dust3d/thirdparty/cgal/CGAL-5.1/include/CGAL/Triangular_expansion_visibi...

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// Copyright (c) 2013 Technical University Braunschweig (Germany).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v5.1/Visibility_2/include/CGAL/Triangular_expansion_visibility_2.h $
// $Id: Triangular_expansion_visibility_2.h 8bb22d5 2020-03-26T14:23:37+01:00 Sébastien Loriot
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s): Michael Hemmer <michael.hemmer@cgal.org>
//
#ifndef CGAL_TRIANGULAR_EXPANSION_VISIBILITY_2_H
#define CGAL_TRIANGULAR_EXPANSION_VISIBILITY_2_H
#include <CGAL/license/Visibility_2.h>
#include <CGAL/Arrangement_2.h>
#include <boost/shared_ptr.hpp>
#include <CGAL/boost/iterator/transform_iterator.hpp>
#include <CGAL/Constrained_Delaunay_triangulation_2.h>
#include <CGAL/Arr_observer.h>
#include <CGAL/assertions.h>
#include <CGAL/use.h>
namespace CGAL {
template<class Arrangement_2_ , class RegularizationCategory = CGAL::Tag_true >
class Triangular_expansion_visibility_2 {
typedef typename Arrangement_2_::Geometry_traits_2 Geometry_traits_2;
typedef typename Geometry_traits_2::Kernel K;
typedef Triangular_expansion_visibility_2<
Arrangement_2_, RegularizationCategory> Self;
public:
typedef Arrangement_2_ Arrangement_2;
typedef typename Arrangement_2::Traits_2 Traits_2;
typedef typename Arrangement_2::Halfedge Halfedge;
typedef typename Arrangement_2::Halfedge_const_handle Halfedge_const_handle;
typedef typename Arrangement_2::Halfedge_handle Halfedge_handle;
typedef typename Arrangement_2::Edge_const_iterator Edge_const_iterator;
typedef typename Arrangement_2::Ccb_halfedge_const_circulator
Ccb_halfedge_const_circulator;
typedef typename Arrangement_2::Ccb_halfedge_circulator
Ccb_halfedge_circulator;
typedef typename Arrangement_2::Face_const_handle Face_const_handle;
typedef typename Arrangement_2::Face_handle Face_handle;
typedef typename Arrangement_2::Vertex_const_handle Vertex_const_handle;
typedef typename Arrangement_2::Vertex_handle Vertex_handle;
typedef typename K::Point_2 Point_2;
typedef typename Geometry_traits_2::Ray_2 Ray_2;
typedef typename Geometry_traits_2::Segment_2 Segment_2;
typedef typename Geometry_traits_2::Line_2 Line_2;
typedef typename Geometry_traits_2::Vector_2 Vector_2;
typedef typename Geometry_traits_2::Direction_2 Direction_2;
typedef typename Geometry_traits_2::FT Number_type;
typedef typename Geometry_traits_2::Object_2 Object_2;
typedef RegularizationCategory Regularization_category;
typedef CGAL::Tag_true Supports_general_polygon_category;
typedef CGAL::Tag_true Supports_simple_polygon_category;
private:
typedef CGAL::Triangulation_vertex_base_2<K> Vb;
typedef CGAL::Constrained_triangulation_face_base_2<K> Fb;
typedef CGAL::Triangulation_data_structure_2<Vb, Fb> TDS;
typedef CGAL::No_constraint_intersection_requiring_constructions_tag Itag;
typedef CGAL::Constrained_Delaunay_triangulation_2<K, TDS, Itag> CDT;
typedef std::pair<Point_2, Point_2> Constraint;
// Functor to create edge constraints for the CDT out of Halfedges
struct Make_constraint
{
typedef Constraint result_type;
Constraint operator()(const Halfedge& edge) const {
return std::make_pair(edge.source()->point(),
edge.target()->point());
}
};
// Observer to track any changes of the attached arrangement.
