get_vertex(sDel_v, sVor_c);
// vh: dimension are (01,02,03,13)
ch = add_cell(vh,orient,mixed_cell_simplex);
}
}
}
}
ccir ++;
} while (ccir != cstart);
}
}
}
}
// Constructs 2-cells of the mixed complex corresponding to facets
// of the regular triangulation
template <
class RegularTriangulation_3,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3>
void
Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3>::
construct_2_cells() {
Rt_Simplex sDel_v, sDel_e, sDel_f, sVor_f, sVor_c;
Tmc_Vertex_handle vh[4]; // Implicit function over vLabels is increasing ...
Rt_Cell_handle rt_ch;
int index;
for (Rt_Finite_facets_iterator fit = regular.finite_facets_begin();
fit != regular.finite_facets_end();
fit ++) {
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);
Tmc_Vertex_handle 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,simplex);
vh[2] = get_vertex(sDel_e, sVor_c);
add_cell(vh,1-orient,simplex);
vh[1] = get_vertex(sDel_v, sVor_c);
add_cell(vh,orient,simplex);
}
}
}
}
}
}
// 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,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3>
void
Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3>::
construct_3_cells() {
Rt_Simplex sDel_v, sDel_e, sDel_f, sDel_c, sVor_c;
Tmc_Vertex_handle vh[4];
Tmc_Cell_handle ch;
for (Rt_Finite_cells_iterator cit = regular.finite_cells_begin();
cit != regular.finite_cells_end();
cit++) {
// 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(cit));
sVor_c = get_anchor_vor(Rt_Simplex(cit));
Rt_Simplex simplex = Rt_Simplex(cit);
vh[0] = get_vertex(sDel_c, sVor_c);
for (int fi=0; fi<4; fi++) {
sDel_f = get_anchor_del(Rt_Simplex(Rt_Facet(cit, 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(cit->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(cit, index0, index1)));
vh[2] = get_vertex(sDel_e, sVor_c);
// index_13[cit].V[edge_index[index0][index1]];
vh[3] = get_vertex(sDel_v, sVor_c);
// index_03[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;
}
ch = add_cell(vh, orient, simplex);
}
}
}
}
}
}
}
}
// Adds a vertex to the simplicial complex
template <
class RegularTriangulation_3,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3>
typename Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3>::Tmc_Vertex_handle
Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3>::
add_vertex (Symb_anchor const &anchor)
{
Tmc_Vertex_handle vh;
vh = triangulation_incr_builder.add_vertex();
vh->point() = get_anchor(anchor.first, anchor.second);
observer.after_vertex_insertion(anchor.first, anchor.second, vh);
return vh;
}
// Gets a vertex from the simplicial complex based on the anchors
template <
class RegularTriangulation_3,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3>
typename Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3>::Tmc_Vertex_handle
Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_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);
Tmc_Vertex_handle vh = anchors[Symb_anchor(sDel2,sVor2)];
CGAL_assertion(vh != Tmc_Vertex_handle());
return vh;
}
// Adds a cell to the simplicial complex
template <
class RegularTriangulation_3,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3>
typename Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3>::Tmc_Cell_handle
Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3>::
add_cell(Tmc_Vertex_handle vh[], int orient, Rt_Simplex s) {
assert((orient==0) || (orient==1));
assert(vh[0] != Tmc_Vertex_handle()); assert(vh[1] != Tmc_Vertex_handle());
assert(vh[2] != Tmc_Vertex_handle()); assert(vh[3] != Tmc_Vertex_handle());
assert(vh[1] != vh[2]); assert(vh[1] != vh[3]); assert(vh[1] != vh[4]);
assert(vh[2] != vh[3]); assert(vh[2] != vh[4]); assert(vh[3] != vh[4]);
Tmc_Cell_handle ch;
if (orient) {
if (orientation(vh[0]->point(), vh[1]->point(),
vh[2]->point(), vh[3]->point()) != POSITIVE) {
std::cout << orientation(vh[0]->point(), vh[1]->point(),
vh[2]->point(), vh[3]->point())<< std::endl;
}
CGAL_assertion(orientation(
vh[0]->point(), vh[1]->point(),
vh[2]->point(), vh[3]->point()) == POSITIVE);
ch = triangulation_incr_builder.add_cell(vh[0], vh[1], vh[2], vh[3]);
} else {
CGAL_assertion(orientation(
vh[0]->point(), vh[1]->point(),
vh[3]->point(), vh[2]->point()) == POSITIVE);
ch = triangulation_incr_builder.add_cell(vh[0], vh[1], vh[3], vh[2]);
}
observer.after_cell_insertion(s, ch);
return ch;
}
template <
class RegularTriangulation_3,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3>
typename TriangulatedMixedComplex_3::Geom_traits::Point_3
Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3>::
get_orthocenter(Rt_Simplex const &s) {
Rt_Vertex_handle vh;
Rt_Edge e;
Rt_Facet f;
Rt_Cell_handle ch;
Tmc_Point result;
switch (s.dimension()) {
case 0:
vh=s;
result = r2t_converter_object(vh->point());
break;
case 1:
e=s;
result = orthocenter_obj(
r2t_converter_object(e.first->vertex(e.second)->point()),
r2t_converter_object(e.first->vertex(e.third)->point()));
break;
case 2:
f=s;
result = orthocenter_obj(
r2t_converter_object(
f.first->vertex((f.second+1)&3)->point()),
r2t_converter_object(
f.first->vertex((f.second+2)&3)->point()),
r2t_converter_object(
f.first->vertex((f.second+3)&3)->point()));
break;
case 3:
ch=s;
result = orthocenter_obj(
r2t_converter_object(ch->vertex(0)->point()),
r2t_converter_object(ch->vertex(1)->point()),
r2t_converter_object(ch->vertex(2)->point()),
r2t_converter_object(ch->vertex(3)->point()));
break;
}
return result;
}
template <
class RegularTriangulation_3,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3>
typename TriangulatedMixedComplex_3::Geom_traits::Point_3
Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3>::
get_anchor(Rt_Simplex const &sDel, Rt_Simplex const &sVor)
{
Tmc_Point dfoc = get_orthocenter(sDel);
Tmc_Point vfoc = get_orthocenter(sVor);
return construct_anchor_point(dfoc, vfoc);
}
template <
class RegularTriangulation_3,
class TriangulatedMixedComplex_3,
class TriangulatedMixedComplexObserver_3>
void triangulate_mixed_complex_3(
RegularTriangulation_3 &rt,
typename RegularTriangulation_3::Geom_traits::FT const & shrink_factor,
TriangulatedMixedComplex_3 &tmc,
TriangulatedMixedComplexObserver_3 &observer)
{
typedef Mixed_complex_triangulator_3<
RegularTriangulation_3,
TriangulatedMixedComplex_3,
TriangulatedMixedComplexObserver_3> Mixed_complex_triangulator;
Mixed_complex_triangulator(rt, shrink_factor, tmc, observer);
}
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 &triangulated_mixed_complex)
{
Triangulated_mixed_complex_observer_3<
TriangulatedMixedComplex_3, const RegularTriangulation_3>
observer(shrink_factor);
triangulate_mixed_complex_3(
regular, shrink_factor, triangulated_mixed_complex, observer);
}
CGAL_END_NAMESPACE
#endif // CGAL_TRIANGULATE_MIXED_COMPLEX_H
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