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1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 | // Copyright (c) 1997 ETH Zurich (Switzerland).
// 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
// 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) : Lutz Kettner <kettner@mpi-sb.mpg.de>)
#ifndef CGAL_POLYHEDRON_3_H
#define CGAL_POLYHEDRON_3_H 1
#include <CGAL/basic.h>
#include <algorithm>
#include <cstddef>
#include <CGAL/HalfedgeDS_iterator.h>
#include <CGAL/Iterator_project.h>
#include <CGAL/function_objects.h>
#include <CGAL/N_step_adaptor_derived.h>
#include <CGAL/Polyhedron_items_3.h>
#include <CGAL/HalfedgeDS_default.h>
#include <CGAL/HalfedgeDS_const_decorator.h>
#include <CGAL/HalfedgeDS_decorator.h>
#include <CGAL/Modifier_base.h>
#include <CGAL/IO/Verbose_ostream.h>
#include <CGAL/Polyhedron_traits_3.h>
namespace CGAL {
template <class VertexBase>
class I_Polyhedron_vertex : public VertexBase {
public:
typedef VertexBase Base;
//typedef typename Base::HalfedgeDS HDS;
typedef typename Base::Point Point;
typedef Point Point_3;
// Handles have to explicitly repeated, although they are derived
typedef typename Base::Vertex_handle Vertex_handle;
typedef typename Base::Halfedge_handle Halfedge_handle;
typedef typename Base::Face_handle Face_handle;
typedef typename Base::Face_handle Facet_handle;
typedef typename Base::Vertex_const_handle Vertex_const_handle;
typedef typename Base::Halfedge_const_handle Halfedge_const_handle;
typedef typename Base::Face_const_handle Face_const_handle;
typedef typename Base::Face_const_handle Facet_const_handle;
typedef typename Base::Halfedge Halfedge;
typedef typename Base::Face Face;
typedef typename Base::Face Facet;
// Supported options by HDS.
typedef typename Base::Supports_vertex_halfedge
Supports_vertex_halfedge;
typedef typename Base::Supports_vertex_point Supports_vertex_point;
// Circulator category.
typedef typename Halfedge::Supports_halfedge_prev Supports_prev;
public:
// Circulator category.
typedef HalfedgeDS_circulator_traits<Supports_prev> Ctr;
typedef typename Ctr::iterator_category circulator_category;
// Circulators around a vertex and around a facet.
typedef I_HalfedgeDS_facet_circ< Halfedge_handle, circulator_category>
Halfedge_around_facet_circulator;
typedef I_HalfedgeDS_vertex_circ< Halfedge_handle, circulator_category>
Halfedge_around_vertex_circulator;
typedef I_HalfedgeDS_facet_circ<
Halfedge_const_handle,
circulator_category> Halfedge_around_facet_const_circulator;
typedef I_HalfedgeDS_vertex_circ<
Halfedge_const_handle,
circulator_category> Halfedge_around_vertex_const_circulator;
typedef typename Halfedge_around_vertex_circulator::size_type
size_type;
typedef typename Halfedge_around_vertex_circulator::difference_type
difference_type;
public:
// We need to repeat the constructors here.
I_Polyhedron_vertex() {}
I_Polyhedron_vertex( const VertexBase& b) : VertexBase(b) {}
I_Polyhedron_vertex( const Point_3& p) : VertexBase(p) {}
// New Access Functions (not provided in VertexBase).
Halfedge_around_vertex_circulator vertex_begin() {
// a circulator of halfedges around the vertex (clockwise).
return Halfedge_around_vertex_circulator( this->halfedge());
}
Halfedge_around_vertex_const_circulator vertex_begin() const {
// a circulator of halfedges around the vertex (clockwise).
return Halfedge_around_vertex_const_circulator( this->halfedge());
}
// the degree of the vertex, i.e., edges emanating from this vertex
std::size_t vertex_degree() const {
return this->halfedge()->vertex_degree();
}
size_type degree() const { return vertex_degree(); } //backwards compatible
// returns true if the vertex has exactly two incident edges
bool is_bivalent() const { return this->halfedge()->is_bivalent(); }
// returns true if the vertex has exactly three incident edges
bool is_trivalent() const { return this->halfedge()->is_trivalent(); }
// No longer hidden. Now the restricted version with precondition.
// sets incident halfedge to h. Precondition: h is incident, i.e.,
// h->vertex() == v.
void set_halfedge( Halfedge_handle hh) {
CGAL_assertion( &*(hh->vertex()) == this);
Base::set_halfedge(hh);
}
};
// A halfedge is an oriented edge. Both orientations exist, i.e.
// an edge is represented by two opposite halfedges. The geometric
// relations are as follows:
//
// _ _ _ .
// / |\.
// | \.
// / \ next half
// \ edge
// / \.
