// Copyright (c) 1997 INRIA Sophia-Antipolis (France).
// 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.
//
// $Source: /CVSROOT/CGAL/Packages/Triangulation_2/include/CGAL/Constrained_triangulation_2.h,v $
// $Revision: 1.101 $ $Date: 2004/10/19 14:02:40 $
// $Name: $
//
// Author(s) : Mariette Yvinec, Jean Daniel Boissonnat
#ifndef CGAL_CONSTRAINED_TRIANGULATION_2_H
#define CGAL_CONSTRAINED_TRIANGULATION_2_H
#include <set>
#include <CGAL/triangulation_assertions.h>
#include <CGAL/Triangulation_short_names_2.h>
#include <CGAL/Triangulation_2.h>
#include <CGAL/Constrained_triangulation_face_base_2.h>
#include <CGAL/iterator.h>
#ifdef CGAL_REP_CLASS_DEFINED
#include <CGAL/intersections.h>
#include <CGAL/squared_distance_2.h>
#endif
CGAL_BEGIN_NAMESPACE
struct No_intersection_tag{};
struct Exact_intersections_tag{}; // to be used with an exact number type
struct Exact_predicates_tag{}; // to be used with filtered exact number
template < class Gt,
class Tds = Triangulation_data_structure_2 <
Triangulation_vertex_base_2<Gt>,
Constrained_triangulation_face_base_2<Gt> >,
class Itag = No_intersection_tag >
class Constrained_triangulation_2 : public Triangulation_2<Gt,Tds>
{
public:
typedef Triangulation_2<Gt,Tds> Triangulation;
typedef Constrained_triangulation_2<Gt,Tds,Itag> Constrained_triangulation;
typedef typename Triangulation::Edge Edge;
typedef typename Triangulation::Vertex Vertex;
typedef typename Triangulation::Vertex_handle Vertex_handle;
typedef typename Triangulation::Face_handle Face_handle;
typedef typename Triangulation::Locate_type Locate_type;
typedef typename Triangulation::All_faces_iterator All_faces_iterator;
typedef typename Triangulation::Face_circulator Face_circulator;
typedef typename Triangulation::Edge_circulator Edge_circulator;
typedef typename Triangulation::Vertex_circulator Vertex_circulator;
typedef typename Triangulation::Line_face_circulator Line_face_circulator;
#ifndef CGAL_CFG_USING_BASE_MEMBER_BUG_2
using Triangulation::number_of_vertices;
using Triangulation::cw;
using Triangulation::ccw;
using Triangulation::dimension;
using Triangulation::geom_traits;
using Triangulation::all_faces_begin;
using Triangulation::all_faces_end;
#endif
typedef Gt Geom_traits;
typedef Itag Intersection_tag;
typedef typename Geom_traits::Point_2 Point;
typedef typename Geom_traits::Segment_2 Segment;
typedef std::pair<Point,Point> Constraint;
typedef std::list<Edge> List_edges;
typedef std::list<Face_handle> List_faces;
typedef std::list<Vertex_handle> List_vertices;
typedef std::list<Constraint> List_constraints;
// Tag to mark the presence of a hierarchy of constraints
typedef Tag_false Constraint_hierarchy_tag;
class Less_edge;
typedef std::set<Edge,Less_edge> Edge_set;
Constrained_triangulation_2(const Gt& gt = Gt()) : Triangulation(gt) { }
Constrained_triangulation_2(const Constrained_triangulation_2& ct)
: Triangulation(ct) {}
Constrained_triangulation_2(std::list<Constraint>& lc, const Gt& gt=Gt())
: Triangulation_2<Gt,Tds>(gt)
{
typename List_constraints::iterator lcit=lc.begin();
for( ;lcit != lc.end(); lcit++) {
insert( (*lcit).first, (*lcit).second);
}
CGAL_triangulation_postcondition( this->is_valid() );
}
template<class InputIterator>
Constrained_triangulation_2(InputIterator it,
InputIterator last,
const Gt& gt=Gt() )
: Triangulation_2<Gt,Tds>(gt)
{
for ( ; it != last; it++) {
insert_constraint((*it).first, (*it).second);
}
CGAL_triangulation_postcondition( this->is_valid() );
}
//TODO Is that destructor correct ?
