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cgal/Subdivision_method_3/include/CGAL/Subdivision_method_impl_3.h

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// ======================================================================
//
// Copyright (c) 2005-2017 GeometryFactory (France). All Rights Reserved.
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 3 of the License,
// or (at your option) any later version.
//
// 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): Le-Jeng Shiue <Andy.Shiue@gmail.com>
//
// ======================================================================
#ifndef CGAL_POLYHEDRON_SUBDIVISION_IMPL_H_02102006
#define CGAL_POLYHEDRON_SUBDIVISION_IMPL_H_02102006
#include <CGAL/basic.h>
#include <vector>
#include <CGAL/circulator.h>
#include <CGAL/Polyhedron_decorator_3.h>
#include <CGAL/boost/graph/helpers.h>
#include <CGAL/boost/graph/copy_face_graph.h>
#include <boost/foreach.hpp>
#include <boost/unordered_map.hpp>
#include <boost/unordered_set.hpp>
namespace CGAL {
// ======================================================================
namespace Subdivision_method_3 {
namespace Private {
// ======================================================================
template <class Poly, class VertexPointMap, class Mask>
void PQQ_1step(Poly& p, VertexPointMap vpm, Mask mask) {
typedef Polyhedron_decorator_3<Poly> PD;
typedef typename boost::graph_traits<Poly>::vertex_descriptor vertex_descriptor;
typedef typename boost::graph_traits<Poly>::halfedge_descriptor halfedge_descriptor;
typedef typename boost::graph_traits<Poly>::edge_descriptor edge_descriptor;
typedef typename boost::graph_traits<Poly>::vertex_iterator vertex_iterator;
typedef typename boost::graph_traits<Poly>::edge_iterator edge_iterator;
typedef typename boost::graph_traits<Poly>::face_iterator face_iterator;
typedef Halfedge_around_face_circulator<Poly> Halfedge_around_facet_circulator;
// Build a new vertices buffer has the following structure
//
// 0 1 ... e_begin ... f_begin ... (end_of_buffer)
// 0 ... e_begin-1 : store the positions of the vertex-vertices
// e_begin ... f_begin-1 : store the positions of the edge-vertices
// f_begin ... (end) : store the positions of the face-vertices
// The index of the vertices buffer should 1-1 map to the distance
// of the corresponding iterator to the begin of the iterator.
typename boost::graph_traits<Poly>::vertices_size_type num_vertex = num_vertices(p);
typename boost::graph_traits<Poly>::halfedges_size_type num_edge = num_halfedges(p)/2;
typename boost::graph_traits<Poly>::faces_size_type num_facet = num_faces(p);
// If Polyhedron is using vector, we need to reserve the memory to prevent
// the CGAL_assertion.
// This function for polyhedron using list is VOID.
p.reserve(num_vertex+num_edge+num_facet, 4*2*num_edge, 4*num_edge/2);
typedef typename boost::property_traits<VertexPointMap>::value_type Point;
Point* vertex_point_buffer = new Point[num_vertex + num_edge + num_facet];
Point* edge_point_buffer = vertex_point_buffer + num_vertex;
Point* face_point_buffer = edge_point_buffer + num_edge;
int i=0;
boost::unordered_map<vertex_descriptor,int> v_index;
BOOST_FOREACH(vertex_descriptor vh, vertices(p)){
v_index[vh]= i++;
}
std::vector<bool> v_onborder(num_vertex);
face_iterator fitr = faces(p).first;
for (size_t i = 0; i < num_facet; i++, ++fitr)
mask.face_node(*fitr, face_point_buffer[i]);
{
std::size_t i = 0;
BOOST_FOREACH(edge_descriptor ed, edges(p)){
if(is_border(ed,p)){
int v = v_index[target(ed,p)];
v_onborder[v] = true;
mask.border_node(halfedge(ed,p), edge_point_buffer[i], vertex_point_buffer[v]);
}else{
mask.edge_node(halfedge(ed,p), edge_point_buffer[i]);
}
++i;
}
}
vertex_iterator vitr = vertices(p).first;
for (size_t i = 0; i < num_vertex; i++, ++vitr)
if (!v_onborder[v_index[*vitr]]) mask.vertex_node(*vitr, vertex_point_buffer[i]);
// Build the connectivity using insert_vertex() and insert_edge()
// 1. insert_vertex() to all edges and set them to new positions
// 2. insert_edge() between 2 randomly selected neighboring new inserted
// vertices
// 3. insert_vertex() to the new inserted edge and set them to new positions
// 4. insert_edge() between all other new inserted vertices of step 1 and
// the new inserted vertex of step 3
// Step 1.