//
// | O incident vertex
// facet ,
// | /| |
// / | | opposite
// \ | | half edge
// half | |
// \ edge | | /
// | |/
// \_ _ _ _ _ _ '
//
template <class HalfedgeBase>
class I_Polyhedron_halfedge : public HalfedgeBase {
public:
typedef HalfedgeBase Base;
typedef typename Base::HalfedgeDS HDS;
// Handles have to explicitly repeated, although they are derived
typedef typename Base::Vertex_handle Vertex_handle;
typedef typename Base::Halfedge_handle Halfedge_handle;
typedef typename Base::Face_handle Face_handle;
typedef typename Base::Face_handle Facet_handle;
typedef typename Base::Vertex_const_handle Vertex_const_handle;
typedef typename Base::Halfedge_const_handle Halfedge_const_handle;
typedef typename Base::Face_const_handle Face_const_handle;
typedef typename Base::Face_const_handle Facet_const_handle;
typedef typename Base::Vertex Vertex;
typedef typename Base::Face Face;
typedef typename Base::Face Facet;
// Supported options by HDS.
typedef typename Base::Supports_halfedge_prev Supports_halfedge_prev;
typedef typename Base::Supports_halfedge_vertex
Supports_halfedge_vertex;
typedef typename Base::Supports_halfedge_face Supports_halfedge_face;
// Circulator category.
typedef typename Base::Supports_halfedge_prev Supports_prev;
public:
// Circulator category.
typedef HalfedgeDS_circulator_traits<Supports_prev> Ctr;
typedef typename Ctr::iterator_category circulator_category;
// Circulators around a vertex and around a facet.
typedef I_HalfedgeDS_facet_circ< Halfedge_handle, circulator_category>
Halfedge_around_facet_circulator;
typedef I_HalfedgeDS_vertex_circ< Halfedge_handle, circulator_category>
Halfedge_around_vertex_circulator;
typedef I_HalfedgeDS_facet_circ<
Halfedge_const_handle,
circulator_category> Halfedge_around_facet_const_circulator;
typedef I_HalfedgeDS_vertex_circ<
Halfedge_const_handle,
circulator_category> Halfedge_around_vertex_const_circulator;
public:
I_Polyhedron_halfedge() {}
I_Polyhedron_halfedge( const HalfedgeBase& b) : HalfedgeBase(b) {}
// New Access Functions (not provided in HalfedgeBase).
// Change semantic of prev: it is always available at this level.
// If the HDS does not provide a prev-function, the previous
// halfedge will be searched around the incident facet.
private:
Halfedge_handle find_prev( Halfedge_handle, Tag_true) {
return Base::prev();
}
Halfedge_const_handle find_prev( Halfedge_const_handle, Tag_true) const {
return Base::prev();
}
Halfedge_handle find_prev( Halfedge_handle h, Tag_false) const {
CGAL_precondition( &*h != this); // we have at least 2-gons
while ( &*(h->next()) != this)
h = h->next();
return h;
}
Halfedge_const_handle find_prev( Halfedge_const_handle h, Tag_false) const{
CGAL_precondition( &*h != this); // we have at least 2-gons
while ( &*(h->next()) != this)
h = h->next();
return h;
}
public:
Halfedge_handle prev() {
return find_prev( this->next(), Supports_halfedge_prev());
}
Halfedge_const_handle prev() const {
return find_prev( this->next(), Supports_halfedge_prev());
}
// Make face-functions also available as facet-functions.
Face_handle facet() { return this->face();}
Face_const_handle facet() const { return this->face();}
// the next halfedge around the vertex (clockwise). This is equal to
// `h.next()->opposite()'.
Halfedge_handle next_on_vertex() { return this->next()->opposite(); }
Halfedge_const_handle next_on_vertex() const {
return this->next()->opposite();
}
// the previous halfedge around the vertex (counterclockwise). Is
// equal to `h.opposite()->prev()'.
Halfedge_handle prev_on_vertex() { return this->opposite()->prev(); }
Halfedge_const_handle prev_on_vertex() const {
return this->opposite()->prev();
}
bool is_border_edge() const {
// is true if `h' or `h.opposite()' is a border halfedge.
return (this->opposite()->is_border() || this->is_border());
}
// a circulator of halfedges around the vertex (clockwise).
Halfedge_around_vertex_circulator vertex_begin() {
return Halfedge_around_vertex_circulator(
HDS::halfedge_handle(this));
}
Halfedge_around_vertex_const_circulator vertex_begin() const {
return Halfedge_around_vertex_const_circulator(
HDS::halfedge_handle(this));
}
// a circulator of halfedges around the facet (counterclockwise).