virtual ~Constrained_triangulation_2() {}
// INSERTION
Vertex_handle insert(const Point& p,
Face_handle start = Face_handle() );
Vertex_handle insert(const Point& p,
Locate_type lt,
Face_handle loc,
int li );
Vertex_handle push_back(const Point& a);
// template < class InputIterator >
// int insert(InputIterator first, InputIterator last);
void insert_constraint(const Point& a, const Point& b);
void insert_constraint(Vertex_handle va, Vertex_handle vb);
void push_back(const Constraint& c);
void remove(Vertex_handle v);
void remove_constrained_edge(Face_handle f, int i);
void remove_incident_constraints(Vertex_handle v);
// to be used by Constrained_triangulation_plus_2
template <class OutputItFaces>
OutputItFaces
remove_constrained_edge(Face_handle f, int i, OutputItFaces out)
{
remove_constrained_edge(f, i);
return out;
}
//for backward compatibility
void remove_constraint(Face_handle f, int i) {remove_constrained_edge(f,i);}
void insert(Point a, Point b) { insert_constraint(a, b);}
void insert(Vertex_handle va, Vertex_handle vb) {insert_constraint(va,vb);}
// QUERY
bool is_constrained(Edge e) const;
bool are_there_incident_constraints(Vertex_handle v) const;
bool is_valid(bool verbose = false, int level = 0) const;
// template<class OutputItEdges>
// OutputItEdges incident_constraints(Vertex_handle v,
// OutputItEdges out) const;
class Less_edge
: public std::binary_function<Edge, Edge, bool>
{
public:
Less_edge() {}
bool operator() (const Edge& e1, const Edge& e2) const
{
int ind1=e1.second, ind2=e2.second;
return( (&(*e1.first) < &(*e2.first))
|| ( (&(*e1.first) == &(*e2.first)) && (ind1 < ind2)));
}
};
void file_output(std::ostream& os) const;
protected:
virtual Vertex_handle virtual_insert(const Point& a,
Face_handle start = Face_handle());
virtual Vertex_handle virtual_insert(const Point& a,
Locate_type lt,
Face_handle loc,
int li );
//Vertex_handle special_insert_in_edge(const Point & a, Face_handle f, int i);
void update_constraints_incident(Vertex_handle va,
Vertex_handle c1,
Vertex_handle c2);
void clear_constraints_incident(Vertex_handle va);
void update_constraints_opposite(Vertex_handle va);
void update_constraints(const List_edges &hole);
void mark_constraint(Face_handle fr, int i);
virtual Vertex_handle intersect(Face_handle f, int i,
Vertex_handle vaa,
Vertex_handle vbb);
Vertex_handle intersect(Face_handle f, int i,
Vertex_handle vaa,
Vertex_handle vbb,
No_intersection_tag);
Vertex_handle intersect(Face_handle f, int i,
Vertex_handle vaa,
Vertex_handle vbb,
Exact_intersections_tag);
Vertex_handle intersect(Face_handle f, int i,
Vertex_handle vaa,
Vertex_handle vbb,
Exact_predicates_tag);
public:
// made public for Laurent to find out deleted faces
// when inserting a constraint with most probably
// no intersection
bool find_intersected_faces(Vertex_handle va,
Vertex_handle vb,
List_faces & intersected_faces,
List_edges & list_ab,
List_edges & list_ba,
Vertex_handle& vi);
protected:
virtual void triangulate_hole(List_faces& intersected_faces,
List_edges& conflict_boundary_ab,
List_edges& conflict_boundary_ba);
void triangulate_hole(List_faces& intersected_faces,
List_edges& conflict_boundary_ab,
List_edges& conflict_boundary_ba,
List_edges& new_edges);
void triangulate_half_hole(List_edges & list_edges,
List_edges & new_edges);
void remove_1D(Vertex_handle v);
void remove_2D(Vertex_handle v);
//templated member function
public:
// the int parameter is a work around for VC7 to compile
template < class InputIterator >
#if defined(_MSC_VER) || defined(__SUNPRO_CC)
int insert(InputIterator first, InputIterator last, int i = 0)
#else
int insert(InputIterator first, InputIterator last)
#endif
{
int n = number_of_vertices();
while(first != last){
insert(*first);
++first;
}
return number_of_vertices() - n;
}
//deprecated
template<class OutputIterator>
bool are_there_incident_constraints(Vertex_handle v,
OutputIterator out) const
{
Edge_circulator ec=incident_edges(v), done(ec);
bool are_there = false;
if (ec == 0) return are_there;
do {
if(is_constrained(*ec)) {
*out++ = *ec;
are_there = true;
}
ec++;
} while (ec != done);
return are_there;
}
template<class OutputItEdges>
OutputItEdges incident_constraints(Vertex_handle v,
OutputItEdges out) const {
Edge_circulator ec=incident_edges(v), done(ec);
if (ec == 0) return out;
do {
if(is_constrained(*ec)) *out++ = *ec;
ec++;
} while (ec != done);
return out;
}
// the following fonctions are overloaded
// to take care of constraint marks
template<class EdgeIt>
Vertex_handle star_hole( const Point& p,
EdgeIt edge_begin,
EdgeIt edge_end) {
std::list<Face_handle> empty_list;
return star_hole(p,
edge_begin,
edge_end,
empty_list.begin(),
empty_list.end());
}
template<class EdgeIt, class FaceIt>
Vertex_handle star_hole( const Point& p,
EdgeIt edge_begin,
EdgeIt edge_end,
FaceIt face_begin,
FaceIt face_end)
{
Vertex_handle v = Triangulation::star_hole(p,
edge_begin,
edge_end,
face_begin,
face_end);
// restore constraint status for new faces.