class Observer : public Arr_observer<Arrangement_2>
{
typedef Arr_observer<Arrangement_2> Base;
typedef Observer Self;
public:
bool has_changed;
Observer() : Base(), has_changed(false)
{}
Observer(const Arrangement_2& arr)
: Base(const_cast<Arrangement_2&>(arr)), has_changed(false)
{}
// Arr_observer interface
void after_attach() { has_changed = false; }
void after_global_change() { has_changed = true; }
void after_create_vertex(Vertex_handle) { has_changed = true; }
void after_create_boundary_vertex(Vertex_handle) { has_changed = true; }
void after_create_edge(Halfedge_handle) { has_changed = true; }
void after_modify_vertex(Vertex_handle) { has_changed = true; }
void after_modify_edge(Halfedge_handle) { has_changed = true; }
void after_split_edge(Halfedge_handle, Halfedge_handle) {
has_changed = true; }
void after_split_fictitious_edge(Halfedge_handle, Halfedge_handle) {
has_changed = true; }
void after_split_face(Face_handle, Face_handle, bool) {
has_changed = true; }
void after_split_outer_ccb(Face_handle, Ccb_halfedge_circulator,
Ccb_halfedge_circulator) {
has_changed = true; }
void after_split_inner_ccb(Face_handle, Ccb_halfedge_circulator,
Ccb_halfedge_circulator) {
has_changed = true; }
void after_add_outer_ccb(Ccb_halfedge_circulator) { has_changed = true; }
void after_add_inner_ccb(Ccb_halfedge_circulator) { has_changed = true; }
void after_add_isolated_vertex(Vertex_handle) { has_changed = true; }
void after_merge_edge(Halfedge_handle) { has_changed = true; }
void after_merge_fictitious_edge(Halfedge_handle) { has_changed = true; }
void after_merge_face(Face_handle) { has_changed = true; }
void after_merge_outer_ccb(Face_handle, Ccb_halfedge_circulator) {
has_changed = true; }
void after_merge_inner_ccb(Face_handle, Ccb_halfedge_circulator) {
has_changed = true; }
void after_move_outer_ccb(Ccb_halfedge_circulator) { has_changed = true; }
void after_move_inner_ccb(Ccb_halfedge_circulator) { has_changed = true; }
void after_move_isolated_vertex(Vertex_handle) { has_changed = true; }
void after_remove_vertex() { has_changed = true; }
void after_remove_edge() { has_changed = true; }
void after_remove_outer_ccb(Face_handle) { has_changed = true; }
void after_remove_inner_ccb(Face_handle) { has_changed = true; }
};
private:
const Arrangement_2* p_arr;
// May change during visibility computation
mutable Observer observer;
mutable boost::shared_ptr<CDT> p_cdt;
mutable std::vector<Segment_2> needles;
// Copy constructor and assignment not supported
Triangular_expansion_visibility_2(const Self&);
Self& operator= (const Self& );
public:
Triangular_expansion_visibility_2() : p_arr(nullptr){}
/*! Constructor given an arrangement. */
Triangular_expansion_visibility_2 (const Arrangement_2& arr)
: p_arr(&arr), observer(arr)
{
init_cdt();
}
const std::string name() const { return std::string("T_visibility_2"); }
bool is_attached() const {
//std::cout << "is_attached" << std::endl;
return (p_arr != nullptr);
}
void attach(const Arrangement_2& arr) {
if(p_arr != &arr){
p_arr = &arr;
observer.detach();
observer.attach(const_cast<Arrangement_2&>(arr));
init_cdt();
}
//std::cout << "attach done" << std::endl;
}
void detach() {
//std::cout << "detach" << std::endl;
observer.detach();
p_arr = nullptr;
p_cdt.reset();
}
const Arrangement_2& arrangement_2() const {
return *p_arr;
}
template <typename VARR>
typename VARR::Face_handle
compute_visibility(const Point_2& q,
const Face_const_handle face,
VARR& out_arr )
const {
//std::cout << "query in face interior" << std::endl;
if(observer.has_changed) {
init_cdt();
}
out_arr.clear();
needles.clear();
CGAL_USE(face);
CGAL_assertion(!face->is_unbounded());
std::vector<Point_2> raw_output;