Halfedge_around_facet_circulator facet_begin() {
return Halfedge_around_facet_circulator(
HDS::halfedge_handle(this));
}
Halfedge_around_facet_const_circulator facet_begin() const {
return Halfedge_around_facet_const_circulator(
HDS::halfedge_handle(this));
}
// the degree of the incident vertex, i.e., edges emanating from this
// vertex
std::size_t vertex_degree() const {
return circulator_size( vertex_begin());
}
// the degree of the incident facet, i.e., edges on the boundary of this
// facet
std::size_t facet_degree() const {
return circulator_size( facet_begin());
}
// returns true if the incident vertex has exactly two incident edges
bool is_bivalent() const {
CGAL_precondition( this != &* (this->next()->opposite()));
return (this == &* (this->next()->opposite()->next()->opposite()));
}
// returns true if the incident vertex has exactly three incident edges
bool is_trivalent() const {
CGAL_precondition( this != &* (this->next()->opposite()));
return ( this != &* (this->next()->opposite()->next()->opposite())
&& this == &* (this->next()->opposite()->next()->opposite()
->next()->opposite()));
}
// returns true if the incident facet is a triangle.
bool is_triangle() const {
CGAL_precondition( this != &* (this->next()));
CGAL_precondition( this != &* (this->next()->next()));
return (this == &* (this->next()->next()->next()));
}
// returns true if the incident facet is a quadrilateral.
bool is_quad() const {
CGAL_precondition( this != &* (this->next()));
CGAL_precondition( this != &* (this->next()->next()));
return (this == &* (this->next()->next()->next()->next()));
}
private:
// Hide some other functions of H.
void set_next( Halfedge_handle hh) { Base::set_next(hh);}
void set_prev( Halfedge_handle hh) { Base::set_prev(hh);}
void set_vertex( Vertex_handle vv) { Base::set_vertex(vv);}
void set_face( Face_handle ff) { Base::set_face(ff);}
void set_facet( Face_handle ff) { set_face(ff);}
};
template <class FacetBase>
class I_Polyhedron_facet : public FacetBase {
public:
typedef FacetBase Base;
//typedef typename Base::HalfedgeDS HDS;
typedef typename Base::Plane Plane;
typedef Plane Plane_3;
// Handles have to explicitly repeated, although they are derived
typedef typename Base::Vertex_handle Vertex_handle;
typedef typename Base::Halfedge_handle Halfedge_handle;
typedef typename Base::Face_handle Face_handle;
typedef typename Base::Face_handle Facet_handle;
typedef typename Base::Vertex_const_handle Vertex_const_handle;
typedef typename Base::Halfedge_const_handle Halfedge_const_handle;
typedef typename Base::Face_const_handle Face_const_handle;
typedef typename Base::Face_const_handle Facet_const_handle;
typedef typename Base::Vertex Vertex;
typedef typename Base::Halfedge Halfedge;
// Supported options by HDS.
typedef typename Base::Supports_face_halfedge Supports_face_halfedge;
typedef typename Base::Supports_face_plane Supports_face_plane;
// No longer required.
typedef Tag_false Supports_face_normal;
// Circulator category.
typedef typename Halfedge::Supports_halfedge_prev Supports_prev;
public:
// Circulator category.
typedef HalfedgeDS_circulator_traits<Supports_prev> Ctr;
typedef typename Ctr::iterator_category circulator_category;
// Circulators around a vertex and around a facet.
typedef I_HalfedgeDS_facet_circ< Halfedge_handle, circulator_category>
Halfedge_around_facet_circulator;
typedef I_HalfedgeDS_vertex_circ< Halfedge_handle, circulator_category>
Halfedge_around_vertex_circulator;
typedef I_HalfedgeDS_facet_circ<
Halfedge_const_handle,
circulator_category> Halfedge_around_facet_const_circulator;
typedef I_HalfedgeDS_vertex_circ<
Halfedge_const_handle,
circulator_category> Halfedge_around_vertex_const_circulator;
typedef typename Halfedge_around_vertex_circulator::size_type
size_type;
typedef typename Halfedge_around_vertex_circulator::difference_type
difference_type;
public:
// We need to repeat the constructors here.
I_Polyhedron_facet() {}
I_Polyhedron_facet( const FacetBase& b) : FacetBase(b) {}
// New Access Functions (not provided in FacetBase).
Halfedge_around_facet_circulator facet_begin() {
// a circulator of halfedges around the facet (counterclockwise).
return Halfedge_around_facet_circulator( this->halfedge());
}
Halfedge_around_facet_const_circulator facet_begin() const {
// a circulator of halfedges around the facet (counterclockwise).
return Halfedge_around_facet_const_circulator( this->halfedge());
}
// the degree of the incident facet, i.e., edges on the boundary of this
// facet
std::size_t facet_degree() const {return this->halfedge()->facet_degree();}
size_type size() const { return facet_degree(); } // backwards compatible
// returns true if the facet is a triangle.
bool is_triangle() const { return this->halfedge()->is_triangle(); }
// returns true if the facet is a quadrilateral.
bool is_quad() const { return this->halfedge()->is_quad(); }
// No longer hidden. Now the restricted version with precondition.