int vindex;
Face_handle fh;
int ih;
Face_circulator fc = incident_faces(v), done(fc);
do {
vindex = fc->index(v);
fc->set_constraint(cw(vindex), false);
fc->set_constraint(ccw(vindex), false);
fh = fc->neighbor(vindex);
ih = fc->mirror_index(vindex);
fc->set_constraint(vindex, fh->is_constrained(ih));
} while (++fc != done);
return v;
}
};
template < class Gt, class Tds, class Itag >
inline
typename Constrained_triangulation_2<Gt,Tds,Itag>::Vertex_handle
Constrained_triangulation_2<Gt,Tds,Itag>::
virtual_insert(const Point& a, Face_handle start)
// virtual version of insert
{
return insert(a,start);
}
template < class Gt, class Tds, class Itag >
inline
typename Constrained_triangulation_2<Gt,Tds,Itag>::Vertex_handle
Constrained_triangulation_2<Gt,Tds,Itag>::
virtual_insert(const Point& a,
Locate_type lt,
Face_handle loc,
int li )
// virtual version of insert
{
return insert(a,lt,loc,li);
}
template < class Gt, class Tds, class Itag >
inline
typename Constrained_triangulation_2<Gt,Tds,Itag>::Vertex_handle
Constrained_triangulation_2<Gt,Tds,Itag>::
insert(const Point& a, Face_handle start)
// inserts point a
// in addition to what is done for non constrained triangulations
// constrained edges are updated
{
Face_handle loc;
int li;
Locate_type lt;
loc = locate(a, lt, li, start);
return Constrained_triangulation::insert(a,lt,loc,li);
}
template < class Gt, class Tds, class Itag >
typename Constrained_triangulation_2<Gt,Tds,Itag>::Vertex_handle
Constrained_triangulation_2<Gt,Tds,Itag>::
insert(const Point& a, Locate_type lt, Face_handle loc, int li)
// insert a point p, whose localisation is known (lt, f, i)
// in addition to what is done for non constrained triangulations
// constrained edges are updated
{
Vertex_handle va;
Vertex_handle v1, v2;
bool insert_in_constrained_edge = false;
if ( lt == Triangulation::EDGE && loc->is_constrained(li) ){
insert_in_constrained_edge = true;
v1=loc->vertex(ccw(li)); //endpoint of the constraint
v2=loc->vertex(cw(li)); // endpoint of the constraint
}
va = Triangulation::insert(a,lt,loc,li);
if (insert_in_constrained_edge) update_constraints_incident(va, v1,v2);
else if(lt != Triangulation::VERTEX) clear_constraints_incident(va);
if (dimension() == 2) update_constraints_opposite(va);
return va;
}
// template < class Gt, class Tds, class Itag >
// typename Constrained_triangulation_2<Gt,Tds,Itag>::Vertex_handle
// Constrained_triangulation_2<Gt, Tds, Itag>::
// special_insert_in_edge(const Point & a, Face_handle f, int i)
// // insert point p in edge(f,i)
// // bypass the precondition for point a to be in edge(f,i)
// // update constrained status
// {
// Vertex_handle va;
// Vertex_handle c1,c2;
// c1 = f->vertex(cw(i)); //endpoint of edge
// c2 = f->vertex(ccw(i)); //endpoint of edge
// bool insert_in_constrained_edge = f->is_constrained(i);
// va = this->_tds.insert_in_edge(f, i);
// va->set_point(a);
// if (insert_in_constrained_edge) update_constraints_incident(va, c1,c2);
// else clear_constraints_incident(va);
// if (dimension() == 2) update_constraints_opposite(va);
// return va;
// }
template < class Gt, class Tds, class Itag >
inline void
Constrained_triangulation_2<Gt,Tds,Itag>::
insert_constraint(const Point& a, const Point& b)
// the algorithm first inserts a and b,
// and then forces the constraint [va,vb]
{
Vertex_handle va= virtual_insert(a);
Vertex_handle vb= virtual_insert(b);
if ( va != vb) insert_constraint(va,vb);
}
template <class Gt, class Tds, class Itag >
inline void
Constrained_triangulation_2<Gt,Tds,Itag>::
insert_constraint(Vertex_handle vaa, Vertex_handle vbb)
// forces the constrained [va,vb]
// [va,vb] will eventually be splitted into several edges
// if a vertex vc of t lies on segment ab
// of if ab intersect some constrained edges
{
CGAL_triangulation_precondition( vaa != vbb);
Vertex_handle vi;
Face_handle fr;
int i;
if(includes_edge(vaa,vbb,vi,fr,i)) {