typename CDT::Face_handle fh = p_cdt->locate(q);
raw_output.push_back(fh->vertex(1)->point());
if(!p_cdt->is_constrained(get_edge(fh,0))){
//std::cout<< "edge 0 is not constrained" << std::endl;
expand_edge(
q,
fh->vertex(2)->point(),
fh->vertex(1)->point(),
fh,0,std::back_inserter(raw_output));
}
raw_output.push_back(fh->vertex(2)->point());
if(!p_cdt->is_constrained(get_edge(fh,1))){
//std::cout << "edge 1 is not constrained" << std::endl;
expand_edge(
q,
fh->vertex(0)->point(),
fh->vertex(2)->point(),
fh,1,std::back_inserter(raw_output));
}
raw_output.push_back(fh->vertex(0)->point());
if(!p_cdt->is_constrained(get_edge(fh,2))){
//std::cout << "edge 2 is not constrained" << std::endl;
expand_edge(
q,
fh->vertex(1)->point(),
fh->vertex(0)->point(),
fh,2,std::back_inserter(raw_output));
}
return output(raw_output,out_arr);
}
template <typename VARR>
typename VARR::Face_handle
compute_visibility(const Point_2& q,
const Halfedge_const_handle he,
VARR& out_arr)
const {
//std::cout << "visibility_region he" << std::endl;
if(observer.has_changed) {
init_cdt();
}
CGAL_assertion(!he->face()->is_unbounded());
out_arr.clear();
needles.clear();
std::vector<Point_2> raw_output;
typename CDT::Locate_type location;
int index;
typename CDT::Face_handle fh = p_cdt->locate(q,location,index);
CGAL_assertion(location == CDT::EDGE || location == CDT::VERTEX);
//the following code tries to figure out which triangle one should start in.
if(location == CDT::EDGE){
//std::cout << "query on edge" << std::endl;
// this is the easy part, there are only two possible faces
// index indicates the edge = vertex on the other side of the edge
// the next vertex in cw order should be the target of given edge
if(fh->vertex(p_cdt->cw(index))->point() != he->target()->point()){
//std::cout << "need to swap face" << std::endl;
// take face on the other side if this is not the case
typename CDT::Face_handle nfh = fh->neighbor(index);
index = nfh->index(fh);
fh = nfh;
}
CGAL_assertion(fh->vertex(p_cdt->cw(index))->point() == he->target()->point());
CGAL_assertion(!p_cdt->is_infinite(fh->vertex(index)));
// output the edge the query lies on
raw_output.push_back(he->source()->point());
raw_output.push_back(he->target()->point());
if(!p_cdt->is_constrained(get_edge(fh,p_cdt->ccw(index)))){
expand_edge(
q,
fh->vertex(index)->point(), //left
he->target()->point() , //right
fh,
p_cdt->ccw(index),
std::back_inserter(raw_output));
}
raw_output.push_back(fh->vertex(index)->point());
if(!p_cdt->is_constrained(get_edge(fh,p_cdt->cw(index)))){
expand_edge(
q,
he->source()->point() , //left
fh->vertex(index)->point(), //right
fh,
p_cdt->cw(index),
std::back_inserter(raw_output));
}
}
if(location == CDT::VERTEX){
//std::cout << "query on vertex" << std::endl;
//bool query_point_on_vertex_is_not_working_yet = false;
//CGAL_assertion(query_point_on_vertex_is_not_working_yet);
CGAL_assertion(q == he->target()->point());
CGAL_assertion(fh->vertex(index)->point() == he->target()->point());
// push points that are seen anyway
// raw_output.push_back(he->source()->point()); inserted last
raw_output.push_back(he->target()->point());
raw_output.push_back(he->next()->target()->point());
// now start in the triangle that contains he->next()
while(
p_cdt->is_infinite(fh->vertex(p_cdt->ccw(index))) ||
he->next()->target()->point() !=
fh->vertex(p_cdt->ccw(index))->point()
)
{
typename CDT::Face_handle nfh = fh->neighbor(p_cdt->ccw(index));
int nindex = nfh->index(fh);
index = p_cdt->ccw(nindex);
fh = nfh;
CGAL_assertion(he->target()->point() == fh->vertex(index)->point());
}
CGAL_assertion(he->next()->source()->point() == fh->vertex(index)->point());
CGAL_assertion(he->next()->target()->point() ==