// sets incident halfedge to h. Precondition: h is incident, i.e.,
// h->face() == v.
void set_halfedge( Halfedge_handle hh) {
CGAL_assertion( &*(hh->facet()) == this);
Base::set_halfedge(hh);
}
};
template < class Items>
class I_Polyhedron_derived_items_3 {
public:
template < class Refs, class Traits>
class Vertex_wrapper {
public:
typedef typename Items::template Vertex_wrapper<Refs,Traits> VWrap;
typedef typename VWrap::Vertex Vertex_base;
typedef I_Polyhedron_vertex< Vertex_base> Vertex;
};
template < class Refs, class Traits>
class Halfedge_wrapper {
public:
typedef typename Items::template Halfedge_wrapper<Refs,Traits> HWrap;
typedef typename HWrap::Halfedge Halfedge_base;
typedef I_Polyhedron_halfedge< Halfedge_base> Halfedge;
};
template < class Refs, class Traits>
class Face_wrapper {
public:
typedef typename Items::template Face_wrapper<Refs,Traits> FWrap;
typedef typename FWrap::Face Face_base;
typedef I_Polyhedron_facet< Face_base> Face;
};
};
template < class PolyhedronTraits_3,
class PolyhedronItems_3 = Polyhedron_items_3,
template < class T, class I, class A>
class T_HDS = HalfedgeDS_default,
class Alloc = CGAL_ALLOCATOR(int)>
class Polyhedron_3 {
//
// DEFINITION
//
// The boundary representation of a 3d-polyhedron P of the type
// Polyhedron consists of vertices, edges and facets. The
// vertices are points in space. The edges are straight line
// segments. The facets are planar polygons. We restrict here
// the facets to be simple planar polygons without holes and the
// boundary of the polyhedron to be an oriented 2-manifold. Thus
// facets are consistently oriented and an edge is incident to
// exactly two facets. We restrict the representation further
// that an edge has two distinct incident endpoints and
// following duality that an edge has two distinct incident
// facets. The class Polyhedron is able to guarantee
// the combinatorial properties, but not all geometric
// properties. Support functions are provided for testing
// geometric properties, e.g. test for self intersections which
// is too expensive to be guaranteed as a class invariant.
public:
typedef Polyhedron_3< PolyhedronTraits_3, PolyhedronItems_3, T_HDS, Alloc>
Self;
typedef PolyhedronTraits_3 Traits;
typedef PolyhedronItems_3 Items;
typedef I_Polyhedron_derived_items_3<Items> Derived_items;
typedef T_HDS< Traits, Derived_items, Alloc> HDS;
typedef HDS HalfedgeDS;
// portability with older CGAL release
typedef HDS Halfedge_data_structure;
typedef Alloc Allocator;
typedef Alloc allocator_type; // STL name
// Container stuff.
typedef typename HDS::size_type size_type;
typedef typename HDS::difference_type difference_type;
typedef typename HDS::iterator_category iterator_category;
typedef typename HDS::Supports_removal Supports_removal;
// Geometry
typedef typename Traits::Point_3 Point_3;
typedef typename Traits::Plane_3 Plane_3;
// No longer required.
//typedef typename Traits::Normal Normal;
// Items
typedef typename HDS::Vertex Vertex;
typedef typename HDS::Halfedge Halfedge;
typedef typename HDS::Face Face;
typedef typename Vertex::Base VBase;
typedef typename Halfedge::Base HBase;
typedef typename Face::Base FBase;
// Handles and Iterators
typedef typename HDS::Vertex_handle Vertex_handle;
typedef typename HDS::Halfedge_handle Halfedge_handle;
typedef typename HDS::Face_handle Face_handle;
typedef typename HDS::Vertex_iterator Vertex_iterator;
typedef typename HDS::Halfedge_iterator Halfedge_iterator;
typedef typename HDS::Face_iterator Face_iterator;
typedef typename HDS::Vertex_const_handle Vertex_const_handle;
typedef typename HDS::Halfedge_const_handle Halfedge_const_handle;
typedef typename HDS::Face_const_handle Face_const_handle;
typedef typename HDS::Vertex_const_iterator Vertex_const_iterator;
typedef typename HDS::Halfedge_const_iterator Halfedge_const_iterator;
typedef typename HDS::Face_const_iterator Face_const_iterator;
// Auxiliary iterators for convenience
typedef Project_point<Vertex> Proj_point;
typedef Iterator_project<Vertex_iterator, Proj_point>
Point_iterator;
typedef Iterator_project<Vertex_const_iterator, Proj_point,
const Point_3&, const Point_3*> Point_const_iterator;
typedef Project_plane<Face> Proj_plane;
typedef Iterator_project<Face_iterator, Proj_plane>
Plane_iterator;
typedef Iterator_project<Face_const_iterator, Proj_plane,
const Plane_3&, const Plane_3*> Plane_const_iterator;
typedef N_step_adaptor_derived<Halfedge_iterator, 2>
Edge_iterator;
typedef N_step_adaptor_derived<Halfedge_const_iterator, 2>
Edge_const_iterator;
// All face related types get a related facet type name.
typedef Face Facet;
typedef Face_handle Facet_handle;
typedef Face_iterator Facet_iterator;
typedef Face_const_handle Facet_const_handle;
typedef Face_const_iterator Facet_const_iterator;
// Supported options by HDS.
typedef typename VBase::Supports_vertex_halfedge
Supports_vertex_halfedge;
typedef typename HBase::Supports_halfedge_prev Supports_halfedge_prev;
typedef typename HBase::Supports_halfedge_prev Supports_prev;
typedef typename HBase::Supports_halfedge_vertex
Supports_halfedge_vertex;
typedef typename HBase::Supports_halfedge_face Supports_halfedge_face;
typedef typename FBase::Supports_face_halfedge Supports_face_halfedge;
// Supported options especially for Polyhedron_3.