mark_constraint(fr,i);
if (vi != vbb) {
insert_constraint(vi,vbb);
}
return;
}
List_faces intersected_faces;
List_edges conflict_boundary_ab, conflict_boundary_ba;
bool intersection = find_intersected_faces( vaa, vbb,
intersected_faces,
conflict_boundary_ab,
conflict_boundary_ba,
vi);
if ( intersection) {
if (vi != vaa && vi != vbb) {
insert_constraint(vaa,vi);
insert_constraint(vi,vbb);
}
else insert_constraint(vaa,vbb);
return;
}
triangulate_hole(intersected_faces,
conflict_boundary_ab,
conflict_boundary_ba);
if (vi != vbb) {
insert_constraint(vi,vbb);
}
return;
}
template <class Gt, class Tds, class Itag >
bool
Constrained_triangulation_2<Gt,Tds,Itag>::
find_intersected_faces(Vertex_handle vaa,
Vertex_handle vbb,
List_faces & intersected_faces,
List_edges & list_ab,
List_edges & list_ba,
Vertex_handle & vi)
// vi is set to the first vertex of the triangulation on [vaa,vbb].
// Return true if an intersection with a constrained edge is
// encountered, false otherwise
// When false :
// intersected_faces contains the list if faces intersected by [va,vi]
// list_ab and list_ba represents the boundary of the union
// of the intersected faces oriented cw
// list_ab consists of the edges from vaa to vi (i.e. on the left of a->b)
// list_ba " " from vi to vaa (i.e. on the right of a->b)
{
const Point& aa = vaa->point();
const Point& bb = vbb->point();
Line_face_circulator current_face=Line_face_circulator(vaa, this, bb);
int ind=current_face->index(vaa);
// to deal with the case where the first crossed edge
// is constrained
if(current_face->is_constrained(ind)) {
vi=intersect(current_face, ind, vaa, vbb);
return true;
}
Face_handle lf= current_face->neighbor(ccw(ind));
Face_handle rf= current_face->neighbor(cw(ind));
Orientation orient;
Face_handle previous_face;
Vertex_handle current_vertex;
list_ab.push_back(Edge(lf, lf->index(current_face)));
list_ba.push_front(Edge(rf, rf->index(current_face)));
intersected_faces.push_front(current_face);
// initcd
previous_face=current_face;
++current_face;
ind=current_face->index(previous_face);
current_vertex=current_face->vertex(ind);
// loop over triangles intersected by ab
bool done = false;
while (current_vertex != vbb && !done) {
orient = orientation(aa,bb,current_vertex->point());
int i1, i2;
switch (orient) {
case COLLINEAR :
done = true; // current_vertex is the new endpoint
break;
case LEFT_TURN :
case RIGHT_TURN :
if (orient == LEFT_TURN) {
i1 = ccw(ind) ; //index of second intersected edge of current_face
i2 = cw(ind); //index of non intersected edge of current_face
}
else {
i1 = cw(ind) ; //index of second intersected edge of current_face
i2 = ccw(ind); //index of non intersected edge of current_face
}
if(current_face->is_constrained(i1)) {
vi = intersect(current_face, i1, vaa,vbb);
return true;
}
else {
lf= current_face->neighbor(i2);
intersected_faces.push_front(current_face);
if (orient == LEFT_TURN)
list_ab.push_back(Edge(lf, lf->index(current_face)));
else // orient == RIGHT_TURN
list_ba.push_front(Edge(lf, lf->index(current_face)));
previous_face=current_face;
++current_face;
ind=current_face->index(previous_face);
current_vertex=current_face->vertex(ind);
}
break;
}
}
// last triangle
vi = current_vertex;
intersected_faces.push_front(current_face);
lf= current_face->neighbor(cw(ind));
list_ab.push_back(Edge(lf, lf->index(current_face)));
rf= current_face->neighbor(ccw(ind));
list_ba.push_front(Edge(rf, rf->index(current_face)));
return false;
}
template <class Gt, class Tds, class Itag >
typename Constrained_triangulation_2<Gt,Tds,Itag>::Vertex_handle
Constrained_triangulation_2<Gt,Tds,Itag>::
intersect(Face_handle f, int i,
Vertex_handle vaa,
Vertex_handle vbb)
{
return intersect(f, i, vaa, vbb, Itag());
}
template <class Gt, class Tds, class Itag >
typename Constrained_triangulation_2<Gt,Tds,Itag>::Vertex_handle