fh->vertex(p_cdt->ccw(index))->point());
CGAL_assertion(!p_cdt->is_infinite(fh));
CGAL_assertion(p_cdt->is_constrained(get_edge(fh,p_cdt->cw(index))));
while(he->source()->point() != fh->vertex(p_cdt->ccw(index))->point()){
if(!p_cdt->is_constrained(get_edge(fh,index))){
expand_edge(
q,
fh->vertex(p_cdt-> cw(index))->point(), //left
fh->vertex(p_cdt->ccw(index))->point(), //right
fh,
index,
std::back_inserter(raw_output));
}
// push left end point of edge into output
raw_output.push_back(fh->vertex(p_cdt-> cw(index))->point());
// take the next triangle around q in ccw order
typename CDT::Face_handle nfh = fh->neighbor(p_cdt->ccw(index));
int nindex = nfh->index(fh);
index = p_cdt->ccw(nindex);
fh = nfh;
CGAL_assertion(fh->vertex(index)->point() == he->target()->point());
}
}
return output(raw_output,out_arr);
}
private:
typename CDT::Edge get_edge(typename CDT::Face_handle fh, int i) const {
return std::make_pair(fh,i);
}
Point_2 ray_seg_intersection(
const Point_2& q, const Point_2& b, // the ray
const Point_2& s, const Point_2& t // the segment
) const {
Ray_2 ray(q,b);
Segment_2 seg(s,t);
CGAL_assertion(typename K::Do_intersect_2()(ray,seg));
CGAL::Object obj = typename K::Intersect_2()(ray,seg);
Point_2 result = object_cast<Point_2>(obj);
return result;
}
void collect_needle(
const Point_2& q,
const typename CDT::Vertex_handle vh,
const typename CDT::Face_handle fh,
int index)
const {
// the expanded edge should not be constrained
CGAL_assertion(!p_cdt->is_constrained(get_edge(fh,index)));
CGAL_assertion(!p_cdt->is_infinite(fh));
// go into the new face
const typename CDT::Face_handle nfh(fh->neighbor(index));
CGAL_assertion(!p_cdt->is_infinite(nfh));
// get indices of neighbors
int nindex = nfh->index(fh); // index of new vertex and old face
int rindex = p_cdt->ccw(nindex); // index of face behind right edge
int lindex = p_cdt-> cw(nindex); // index of face behind left edge
// get vertices seen from entering edge
const typename CDT::Vertex_handle nvh(nfh->vertex(nindex));
const typename CDT::Vertex_handle rvh(nfh->vertex(p_cdt->cw (nindex)));
const typename CDT::Vertex_handle lvh(nfh->vertex(p_cdt->ccw(nindex)));
CGAL_assertion(!p_cdt->is_infinite(nvh));
CGAL_assertion(!p_cdt->is_infinite(lvh));
CGAL_assertion(!p_cdt->is_infinite(rvh));
// get edges seen from entering edge
typename CDT::Edge re = get_edge(nfh,p_cdt->ccw(nindex));
typename CDT::Edge le = get_edge(nfh,p_cdt-> cw(nindex));
// do orientation computation once for new vertex
typename K::Orientation_2 orientation =
p_cdt->geom_traits().orientation_2_object();
CGAL::Orientation orient = orientation(q,vh->point(),nvh->point());
//std::cout << "\n collect_needle" <<std::endl;
//std::cout << "q "<< q << std::endl ;
//std::cout << "vh->point() "<< vh->point() << std::endl;
//std::cout << "lvh->point() "<< lvh->point() << std::endl ;
//std::cout << "nvh->point() "<< nvh->point() << std::endl ;
//std::cout << "rvh->point() "<< rvh->point() << std::endl<< std::endl;
switch ( orient ) {
case CGAL::COUNTERCLOCKWISE:
// looking on to the right edge
if(p_cdt->is_constrained(re)) {
if(vh != rvh) {
Point_2 p = ray_seg_intersection(q, vh->point(),
nvh->point(), rvh->point());
//std::cout << vh->point() <<" -1- "<< p <<std::endl;
needles.push_back(Segment_2(vh->point(),p));
}
} else {
collect_needle(q,vh,nfh,rindex);
}
break;
case CGAL::CLOCKWISE:
// looking on to the left edge
if(p_cdt->is_constrained(le)){
if(vh != lvh){
Point_2 p = ray_seg_intersection(q, vh->point(),
nvh->point(), lvh->point());
//std::cout << vh->point() <<" -2- "<< p <<std::endl;
needles.push_back(Segment_2(vh->point(),p));
}
} else {
collect_needle(q,vh,nfh,lindex);
}
break;
default:
CGAL_assertion(orient == CGAL::COLLINEAR);