typedef typename VBase::Supports_vertex_point Supports_vertex_point;
typedef typename FBase::Supports_face_plane Supports_face_plane;
// No longer required.
typedef Tag_false Supports_face_normal;
// Renamed versions for facet
typedef Supports_halfedge_face Supports_halfedge_facet;
typedef Supports_face_halfedge Supports_facet_halfedge;
typedef Supports_face_plane Supports_facet_plane;
// No longer required.
typedef Supports_face_normal Supports_facet_normal;
public:
// Circulator category.
typedef HalfedgeDS_circulator_traits<Supports_prev> Ctr;
typedef typename Ctr::iterator_category circulator_category;
// Circulators around a vertex and around a facet.
typedef I_HalfedgeDS_facet_circ< Halfedge_handle, circulator_category>
Halfedge_around_facet_circulator;
typedef I_HalfedgeDS_vertex_circ< Halfedge_handle, circulator_category>
Halfedge_around_vertex_circulator;
typedef I_HalfedgeDS_facet_circ<
Halfedge_const_handle,
circulator_category> Halfedge_around_facet_const_circulator;
typedef I_HalfedgeDS_vertex_circ<
Halfedge_const_handle,
circulator_category> Halfedge_around_vertex_const_circulator;
protected:
HDS hds; // the boundary representation.
Traits m_traits;
// CREATION
public:
Polyhedron_3( const Traits& trts = Traits()) : m_traits(trts) {}
// the empty polyhedron `P'.
Polyhedron_3( size_type v, size_type h, size_type f,
const Traits& traits = Traits())
: hds(v,h,f), m_traits(traits) {}
// a polyhedron `P' with storage reserved for v vertices, h
// halfedges, and f facets. The reservation sizes are a hint for
// optimizing storage allocation.
void reserve( size_type v, size_type h, size_type f) {
// reserve storage for v vertices, h halfedges, and f facets. The
// reservation sizes are a hint for optimizing storage allocation.
// If the `capacity' is already greater than the requested size
// nothing happens. If the `capacity' changes all iterators and
// circulators invalidates.
hds.reserve(v,h,f);
}
protected:
Halfedge_handle
make_triangle( Vertex_handle v1, Vertex_handle v2, Vertex_handle v3) {
HalfedgeDS_decorator<HDS> decorator(hds);
Halfedge_handle h = hds.edges_push_back( Halfedge(), Halfedge());
h->HBase::set_next( hds.edges_push_back( Halfedge(), Halfedge()));
h->next()->HBase::set_next( hds.edges_push_back( Halfedge(),
Halfedge()));
h->next()->next()->HBase::set_next( h);
decorator.set_prev( h, h->next()->next());
decorator.set_prev( h->next(), h);
decorator.set_prev( h->next()->next(), h->next());
h->opposite()->HBase::set_next( h->next()->next()->opposite());
h->next()->opposite()->HBase::set_next( h->opposite());
h->next()->next()->opposite()->HBase::set_next(
h->next()->opposite());
decorator.set_prev( h->opposite(), h->next()->opposite());
decorator.set_prev( h->next()->opposite(),
h->next()->next()->opposite());
decorator.set_prev( h->next()->next()->opposite(), h->opposite());
// the vertices
decorator.set_vertex( h, v1);
decorator.set_vertex( h->next(), v2);
decorator.set_vertex( h->next()->next(), v3);
decorator.set_vertex( h->opposite(), v3);
decorator.set_vertex( h->next()->opposite(), v1);
decorator.set_vertex( h->next()->next()->opposite(), v2);
decorator.set_vertex_halfedge( h);
decorator.set_vertex_halfedge( h->next());
decorator.set_vertex_halfedge( h->next()->next());
// the facet
Facet_handle f = decorator.faces_push_back( Facet());
decorator.set_face( h, f);
decorator.set_face( h->next(), f);
decorator.set_face( h->next()->next(), f);
decorator.set_face_halfedge( h);
return h;
}
Halfedge_handle
make_tetrahedron( Vertex_handle v1,
Vertex_handle v2,
Vertex_handle v3,
Vertex_handle v4) {
HalfedgeDS_decorator<HDS> decorator(hds);
Halfedge_handle h = make_triangle(v1,v2,v3);
// The remaining tip.