Constrained_triangulation_2<Gt,Tds,Itag>::
intersect(Face_handle , int ,
Vertex_handle ,
Vertex_handle ,
No_intersection_tag)
{
std::cerr << " sorry, this triangulation does not deal with"
<< std::endl
<< " intersecting constraints" << std::endl;
CGAL_triangulation_assertion(false);
return Vertex_handle() ;
}
template <class Gt, class Tds, class Itag >
typename Constrained_triangulation_2<Gt,Tds,Itag>::Vertex_handle
Constrained_triangulation_2<Gt,Tds,Itag>::
intersect(Face_handle f, int i,
Vertex_handle vaa,
Vertex_handle vbb,
Exact_intersections_tag)
// compute the intersection of the constraint edge (f,i)
// with the subconstraint (vaa,vbb) being inserted
// insert the intersection point
// split constraint edge (f,i)
// and return the Vertex_handle of the new Vertex
{
std::cerr << "You are using an exact number types" << std::endl;
std::cerr << "using a Constrained_triangulation_plus_2 class" << std::endl;
std::cerr << "would avoid cascading intersection computation" << std::endl;
std::cerr << " and be much more efficient" << std::endl;
const Point& pa = vaa->point();
const Point& pb = vbb->point();
const Point& pc = f->vertex(cw(i))->point();
const Point& pd = f->vertex(ccw(i))->point();
Point pi;
Itag itag = Itag();
CGAL_triangulation_assertion_code( bool ok = )
intersection(geom_traits(), pa, pb, pc, pd, pi, itag );
CGAL_triangulation_assertion(ok);
Vertex_handle vi = virtual_insert(pi, Triangulation::EDGE, f, i);
return vi;
}
template <class Gt, class Tds, class Itag >
typename Constrained_triangulation_2<Gt,Tds,Itag>::Vertex_handle
Constrained_triangulation_2<Gt,Tds,Itag>::
intersect(Face_handle f, int i,
Vertex_handle vaa,
Vertex_handle vbb,
Exact_predicates_tag)
{
Vertex_handle vcc, vdd;
vcc = f->vertex(cw(i));
vdd = f->vertex(ccw(i));
const Point& pa = vaa->point();
const Point& pb = vbb->point();
const Point& pc = vcc->point();
const Point& pd = vdd->point();
Point pi; //creator for point is required here
Itag itag = Itag();
bool ok = intersection(geom_traits(), pa, pb, pc, pd, pi, itag );
Vertex_handle vi;
if ( !ok) { //intersection detected but not computed
int i = limit_intersection(geom_traits(), pa, pb, pc, pd, itag);
switch(i){
case 0 : vi = vaa; break;
case 1 : vi = vbb; break;
case 2 : vi = vcc; break;
case 3 : vi = vdd; break;
}
}
else{ //intersection computed
remove_constrained_edge(f, i);
vi = virtual_insert(pi, f);
}
// vi == vc or vi == vd may happen even if intersection==true
// due to approximate construction of the intersection
if (vi != vcc && vi != vdd) {
insert_constraint(vcc,vi);
insert_constraint(vi, vdd);
}
else {
insert_constraint(vcc,vdd);
}
return vi;
}
template <class Gt, class Tds, class Itag >
inline
typename Constrained_triangulation_2<Gt,Tds,Itag>::Vertex_handle
Constrained_triangulation_2<Gt,Tds,Itag>::
push_back(const Point &p)
{
return insert(p);
}
template <class Gt, class Tds, class Itag >
inline
void
Constrained_triangulation_2<Gt,Tds,Itag>::
push_back(const Constraint &c)
{
insert(c.first, c.second);
}
template < class Gt, class Tds, class Itag >
void
Constrained_triangulation_2<Gt,Tds,Itag>::
update_constraints_incident(Vertex_handle va,
Vertex_handle c1,
Vertex_handle c2)
// update status of edges incident to a
// after insertion in the constrained edge c1c2
{
if (dimension() == 0) return;
if (dimension()== 1) {
Edge_circulator ec=va->incident_edges(), done(ec);
do {
((*ec).first)->set_constraint(2,true);
}while (++ec != done);
}
else{
//dimension() ==2
int cwi, ccwi, indf;
Face_circulator fc=va->incident_faces(), done(fc);
CGAL_triangulation_assertion(fc != 0);
do {
indf = fc->index(va);
cwi=cw(indf);
ccwi=ccw(indf);
if ((fc->vertex(cwi) == c1)||(fc->vertex(cwi) == c2)) {
fc->set_constraint(ccwi,true);
fc->set_constraint(cwi,false);
}
else {
fc->set_constraint(ccwi,false);
fc->set_constraint(cwi,true);
}
++fc;
} while (fc != done);
}
}
template < class Gt, class Tds ,class Itag >