edge_iterator eitr = edges(p).first;
for (size_t i = 0; i < num_edge; i++, ++eitr) {
vertex_descriptor vh = PD::insert_vertex(p, halfedge(*eitr,p));
put(vpm, vh, edge_point_buffer[i]);
}
fitr = faces(p).first;
// TODO: the topoloy modification can be done by a template function
// and that gives the user a chance to create new topological masks.
for (size_t i = 0; i < num_facet; i++, ++fitr) {
// Step 2.
Halfedge_around_facet_circulator hcir_begin(halfedge(*fitr,p),p);
Halfedge_around_facet_circulator hcir = hcir_begin;
halfedge_descriptor e1 = * ++hcir; // e1 points to the newly inserted vertex
++hcir; // Skips one original vertex
halfedge_descriptor e2 = * ++hcir; // points to the next newly inserted vertex
++hcir; // Must move the cir before inserts the new edge !!
halfedge_descriptor newe = PD::insert_edge(p, e1, e2);
// Step 3.
halfedge_descriptor newv = PD::insert_vertex_return_edge(p, newe);
newv = prev(opposite(newv,p),p); // change newv to the larger face and
// still points to the newly inserted
// vertex
// Update the geometry data of the newly inserted face-vertices
put(vpm, target(newv,p), face_point_buffer[i]);
// Step 4.
while (hcir != hcir_begin) {
e1 = * ++hcir;
++hcir; // Must move the cir before inserts the new edge !!
PD::insert_edge(p, e1, newv);
}
}
// Update the geometry data of the newly inserted vertices by the
// vertices buffer
vitr = vertices(p).first;
for (size_t i = 0; i < num_vertex; i++, ++vitr)
put(vpm, *vitr, vertex_point_buffer[i]);
delete []vertex_point_buffer;
}
// ======================================================================
template <class Poly,class VertexPointMap, class Mask>
void PTQ_1step(Poly& p, VertexPointMap vpm, Mask mask) {
typedef Polyhedron_decorator_3<Poly> PD;
typedef typename boost::graph_traits<Poly>::vertex_descriptor vertex_descriptor;
typedef typename boost::graph_traits<Poly>::halfedge_descriptor halfedge_descriptor;
typedef typename boost::graph_traits<Poly>::edge_descriptor edge_descriptor;
typedef typename boost::graph_traits<Poly>::vertex_iterator vertex_iterator;
typedef typename boost::graph_traits<Poly>::edge_iterator edge_iterator;
typedef typename boost::graph_traits<Poly>::face_iterator face_iterator;
typedef Halfedge_around_face_circulator<Poly> Halfedge_around_face_circulator;
typedef typename boost::property_traits<VertexPointMap>::value_type Point;
// Build a new vertices buffer has the following structure
//
// 0 1 ... e_begin ... f_begin ... (end_of_buffer)
// 0 ... e_begin-1 : store the positions of the vertex-vertices
// e_begin ... (end) : store the positions of the edge-vertices
// The index of the vertices buffer should 1-1 map to the distance
// of the corresponding iterator to the begin of the iterator.
typename boost::graph_traits<Poly>::vertices_size_type num_vertex = num_vertices(p);
typename boost::graph_traits<Poly>::halfedges_size_type num_edge = num_halfedges(p)/2;
typename boost::graph_traits<Poly>::faces_size_type num_facet = num_faces(p);
// If Polyhedron is using vector, we need to reserve the memory to prevent
// the CGAL_assertion.