Halfedge_handle g = hds.edges_push_back( Halfedge(), Halfedge());
decorator.insert_tip( g->opposite(), h->opposite());
decorator.close_tip( g);
decorator.set_vertex( g, v4);
Halfedge_handle e = hds.edges_push_back( Halfedge(), Halfedge());
Halfedge_handle d = hds.edges_push_back( Halfedge(), Halfedge());
decorator.insert_tip( e->opposite(), h->next()->opposite());
decorator.insert_tip( e, g);
decorator.insert_tip( d->opposite(),h->next()->next()->opposite());
decorator.insert_tip( d, e);
decorator.set_vertex_halfedge( g);
// facets
Facet_handle f = decorator.faces_push_back( Facet());
decorator.set_face( h->opposite(), f);
decorator.set_face( g, f);
decorator.set_face( e->opposite(), f);
decorator.set_face_halfedge( g);
f = decorator.faces_push_back( Facet());
decorator.set_face( h->next()->opposite(), f);
decorator.set_face( e, f);
decorator.set_face( d->opposite(), f);
decorator.set_face_halfedge( e);
f = decorator.faces_push_back( Facet());
decorator.set_face( h->next()->next()->opposite(), f);
decorator.set_face( d, f);
decorator.set_face( g->opposite(), f);
decorator.set_face_halfedge( d);
return h;
}
public:
Halfedge_handle make_tetrahedron() {
// the combinatorial structure of a tetrahedron is added to the
// actual polyhedral surface. Returns an arbitrary halfedge of
// this structure.
reserve( 4 + size_of_vertices(),
12 + size_of_halfedges(),
4 + size_of_facets());
HalfedgeDS_decorator<HDS> decorator(hds);
return make_tetrahedron( decorator.vertices_push_back( Vertex()),
decorator.vertices_push_back( Vertex()),
decorator.vertices_push_back( Vertex()),
decorator.vertices_push_back( Vertex()));
}
Halfedge_handle make_tetrahedron( const Point_3& p1,
const Point_3& p2,
const Point_3& p3,
const Point_3& p4) {
reserve( 4 + size_of_vertices(),
12 + size_of_halfedges(),
4 + size_of_facets());
HalfedgeDS_decorator<HDS> decorator(hds);
return make_tetrahedron( decorator.vertices_push_back( Vertex(p1)),
decorator.vertices_push_back( Vertex(p2)),
decorator.vertices_push_back( Vertex(p3)),
decorator.vertices_push_back( Vertex(p4)));
}
Halfedge_handle make_triangle() {
// the combinatorial structure of a single triangle with border
// edges is added to the actual polyhedral surface. Returns an
// arbitrary halfedge of this structure.
reserve( 3 + size_of_vertices(),
6 + size_of_halfedges(),
1 + size_of_facets());
HalfedgeDS_decorator<HDS> decorator(hds);
return make_triangle( decorator.vertices_push_back( Vertex()),
decorator.vertices_push_back( Vertex()),
decorator.vertices_push_back( Vertex()));
}
Halfedge_handle make_triangle( const Point_3& p1,
const Point_3& p2,
const Point_3& p3) {
// the single triangle p_1, p_2, p_3 with border edges is added to
// the actual polyhedral surface. Returns an arbitrary halfedge of
// this structure.
reserve( 3 + size_of_vertices(),
6 + size_of_halfedges(),
1 + size_of_facets());
HalfedgeDS_decorator<HDS> decorator(hds);
return make_triangle( decorator.vertices_push_back( Vertex(p1)),
decorator.vertices_push_back( Vertex(p2)),
decorator.vertices_push_back( Vertex(p3)));
}
// Access Member Functions
allocator_type get_allocator() const { return hds.get_allocator(); }
size_type size_of_vertices() const { return hds.size_of_vertices();}
// number of vertices.
size_type size_of_halfedges() const { return hds.size_of_halfedges();}
// number of all halfedges (including border halfedges).
size_type size_of_facets() const { return hds.size_of_faces();}
// number of facets.
bool empty() const { return size_of_halfedges() == 0; }
size_type capacity_of_vertices() const {
// space reserved for vertices.
return hds.capacity_of_vertices();
}
size_type capacity_of_halfedges() const {
// space reserved for halfedges.
return hds.capacity_of_halfedges();
}
size_type capacity_of_facets() const {
// space reserved for facets.
return hds.capacity_of_faces();
}
std::size_t bytes() const {
// bytes used for the polyhedron.
return sizeof(Self) - sizeof(HDS) + hds.bytes();
}
std::size_t bytes_reserved() const {
// bytes reserved for the polyhedron.
return sizeof(Self) - sizeof(HDS) + hds.bytes_reserved();
}
Vertex_iterator vertices_begin() { return hds.vertices_begin();}
// iterator over all vertices.
Vertex_iterator vertices_end() { return hds.vertices_end();}
Halfedge_iterator halfedges_begin() { return hds.halfedges_begin();}
// iterator over all halfedges
Halfedge_iterator halfedges_end() { return hds.halfedges_end();}
Facet_iterator facets_begin() { return hds.faces_begin();}
// iterator over all facets
Facet_iterator facets_end() { return hds.faces_end();}
// The constant iterators and circulators.