void
Constrained_triangulation_2<Gt,Tds,Itag>::
clear_constraints_incident(Vertex_handle va)
// make the edges incident to a newly created vertex unconstrained
{
Edge_circulator ec=va->incident_edges(), done(ec);
Face_handle f;
int indf;
if ( ec != 0){
do {
f = (*ec).first ;
indf = (*ec).second;
f->set_constraint(indf,false);
if (dimension() == 2) {
f->neighbor(indf)->set_constraint(f->mirror_index(indf),false);
}
} while (++ec != done);
}
return;
}
template < class Gt, class Tds, class Itag >
void
Constrained_triangulation_2<Gt,Tds,Itag>::
update_constraints_opposite(Vertex_handle va)
// update status of edges opposite to a
// after insertion of a
{
CGAL_triangulation_assertion(dimension()==2);
Face_handle f=va->face(), start=f;
int indf;
do {
indf = f->index(va);
if (f->neighbor(indf)->is_constrained(f->mirror_index(indf)) ) {
f->set_constraint(indf,true);
}
else {
f->set_constraint(indf,false);
}
f= f->neighbor(ccw(indf)); // turns ccw around va
} while (f != start);
return;
}
template < class Gt, class Tds, class Itag >
void
Constrained_triangulation_2<Gt,Tds,Itag>::
update_constraints( const List_edges &hole)
{
typename List_edges::const_iterator it = hole.begin();
Face_handle f;
int i;
for ( ; it != hole.end(); it ++) {
f =(*it).first;
i = (*it).second;
if ( f->is_constrained(i) )
(f->neighbor(i))->set_constraint(f->mirror_index(i),true);
else (f->neighbor(i))->set_constraint(f->mirror_index(i),false);
}
}
template < class Gt, class Tds, class Itag >
inline void
Constrained_triangulation_2<Gt,Tds,Itag>::
mark_constraint(Face_handle fr, int i)
{
if (dimension()==1) fr->set_constraint(2, true);
else{
fr->set_constraint(i,true);
fr->neighbor(i)->set_constraint(fr->mirror_index(i),true);
}
return;
}
template < class Gt, class Tds, class Itag >
inline void
Constrained_triangulation_2<Gt,Tds,Itag>::
triangulate_hole(List_faces& intersected_faces,
List_edges& conflict_boundary_ab,
List_edges& conflict_boundary_ba)
{
List_edges new_edges;
triangulate_hole(intersected_faces,
conflict_boundary_ab,
conflict_boundary_ba,
new_edges);
}
template < class Gt, class Tds, class Itag >
void
Constrained_triangulation_2<Gt,Tds,Itag>::
triangulate_hole(List_faces& intersected_faces,
List_edges& conflict_boundary_ab,
List_edges& conflict_boundary_ba,
List_edges& new_edges)
// triangulate the hole limited by conflict_boundary_ab
// and conflict_boundary_ba
// insert the new edges in new-edges
// delete the faces of intersected_faces
{
if ( !conflict_boundary_ab.empty() ) {
triangulate_half_hole(conflict_boundary_ab, new_edges);
triangulate_half_hole(conflict_boundary_ba, new_edges);
// the two faces that share edge ab are neighbors
// their common edge ab is a constraint
Face_handle fr,fl;
fl=(*conflict_boundary_ab.begin()).first;
fr=(*conflict_boundary_ba.begin()).first;
fl->set_neighbor(2, fr);
fr->set_neighbor(2, fl);
fl->set_constraint(2, true);
fr->set_constraint(2, true);
// delete intersected faces
while( ! intersected_faces.empty()) {
fl = intersected_faces.front();
intersected_faces.pop_front();
delete_face(fl);
}
}
}
template < class Gt, class Tds, class Itag >
void
Constrained_triangulation_2<Gt,Tds,Itag>::
remove(Vertex_handle v)
// remove a vertex and updates the constrained edges of the new faces
// precondition : there is no incident constraints
{
CGAL_triangulation_precondition( v != Vertex_handle() );
CGAL_triangulation_precondition( ! is_infinite(v));
CGAL_triangulation_precondition( ! are_there_incident_constraints(v));
if (number_of_vertices() == 1) remove_first(v);
else if (number_of_vertices() == 2) remove_second(v);
else if ( dimension() == 1) remove_1D(v);
else remove_2D(v);
return;
}
template < class Gt, class Tds, class Itag >
void
Constrained_triangulation_2<Gt,Tds,Itag>::
remove_1D(Vertex_handle v)
{
Edge_circulator ec = incident_edges(v), done(ec);
do {
(*ec).first->set_constraint(2,false);