// This function for polyhedron using list is VOID.
p.reserve(num_vertex+num_edge, 2*2*num_edge, 4*num_edge/2);
Point* vertex_point_buffer = new Point[num_vertex + num_edge];
Point* edge_point_buffer = vertex_point_buffer + num_vertex;
int i=0;
boost::unordered_map<vertex_descriptor,int> v_index;
BOOST_FOREACH(vertex_descriptor vh, vertices(p)){
v_index[vh]= i++;
}
std::vector<bool> v_onborder(num_vertex);
{
std::size_t i = 0;
BOOST_FOREACH(edge_descriptor ed, edges(p)){
if(! is_border(ed,p)){
mask.edge_node(halfedge(ed,p), edge_point_buffer[i]);
} else{
int v = v_index[target(ed,p)];
v_onborder[v] = true;
mask.border_node(halfedge(ed,p), edge_point_buffer[i], vertex_point_buffer[v]);
}
++i;
}
}
vertex_iterator vitr = vertices(p).first;
for (size_t i = 0; i < num_vertex; i++, ++vitr)
if (!v_onborder[i]) mask.vertex_node(*vitr, vertex_point_buffer[i]);
// Build the connectivity using insert_vertex() and insert_edge()
// 1. insert_vertex() to all edges and set them to new positions
// 2. insert_edge() between 2 randomly selected neighboring new inserted
// vertices
// 3. insert_vertex() to the new inserted edge and set them to new positions
// 4. insert_edge() between all other new inserted vertices of step 1 and
// the new inserted vertex of step 3
// Step 1.
edge_iterator eitr = edges(p).first;
for (size_t i = 0; i < num_edge; i++, ++eitr) {
vertex_descriptor vh = PD::insert_vertex(p, halfedge(*eitr,p));
put(vpm,vh, edge_point_buffer[i]);
}
face_iterator fitr = faces(p).first;
for (size_t i = 0; i < num_facet; i++, ++fitr) {
// Step 2.
Halfedge_around_face_circulator hcir_begin(halfedge(*fitr,p),p);
Halfedge_around_face_circulator hcir = hcir_begin;
// After linsub, the facet valence = 6
CGAL_assertion(circulator_size(hcir)==6);
halfedge_descriptor e1 = *(++hcir);
++hcir;
halfedge_descriptor e2 = *(++hcir);
++hcir;
halfedge_descriptor e3 = *(++hcir);
e2 = PD::insert_edge(p, e1, e2);
e3 = PD::insert_edge(p, e2, e3);
PD::insert_edge(p, e3, e1);
}
// Update the geometry data of the newly inserted vertices by the
// vertices buffer
vitr = vertices(p).first;
for (size_t i = 0; i < num_vertex; i++, ++vitr)
put(vpm, *vitr, vertex_point_buffer[i]);
delete []vertex_point_buffer;
}
// ======================================================================
template <class Poly, class VertexPointMap, class Mask>
void DQQ_1step(Poly& p, VertexPointMap vpm, Mask mask) {
typedef Polyhedron_decorator_3<Poly> PD;
typedef typename boost::graph_traits<Poly>::vertex_descriptor vertex_descriptor;
typedef typename boost::graph_traits<Poly>::halfedge_descriptor halfedge_descriptor;
typedef typename boost::graph_traits<Poly>::edge_descriptor edge_descriptor;
typedef typename boost::property_traits<VertexPointMap>::value_type Point;
typename boost::graph_traits<Poly>::vertices_size_type num_v = num_vertices(p);
typename boost::graph_traits<Poly>::halfedges_size_type num_e = num_halfedges(p)/2;
typename boost::graph_traits<Poly>::faces_size_type num_f = num_faces(p);
std::vector<halfedge_descriptor> border_halfedges;
size_t num_be = 0 ;// AF= p.size_of_border_edges();
BOOST_FOREACH(edge_descriptor ed, edges(p)){
if(is_border(ed,p)){
++num_be;
border_halfedges.push_back(halfedge(ed,p));
}
}
Point* point_buffer = new Point[num_e*2];
// build the point_buffer
vertex_iterator vitr, vitr_end;
boost::tie(vitr,vitr_end) = vertices(p);
int pi = 0;
BOOST_FOREACH(vertex_descriptor vd, vertices(p)){
BOOST_FOREACH(halfedge_descriptor hd, halfedges_around_target(vd,p)){
if (! is_border(hd,p)){
mask.corner_node(hd, point_buffer[pi++]);
}
}
}
// If Polyhedron is using vector, we need to reserve the memory to prevent
// the CGAL_assertion. This function for polyhedron using list is VOID.