Vertex_const_iterator vertices_begin() const {
return hds.vertices_begin();
}
Vertex_const_iterator vertices_end() const {
return hds.vertices_end();
}
Halfedge_const_iterator halfedges_begin() const {
return hds.halfedges_begin();
}
Halfedge_const_iterator halfedges_end() const {
return hds.halfedges_end();
}
Facet_const_iterator facets_begin() const { return hds.faces_begin();}
Facet_const_iterator facets_end() const { return hds.faces_end();}
// Auxiliary iterators for convinience
Point_iterator points_begin() { return vertices_begin();}
Point_iterator points_end() { return vertices_end();}
Point_const_iterator points_begin() const { return vertices_begin();}
Point_const_iterator points_end() const { return vertices_end();}
Plane_iterator planes_begin() { return facets_begin();}
Plane_iterator planes_end() { return facets_end();}
Plane_const_iterator planes_begin() const { return facets_begin();}
Plane_const_iterator planes_end() const { return facets_end();}
Edge_iterator edges_begin() { return halfedges_begin();}
// iterator over all edges. The iterator refers to halfedges, but
// enumerates only one of the two corresponding opposite
// halfedges.
Edge_iterator edges_end() { return halfedges_end();}
// end of the range over all edges.
Edge_const_iterator edges_begin() const { return halfedges_begin();}
Edge_const_iterator edges_end() const { return halfedges_end();}
Traits& traits() { return m_traits; }
const Traits& traits() const { return m_traits; }
// Combinatorial Predicates
bool is_closed() const {
for ( Halfedge_const_iterator i = halfedges_begin();
i != halfedges_end(); ++i) {
if ( i->is_border())
return false;
}
return true;
}
private:
bool is_pure_bivalent( Tag_true) const {
for ( Vertex_const_iterator i = vertices_begin();
i != vertices_end(); ++i)
if ( ! i->is_bivalent())
return false;
return true;
}
bool is_pure_bivalent( Tag_false) const {
for ( Halfedge_const_iterator i = halfedges_begin();
i != halfedges_end(); ++i)
if ( ! i->is_bivalent())
return false;
return true;
}
public:
// returns true if all vertices have exactly two incident edges
bool is_pure_bivalent() const {
return is_pure_bivalent( Supports_vertex_halfedge());
}
private:
bool is_pure_trivalent( Tag_true) const {
for ( Vertex_const_iterator i = vertices_begin();
i != vertices_end(); ++i)
if ( ! i->is_trivalent())
return false;
return true;
}
bool is_pure_trivalent( Tag_false) const {
for ( Halfedge_const_iterator i = halfedges_begin();
i != halfedges_end(); ++i)
if ( ! i->is_trivalent())
return false;
return true;
}
public:
// returns true if all vertices have exactly three incident edges
bool is_pure_trivalent() const {
return is_pure_trivalent( Supports_vertex_halfedge());
}
private:
bool is_pure_triangle( Tag_true) const {
for ( Facet_const_iterator i = facets_begin();
i != facets_end(); ++i)
if ( ! i->is_triangle())
return false;
return true;
}
bool is_pure_triangle( Tag_false) const {
for ( Halfedge_const_iterator i = halfedges_begin();
i != halfedges_end(); ++i)
if ( ! i->is_border() && ! i->is_triangle())
return false;
return true;
}
public:
// returns true if all facets are triangles
bool is_pure_triangle() const {
return is_pure_triangle( Supports_facet_halfedge());
}
private:
bool is_pure_quad( Tag_true) const {
for ( Facet_const_iterator i = facets_begin();
i != facets_end(); ++i)
if ( ! i->is_quad())
return false;
return true;
}
bool is_pure_quad( Tag_false) const {
for ( Halfedge_const_iterator i = halfedges_begin();
i != halfedges_end(); ++i)
if ( ! i->is_border() && ! i->is_quad())
return false;
return true;
}
public:
// returns true if all facets are quadrilaterals
bool is_pure_quad() const {
return is_pure_quad( Supports_facet_halfedge());
}
// Geometric Predicates
bool
is_triangle( Halfedge_const_handle h1) const {
Halfedge_const_handle h2 = h1->next();
Halfedge_const_handle h3 = h1->next()->next();
// check halfedge combinatorics.
// exact two edges at vertices 1, 2, 3.
if ( h1->opposite()->next() != h3->opposite()) return false;
if ( h2->opposite()->next() != h1->opposite()) return false;
if ( h3->opposite()->next() != h2->opposite()) return false;
// The facet is a triangle.
if ( h1->next()->next()->next() != h1) return false;
if ( check_tag( Supports_halfedge_face())
&& ! h1->is_border_edge())
return false; // implies h2 and h3
CGAL_assertion( ! h1->is_border() || ! h1->opposite()->is_border());
// Assert consistency.
CGAL_assertion( h1 != h2);
CGAL_assertion( h1 != h3);
CGAL_assertion( h3 != h2);
// check prev pointer.
CGAL_assertion_code( HalfedgeDS_items_decorator<HDS> D;)
CGAL_assertion(D.get_prev(h1) == Halfedge_handle() ||
D.get_prev(h1) == h3);
CGAL_assertion(D.get_prev(h2) == Halfedge_handle() ||
D.get_prev(h2) == h1);
CGAL_assertion(D.get_prev(h3) == Halfedge_handle() ||
D.get_prev(h3) == h2);
// check vertices.