} while (++ec != done);
Triangulation::remove_1D(v);
}
template < class Gt, class Tds, class Itag >
void
Constrained_triangulation_2<Gt,Tds,Itag>::
remove_2D(Vertex_handle v)
{
if (test_dim_down(v)) { this->_tds.remove_dim_down(v);}
else {
List_edges hole;
make_hole(v, hole);
List_edges shell=hole; //save hole because it will be emptied by fill_hole
fill_hole(v, hole);
update_constraints(shell);
delete_vertex(v);
}
return;
}
template < class Gt, class Tds, class Itag >
void
Constrained_triangulation_2<Gt,Tds,Itag>::
remove_constrained_edge(Face_handle f, int i)
{
f->set_constraint(i, false);
if (dimension() == 2)
(f->neighbor(i))->set_constraint(f->mirror_index(i), false);
return;
}
template < class Gt, class Tds, class Itag >
void
Constrained_triangulation_2<Gt,Tds,Itag>::
remove_incident_constraints(Vertex_handle v)
{
Edge_circulator ec=incident_edges(v), done(ec);
if (ec == 0) return;
do {
if(is_constrained(*ec)) { remove_constrained_edge((*ec).first,
(*ec).second);}
ec++;
} while (ec != done);
return;
}
template < class Gt, class Tds, class Itag >
inline bool
Constrained_triangulation_2<Gt,Tds,Itag>::
are_there_incident_constraints(Vertex_handle v) const
{
return are_there_incident_constraints(v, Emptyset_iterator());
}
template < class Gt, class Tds, class Itag >
inline bool
Constrained_triangulation_2<Gt,Tds,Itag>::
is_valid(bool verbose, int level) const
{
bool result = Triangulation::is_valid(verbose,level);
for( All_faces_iterator it = all_faces_begin();
it != all_faces_end() ; it++) {
for(int i=0; i<3; i++) {
Face_handle n = it->neighbor(i);
result = result &&
it->is_constrained(i) == n->is_constrained(n->index(it));
}
}
return result;
}
template < class Gt, class Tds, class Itag >
inline bool
Constrained_triangulation_2<Gt,Tds,Itag>::
is_constrained(Edge e) const
{
return (e.first)->is_constrained(e.second);
}
template < class Gt, class Tds, class Itag >
void
Constrained_triangulation_2<Gt,Tds,Itag>::
triangulate_half_hole(List_edges & list_edges, List_edges & new_edges)
// triangulates the polygon whose boundary consists of list_edges
// plus the edge ab joining the two endpoints of list_edges
// the orientation of the polygon (as provided by list_edges) must
// be cw
// the edges of list_edges are assumed to be edges of a
// triangulation that will be updated by the procedure
// the edges that are created are put in list new_edges
// takes linear time
{
Vertex_handle va,vb; // first and last vertices of list_edges
Face_handle newlf;
Face_handle n1,n2,n;
int ind1, ind2,ind;
Orientation orient;
typename List_edges::iterator current, next, tempo;
current=list_edges.begin();
tempo=list_edges.end();
--tempo;
va=((*current).first)->vertex(ccw((*current).second));
vb=((*tempo).first)->vertex(cw((*tempo).second));
next=current;
++next;
do
{
n1=(*current).first;
ind1=(*current).second;
// in case n1 is no longer a triangle of the new triangulation
if ( n1->neighbor(ind1) != Face_handle() ) {
n=n1->neighbor(ind1);
//ind=n1->mirror_index(ind1);
// mirror_index does not work in this case
ind = cw(n->index(n1->vertex(cw(ind1))));
n1=n->neighbor(ind);
ind1= n->mirror_index(ind);
}
n2=(*next).first;
ind2=(*next).second;
// in case n2 is no longer a triangle of the new triangulation
if (n2->neighbor(ind2) != Face_handle() ) {
n=n2->neighbor(ind2);
// ind=n2->mirror_index(ind2);
// mirror_index does not work in this case
ind = cw(n->index(n2->vertex(cw(ind2))));
n2=n->neighbor(ind);
ind2= n->mirror_index(ind);
}
Vertex_handle v0=n1->vertex(ccw(ind1));
Vertex_handle v1=n1->vertex(cw(ind1));
Vertex_handle v2=n2->vertex(cw(ind2));
orient= orientation(v0->point(),v1->point(),v2->point());
switch (orient) {
case RIGHT_TURN :
// creates the new triangle v0v1v2
// updates the neighbors, the constraints
//and the list of new edges
newlf = create_face(v0,v2,v1);
new_edges.push_back(Edge(newlf,2));
newlf->set_neighbor(1, n1);