p.reserve(num_v+num_e+num_f, 2*num_e, (2+4+2)*num_e);
// Build the connectivity using insert_vertex() and insert_edge()
pi = 0;
for (size_t i = 0; i < num_v; ++i) {
vertex_descriptor vh = *vitr;
++vitr;
Halfedge_around_target_circulator<Poly> vcir(vh,p);
size_t vn = degree(vh,p);
for (size_t j = 0; j < vn; ++j) {
halfedge_descriptor e = *vcir;
++vcir;
if (! is_border(e,p)) {
vertex_descriptor v = PD::insert_vertex(p, e);
put(vpm, v, point_buffer[pi++]);
}
}
vcir = Halfedge_around_target_circulator<Poly>(vh,p);
for (size_t j = 0; j < vn; ++j) {
if (! is_border(*vcir,p)) {
halfedge_descriptor e1 = prev(*vcir, p);
++vcir;
if (! is_border(*vcir,p)) {
halfedge_descriptor e2 = opposite(*vcir,p);
PD::insert_edge(p, e1, e2);
}
} else ++vcir;
}
//p.erase_center_vertex(vh->vertex_begin());
}
edge_iterator eitr = edges(p).first;
for (size_t i = 0; i < num_e; ++i) {
halfedge_descriptor eh = halfedge(*eitr,p);
++eitr;
if (! is_border(edge(eh,p),p)) {
PD::insert_edge(p, prev(prev(eh,p),p), eh);
eh = opposite(eh,p);
PD::insert_edge(p, prev(prev(eh,p),p), eh);
Euler::join_face(eh,p);
} else {
if (is_border(eh,p)) {
eh = opposite(eh,p);
PD::insert_edge(p, eh, prev(prev(eh,p),p));
} else
PD::insert_edge(p, prev(prev(eh,p),p), eh);
}
}
// after this point, the original border edges are in front!
//eitr = edges(p).first;
//for (size_t i = 0; i < num_be; ++i) {
//halfedge_descriptor eh = halfedge(*eitr,p);
//++eitr;
BOOST_FOREACH(halfedge_descriptor eeh, border_halfedges){
halfedge_descriptor eh = eeh;
if (is_border(eh,p)){
eh = opposite(eh,p);
}
assert(is_border(eh,p));
halfedge_descriptor ehe = eh;
eh = opposite(prev(eh,p),p);
while (! is_border(eh,p)) {
std::cerr << "before remove_face"<< std::endl;
Euler::remove_face(ehe,p);
ehe = eh;
eh = opposite(prev(eh,p),p);
}
Euler::remove_face(ehe,p);
}
vitr = vertices(p).first;
for (size_t i = 0; i < num_v-num_be; ++i) {
vertex_descriptor vh = *vitr;
++vitr;
Euler::remove_center_vertex(halfedge(vh,p),p);
}
delete []point_buffer;
}
template <class Poly, class VertexPointMap, class Mask>
void DQQ_1step_alt(Poly& p, VertexPointMap vpm, Mask mask) {
typedef typename boost::graph_traits<Poly>::vertex_descriptor vertex_descriptor;
typedef typename boost::graph_traits<Poly>::halfedge_descriptor halfedge_descriptor;
typedef typename boost::graph_traits<Poly>::face_descriptor face_descriptor;
typedef typename boost::property_traits<VertexPointMap>::value_type Point;
// Note that for types like 'Surface_mesh', num_vertices() returns the TOTAL
// number of vertices, which may include removed vertices.
typename boost::graph_traits<Poly>::vertices_size_type num_v = num_vertices(p);
typename boost::graph_traits<Poly>::edges_size_type num_e = num_edges(p);
typename boost::graph_traits<Poly>::faces_size_type num_f = num_faces(p);
// If Poly is using vector, we need to reserve the memory to prevent
// the CGAL_assertion. This function for polyhedron using list is VOID.