// looking on nvh, so it must be reported
// if it wasn't already (triangles rotate around vh)
if(vh != nvh){
//std::cout << vh->point() <<" -3- "<< nvh->point() <<std::endl;
needles.push_back(Segment_2(vh->point(),nvh->point()));
}
// but we may also contiue looking along the vertex
if(!p_cdt->is_constrained(re)) {
collect_needle(q,nvh,nfh,rindex);
}
if(!p_cdt->is_constrained(le)) {
collect_needle(q,nvh,nfh,lindex);
}
break;
}
}
template<class OIT>
OIT expand_edge(
const Point_2& q,
const Point_2& left,
const Point_2& right,
typename CDT::Face_handle fh,
int index,
OIT oit)
const {
// the expanded edge should not be constrained
CGAL_assertion(!p_cdt->is_constrained(get_edge(fh,index)));
CGAL_assertion(!p_cdt->is_infinite(fh));
// go into the new face
const typename CDT::Face_handle nfh(fh->neighbor(index));
CGAL_assertion(!p_cdt->is_infinite(nfh));
// get indices of neighbors
int nindex = nfh->index(fh); // index of new vertex and old face
int rindex = p_cdt->ccw(nindex); // index of face behind right edge
int lindex = p_cdt-> cw(nindex); // index of face behind left edge
// get vertices seen from entering edge
const typename CDT::Vertex_handle nvh(nfh->vertex(nindex));
const typename CDT::Vertex_handle rvh(nfh->vertex(p_cdt->cw (nindex)));
const typename CDT::Vertex_handle lvh(nfh->vertex(p_cdt->ccw(nindex)));
CGAL_assertion(!p_cdt->is_infinite(nvh));
CGAL_assertion(!p_cdt->is_infinite(lvh));
CGAL_assertion(!p_cdt->is_infinite(rvh));
// get edges seen from entering edge
typename CDT::Edge re = get_edge(nfh,p_cdt->ccw(nindex));
typename CDT::Edge le = get_edge(nfh,p_cdt-> cw(nindex));
// do orientation computation once for new vertex
typename K::Orientation_2 orientation =
p_cdt->geom_traits().orientation_2_object();
CGAL::Orientation ro = orientation(q,right,nvh->point());
CGAL::Orientation lo = orientation(q,left ,nvh->point());
CGAL_assertion(typename K::Orientation_2()(q,left ,lvh->point())
!= CGAL::CLOCKWISE);
CGAL_assertion(typename K::Orientation_2()(q,right,rvh->point())
!= CGAL::COUNTERCLOCKWISE);
//std::cout << (ro == CGAL::COUNTERCLOCKWISE) << " " <<
//(lo == CGAL::CLOCKWISE) << std::endl;
//right edge is seen if new vertex is counter clockwise of right boarder
if(ro == CGAL::COUNTERCLOCKWISE){
if(p_cdt->is_constrained(re)){
// the edge is constrained
// report intersection with right boarder ray
// if it is not already the right vertex (already reported)
if(right != rvh->point()){
*oit++ = ray_seg_intersection(q,right,nvh->point(),rvh->point());
}
// then report intersection with left boarder if it exists
if(lo == CGAL::COUNTERCLOCKWISE){
*oit++ = ray_seg_intersection(q,left,nvh->point(),rvh->point());
}
}else{
// the edge is not a constrained
if(lo == CGAL::COUNTERCLOCKWISE){
// no split needed and return
//std::cout<< "h1"<< std::endl;
oit = expand_edge(q,left,right,nfh,rindex,oit);
//std::cout<< "h1 done"<< std::endl;
return oit;
}else{
// spliting at new vertex
//std::cout<< "h2"<< std::endl;
*oit++ = expand_edge(q,nvh->point(),right,nfh,rindex,oit);
//std::cout<< "h2 done"<< std::endl;
}
}
}
//std::cout << "q "<< q << std::endl ;
//std::cout << "lvh->point() "<< lvh->point() << std::endl;
//std::cout << "left "<< left << std::endl ;
//std::cout << "nvh->point() "<< nvh->point() << std::endl ;
//std::cout << "right "<< right << std::endl ;
//std::cout << "rvh->point() "<< rvh->point() << std::endl<< std::endl;
// determin whether new vertex needs to be reported
if(ro != CGAL::CLOCKWISE && lo != CGAL::COUNTERCLOCKWISE){
*oit++ = nvh->point();
}
if(!Regularization_category::value){
CGAL_assertion(!(ro == CGAL::COLLINEAR && lo == CGAL::COLLINEAR));
// we have to check whether a needle starts here.