newlf->set_neighbor(0, n2);
n1->set_neighbor(ind1, newlf);
n2->set_neighbor(ind2, newlf);
if (n1->is_constrained(ind1)) {
newlf->set_constraint(1,true);
}
if (n2->is_constrained(ind2)) {
newlf->set_constraint(0,true);
}
// v0, v1 or v2.face() may have been removed
v0->set_face(newlf);
v1->set_face(newlf);
v2->set_face(newlf);
// update list_edges
tempo=current;
current=list_edges.insert(current, Edge(newlf,2));
list_edges.erase(tempo);
list_edges.erase(next);
next=current;
if (v0 != va) {--current;}
else {++next;}
break;
case LEFT_TURN :
++current; ++next;
break;
case COLLINEAR :
++current; ++next;
break;
}
} while (list_edges.size()>1);
}
template < class Gt, class Tds, class Itag >
void
Constrained_triangulation_2<Gt, Tds, Itag>::
file_output(std::ostream& os) const
{
Triangulation_2<Gt, Tds>::file_output(os);
// write constrained status
typename Tds::Face_iterator ib = this->_tds.face_iterator_base_begin();
for( ; ib != this->_tds.face_iterator_base_end(); ++ib) {
for(int j = 0; j < 3; ++j){
if (ib->is_constrained(j)) { os << "C";}
else { os << "N";}
if(is_ascii(os)){
if(j==2) {
os << "\n";
} else {
os << ' ';
}
}
}
}
}
template < class Gt, class Tds, class Itag >
std::ostream &
operator<<(std::ostream& os,
const Constrained_triangulation_2<Gt,Tds,Itag> &ct)
{
ct.file_output(os);
return os ;
}
//Helping functions to compute intersections of constrained edges
template<class Gt>
bool
intersection(Gt ,
const typename Gt::Point_2& ,
const typename Gt::Point_2& ,
const typename Gt::Point_2& ,
const typename Gt::Point_2& ,
typename Gt::Point_2& ,
No_intersection_tag)
{
return false;
}
template<class Gt>
bool
intersection(Gt gt,
const typename Gt::Point_2& pa,
const typename Gt::Point_2& pb,
const typename Gt::Point_2& pc,
const typename Gt::Point_2& pd,
typename Gt::Point_2& pi,
Exact_intersections_tag)
{
return compute_intersection(gt,pa,pb,pc,pd,pi);
}
template<class Gt>
inline bool
intersection(Gt gt,
const typename Gt::Point_2& pa,
const typename Gt::Point_2& pb,
const typename Gt::Point_2& pc,
const typename Gt::Point_2& pd,
typename Gt::Point_2& pi,
Exact_predicates_tag)
{
return compute_intersection(gt,pa,pb,pc,pd,pi);
}
template<class Gt>
bool
compute_intersection(Gt gt,
const typename Gt::Point_2& pa,
const typename Gt::Point_2& pb,
const typename Gt::Point_2& pc,
const typename Gt::Point_2& pd,
typename Gt::Point_2& pi)
{
typename Gt::Intersect_2 compute_intersec=gt.intersect_2_object();
typename Gt::Construct_segment_2
construct_segment=gt.construct_segment_2_object();
Object result = compute_intersec(construct_segment(pa,pb),
construct_segment(pc,pd));
return assign(pi, result);
}
template<class Gt>
int
limit_intersection(Gt ,
const typename Gt::Point_2& ,
const typename Gt::Point_2& ,
const typename Gt::Point_2& ,
const typename Gt::Point_2& ,
No_intersection_tag)
{
return 0;
}
template<class Gt>
int
limit_intersection(Gt ,
const typename Gt::Point_2& ,
const typename Gt::Point_2& ,
const typename Gt::Point_2& ,
const typename Gt::Point_2& ,
Exact_intersections_tag)
{
return 0;
}
template<class Gt>
int
limit_intersection(Gt gt,
const typename Gt::Point_2& pa,
const typename Gt::Point_2& pb,
const typename Gt::Point_2& pc,
const typename Gt::Point_2& pd,
Exact_predicates_tag)
{
typename Gt::Construct_line_2 line = gt.construct_line_2_object();
typename Gt::Compute_squared_distance_2
distance = gt.compute_squared_distance_2_object();
typename Gt::Line_2 l1 = line(pa,pb);
typename Gt::Line_2 l2 = line(pc,pd);
int i = 0;
typename Gt::FT dx = distance(l2,pa);
typename Gt::FT db = distance(l2,pb);
typename Gt::FT dc = distance(l1,pc);
typename Gt::FT dd = distance(l1,pd);
if ( db < dx ) { dx = db; i = 1;}
if ( dc < dx ) { dx = dc; i = 2;}
if ( dd < dx ) { i = 3;}
return i;
}
CGAL_END_NAMESPACE
#endif //CGAL_CONSTRAINED_TRIANGULATION_2_H
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