Poly newp;
newp.reserve(num_v+num_e+num_f, 2*num_e, (2+4+2)*num_e);
boost::unordered_map<vertex_descriptor, Point> buffer;
// map to go from the halfedge in the original mesh to the halfedge in the
// subdivided mesh
boost::unordered_map<halfedge_descriptor, halfedge_descriptor> old_to_new;
// build new n-faces
BOOST_FOREACH(face_descriptor fd, faces(p)) {
halfedge_descriptor hd = halfedge(fd, p);
std::list<vertex_descriptor> vertices_of_new_face;
// keep the first outside
// it will be used to build the correspondence between old and new halfedges
Point first_pt;
mask.corner_node(hd, first_pt);
vertex_descriptor first_v = add_vertex(newp);
buffer[first_v] = first_pt;
vertices_of_new_face.push_back(first_v);
// loop normally to add the rest of the vertices
halfedge_descriptor done = hd;
hd = next(hd, p);
while(hd != done) {
Point pt;
mask.corner_node(hd, pt);
vertex_descriptor v = add_vertex(newp);
buffer[v] = pt;
vertices_of_new_face.push_back(v);
hd = next(hd, p);
}
face_descriptor new_face = Euler::add_face(vertices_of_new_face, newp);
// find the starting halfedge in new that corresponds to halfedge(fd, p)
halfedge_descriptor nf_hd = halfedge(new_face, newp);
while(target(nf_hd, newp) != first_v) {
nf_hd = next(nf_hd, newp);
}
// build the correspondence old to new halfedges
hd = halfedge(fd, p);
done = nf_hd;
do {
old_to_new[hd] = nf_hd;
hd = next(hd, p);
nf_hd = next(nf_hd, newp);
} while (nf_hd != done);
}
// build new edge-faces
BOOST_FOREACH(halfedge_descriptor hd, halfedges(p)) {
if(is_border(hd, p))
continue;
halfedge_descriptor hd_opp = opposite(hd, p);
if(is_border(hd_opp, p))
continue;
if(hd > hd_opp)
continue;
halfedge_descriptor new_hd = opposite(old_to_new[hd], newp);
halfedge_descriptor new_hd_opp = opposite(old_to_new[hd_opp], newp);
boost::array<vertex_descriptor, 4> v = {{source(new_hd, newp),
target(new_hd, newp),
source(new_hd_opp, newp),
target(new_hd_opp, newp)}};
Euler::add_face(v, newp);
}
// build new vertex-faces
BOOST_FOREACH(vertex_descriptor vd, vertices(p)) {
halfedge_descriptor hd = halfedge(vd, p);
if(is_border(hd, p))
continue;
halfedge_descriptor new_hd = opposite(old_to_new[hd], newp);
halfedge_descriptor new_face_hd = opposite(prev(new_hd, newp), newp), done = new_face_hd;
std::list<vertex_descriptor> vertices_of_new_faces;
do {
vertices_of_new_faces.push_back(source(new_face_hd, newp));
new_face_hd = next(new_face_hd, newp);
} while(new_face_hd != done);
Euler::add_face(vertices_of_new_faces, newp);
}
// copy face graph newp into p to keep a valid pointer to vpm
p.clear();
boost::unordered_map<vertex_descriptor, vertex_descriptor> v2v;
CGAL::copy_face_graph(newp, p, std::inserter(v2v, v2v.end()));
// empty 'buffer' into vpm
typename boost::unordered_map<vertex_descriptor, Point>::iterator umit = buffer.begin(),
umend = buffer.end();
for(; umit!=umend; ++umit) {
vertex_descriptor vd = umit->first;
put(vpm, v2v[vd], umit->second);
}
}
// ======================================================================
template <class Poly, class VertexPointMap, class Mask>
void Sqrt3_1step(Poly& p, VertexPointMap vpm, Mask mask,
const bool refine_border = false) {
// `refine_border` is a boolean that is meant to be true only every SECOND step
// of the subdivision. In particular, this function makes uses of the fact
// that there is at most a single border edge in a face, which is true if
// the mesh is obtained from a sqrt3 subdivision before, but might otherwise
// be wrong.
typedef typename boost::graph_traits<Poly>::vertex_descriptor vertex_descriptor;
typedef typename boost::graph_traits<Poly>::halfedge_descriptor halfedge_descriptor;
typedef typename boost::graph_traits<Poly>::edge_descriptor edge_descriptor;
typedef typename boost::graph_traits<Poly>::face_descriptor face_descriptor;
typedef typename boost::graph_traits<Poly>::edge_iterator edge_iterator;
typedef typename boost::graph_traits<Poly>::face_iterator face_iterator;
typedef typename boost::property_traits<VertexPointMap>::value_type Point;
typename boost::graph_traits<Poly>::vertices_size_type num_v = num_vertices(p);
typename boost::graph_traits<Poly>::halfedges_size_type num_e = num_halfedges(p)/2;
typename boost::graph_traits<Poly>::faces_size_type num_f = num_faces(p);
// reserve enough size for the new points
typename boost::graph_traits<Poly>::faces_size_type new_pts_size = num_f;
if(refine_border) {
BOOST_FOREACH(edge_descriptor ed, CGAL::edges(p)){
if(is_border(ed, p))
++new_pts_size;
}
}
Point* cpt = new Point[new_pts_size];
// size of the subdivided mesh
p.reserve(num_v + new_pts_size, (num_e + 2*num_f + new_pts_size)*2, 3*num_f);
// keep in memory whether a face is incident to the border and, if so, which
// halfedge corresponds to THE (there can only be one) border edge.