if(p_cdt->is_constrained(le) && !p_cdt->is_constrained(re)
&& ro == CGAL::COLLINEAR)
collect_needle(q,nvh,nfh,rindex);
if(p_cdt->is_constrained(re) && !p_cdt->is_constrained(le)
&& lo == CGAL::COLLINEAR)
collect_needle(q,nvh,nfh,lindex);
}
//left edge is seen if new vertex is clockwise of left boarder
if(lo == CGAL::CLOCKWISE){
if(p_cdt->is_constrained(le)){
// the edge is constrained
// report interesection with right boarder if exists
if(ro == CGAL::CLOCKWISE){
*oit++ = ray_seg_intersection(q,right,nvh->point(),lvh->point());
}
// then report intersection with left boarder ray
// if it is not already the left vertex (already reported)
if(left != lvh->point()){
*oit++ = ray_seg_intersection(q,left,nvh->point(),lvh->point());
}
return oit;
}else{
// the edge is not a constrained
if(ro == CGAL::CLOCKWISE){
// no split needed and return
//std::cout<< "h3"<< std::endl;
oit = expand_edge(q,left,right,nfh,lindex,oit);
//std::cout<< "h3 done"<< std::endl;
return oit;
}else{
// spliting at new vertex
//std::cout<< "h4"<< std::endl;
oit = expand_edge(q,left,nvh->point(),nfh,lindex,oit);
//std::cout<< "h4 done"<< std::endl;
return oit;
}
}
}
return oit;
}
template <typename VARR>
typename VARR::Face_handle
output(std::vector<Point_2>& raw_output, VARR& out_arr) const {
if(!needles.empty()){
std::vector<Segment_2> segments(needles.begin(),needles.end());
for(unsigned int i = 0; i < raw_output.size(); i++){
// //std::cout << raw_output[i] << " -- "
// << raw_output[(i+1)%raw_output.size()] << std::endl;
segments.push_back(Segment_2(raw_output[i],
raw_output[(i+1) % raw_output.size()]));
}
CGAL::insert_non_intersecting_curves(out_arr,
segments.begin(),
segments.end());
} else {
typename VARR::Vertex_handle v_last, v_first;
v_last = v_first =
out_arr.insert_in_face_interior(raw_output[0],out_arr.unbounded_face());
for(unsigned int i = 0; i < raw_output.size()-1; i++){
// std::cout << raw_output[i] << " -- "
// << raw_output[(i+1)%raw_output.size()] << std::endl;
if(raw_output[i] < raw_output[(i+1)]){
v_last = out_arr.insert_from_left_vertex (
Segment_2(raw_output[i], raw_output[i+1]), v_last
)->target();
} else {
v_last = out_arr.insert_from_right_vertex(
Segment_2(raw_output[i], raw_output[i+1]), v_last
)->target();
}
}
out_arr.insert_at_vertices(
Segment_2(raw_output.front(), raw_output.back()),
v_last, v_first
);
}
CGAL_assertion(out_arr.number_of_faces() == 2);
if(out_arr.faces_begin()->is_unbounded())
return ++out_arr.faces_begin();
else
return out_arr.faces_begin();
}
void init_cdt() const {
//std::cout<< "==============" <<std::endl;
//std::cout<< "Input Polygon:" <<std::endl;
typedef typename boost::transform_iterator<Make_constraint,
Edge_const_iterator> Iter;
Iter begin = boost::make_transform_iterator(p_arr->edges_begin(),
Make_constraint());
Iter end = boost::make_transform_iterator(p_arr->edges_end(),
Make_constraint());
//std::cout << "init_cdt new CDT" << std::endl;
p_cdt = boost::shared_ptr<CDT>(new CDT(begin, end));
observer.has_changed = false;
//std::cout << "init_cdt done" << std::endl;
//std::cout << std::endl;
}
};
} // namespace CGAL
#endif // CGAL_TRIANGULAR_EXPANSION_VISIBILITY_2_H