std::vector<halfedge_descriptor> face_halfedge_border(num_f,
boost::graph_traits<Poly>::null_halfedge());
// compute the positions of new points
std::size_t i = 0;
std::size_t face_id = 0;
BOOST_FOREACH (face_descriptor fd, faces(p)) {
//ASSERTION_MSG(circulator_size(fitr->facet_begin())==3, "(ERROR) Non-triangle facet!");
if(refine_border) {
BOOST_FOREACH(halfedge_descriptor hd, halfedges_around_face(halfedge(fd, p), p)) {
if(is_border(opposite(hd, p),p)) {
face_halfedge_border[face_id] = hd;
halfedge_descriptor bhd = opposite(hd, p);
mask.edge_node(bhd, cpt[i], cpt[i+1]);
i += 2;
// the border subdivision is only performed every second subdivision
// step and there can thus only be one border edge per face
break;
}
}
if(face_halfedge_border[face_id] == boost::graph_traits<Poly>::null_halfedge())
mask.face_node(fd, cpt[i++]);
} else {
mask.face_node(fd, cpt[i++]);
}
++face_id;
}
// smooth the position of existing vertices
std::list<std::pair<vertex_descriptor, Point> > new_positions;
BOOST_FOREACH(vertex_descriptor vd, vertices(p)){
Point pt;
if(!is_border(vd, p)) {
mask.vertex_node(vd, pt);
new_positions.push_back(std::make_pair(vd, pt));
}
}
// insert the new subdividing points
face_iterator b,e;
boost::tie(b,e) = faces(p);
for(std::size_t i=0, cpt_id=0; i < num_f; ++i, ++b){
face_descriptor fd = *b;
halfedge_descriptor hd = face_halfedge_border[i];
if(refine_border && hd != boost::graph_traits<Poly>::null_halfedge()) {
halfedge_descriptor hd_next = next(hd, p);
halfedge_descriptor new_e1 = Euler::split_edge(hd, p);
halfedge_descriptor new_e2 = Euler::split_edge(hd, p);
put(vpm, target(new_e1, p), cpt[cpt_id++]);
put(vpm, target(new_e2, p), cpt[cpt_id++]);
Euler::split_face(new_e1, hd_next, p);
Euler::split_face(new_e2, hd_next, p);
} else {
halfedge_descriptor center = Euler::add_center_vertex(halfedge(fd,p),p);
put(vpm, target(center,p), cpt[cpt_id++]);
}
}
if(refine_border) {
// collect the new positions for border vertices
BOOST_FOREACH(halfedge_descriptor hd, halfedges(p)) {
// switch to the border halfedge
hd = opposite(hd, p);
if(!is_border(hd, p))
continue;
Point pt;
mask.border_node(hd, pt);
vertex_descriptor vd = target(hd, p);
new_positions.push_back(std::make_pair(vd, pt));
}
}
// actually inserts the new positions in the vertex point property map
typename std::list<std::pair<vertex_descriptor, Point> >::iterator it = new_positions.begin(),
end = new_positions.end();
for(; it!=end; ++it) {
put(vpm, it->first, it->second);
}
// flip the old edges (except the border edges)
edge_iterator eitr = edges(p).first;
for (size_t i = 0; i < num_e; ++i) {
halfedge_descriptor e = halfedge(*eitr,p);
++eitr; // move to next edge before flip since flip destroys current edge
if (! is_border(edge(e,p),p)) {
halfedge_descriptor h = Euler::join_face(e,p);
Euler::split_face(prev(h,p), next(h,p),p);
}
}
CGAL_postcondition(p.is_valid());
delete []cpt;
}
}
}
} //namespace CGAL
#endif //CGAL_POLYHEDRON_SUBDIVISION_H_01292002
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