CGAL_assertion( D.get_vertex(h1) == D.get_vertex( h2->opposite()));
CGAL_assertion( D.get_vertex(h2) == D.get_vertex( h3->opposite()));
CGAL_assertion( D.get_vertex(h3) == D.get_vertex( h1->opposite()));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
D.get_vertex(h1) != D.get_vertex(h2));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
D.get_vertex(h1) != D.get_vertex(h3));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
D.get_vertex(h2) != D.get_vertex(h3));
// check facets.
CGAL_assertion( D.get_face(h1) == D.get_face(h2));
CGAL_assertion( D.get_face(h1) == D.get_face(h3));
return true;
}
bool
is_tetrahedron( Halfedge_const_handle h1) const {
Halfedge_const_handle h2 = h1->next();
Halfedge_const_handle h3 = h1->next()->next();
Halfedge_const_handle h4 = h1->opposite()->next();
Halfedge_const_handle h5 = h2->opposite()->next();
Halfedge_const_handle h6 = h3->opposite()->next();
// check halfedge combinatorics.
// at least three edges at vertices 1, 2, 3.
if ( h4 == h3->opposite()) return false;
if ( h5 == h1->opposite()) return false;
if ( h6 == h2->opposite()) return false;
// exact three edges at vertices 1, 2, 3.
if ( h4->opposite()->next() != h3->opposite()) return false;
if ( h5->opposite()->next() != h1->opposite()) return false;
if ( h6->opposite()->next() != h2->opposite()) return false;
// three edges at v4.
if ( h4->next()->opposite() != h5) return false;
if ( h5->next()->opposite() != h6) return false;
if ( h6->next()->opposite() != h4) return false;
// All facets are triangles.
if ( h1->next()->next()->next() != h1) return false;
if ( h4->next()->next()->next() != h4) return false;
if ( h5->next()->next()->next() != h5) return false;
if ( h6->next()->next()->next() != h6) return false;
// all edges are non-border edges.
if ( h1->is_border()) return false; // implies h2 and h3
CGAL_assertion( ! h2->is_border());
CGAL_assertion( ! h3->is_border());
if ( h4->is_border()) return false;
if ( h5->is_border()) return false;
if ( h6->is_border()) return false;
// Assert consistency.
CGAL_assertion( h1 != h2);
CGAL_assertion( h1 != h3);
CGAL_assertion( h3 != h2);
CGAL_assertion( h4 != h5);
CGAL_assertion( h5 != h6);
CGAL_assertion( h6 != h4);
// check prev pointer.
CGAL_assertion_code( HalfedgeDS_items_decorator<HDS> D;)
CGAL_assertion(D.get_prev(h1) == Halfedge_handle() ||
D.get_prev(h1) == h3);
CGAL_assertion(D.get_prev(h2) == Halfedge_handle() ||
D.get_prev(h2) == h1);
CGAL_assertion(D.get_prev(h3) == Halfedge_handle() ||
D.get_prev(h3) == h2);
CGAL_assertion(D.get_prev(h4) == Halfedge_handle() ||
D.get_prev(h4) == h1->opposite());
CGAL_assertion(D.get_prev(h5) == Halfedge_handle() ||
D.get_prev(h5) == h2->opposite());
CGAL_assertion(D.get_prev(h6) == Halfedge_handle() ||
D.get_prev(h6) == h3->opposite());
// check vertices.
CGAL_assertion( D.get_vertex(h1) == D.get_vertex( h2->opposite()));
CGAL_assertion( D.get_vertex(h1) == D.get_vertex( h5->opposite()));
CGAL_assertion( D.get_vertex(h2) == D.get_vertex( h3->opposite()));
CGAL_assertion( D.get_vertex(h2) == D.get_vertex( h6->opposite()));
CGAL_assertion( D.get_vertex(h3) == D.get_vertex( h1->opposite()));
CGAL_assertion( D.get_vertex(h3) == D.get_vertex( h4->opposite()));
CGAL_assertion( D.get_vertex(h4) == D.get_vertex( h5));
CGAL_assertion( D.get_vertex(h4) == D.get_vertex( h6));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
D.get_vertex(h1) != D.get_vertex(h2));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
D.get_vertex(h1) != D.get_vertex(h3));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
D.get_vertex(h1) != D.get_vertex(h4));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
D.get_vertex(h2) != D.get_vertex(h3));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
D.get_vertex(h2) != D.get_vertex(h4));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
D.get_vertex(h3) != D.get_vertex(h4));
// check facets.
CGAL_assertion( D.get_face(h1) == D.get_face(h2));
CGAL_assertion( D.get_face(h1) == D.get_face(h3));
CGAL_assertion( D.get_face(h4) == D.get_face(h4->next()));
CGAL_assertion( D.get_face(h4) == D.get_face(h1->opposite()));
CGAL_assertion( D.get_face(h5) == D.get_face(h5->next()));
CGAL_assertion( D.get_face(h5) == D.get_face(h2->opposite()));
CGAL_assertion( D.get_face(h6) == D.get_face(h6->next()));
CGAL_assertion( D.get_face(h6) == D.get_face(h3->opposite()));
CGAL_assertion( ! check_tag( Supports_halfedge_face()) ||
D.get_face(h1) != D.get_face(h4));
CGAL_assertion( ! check_tag( Supports_halfedge_face()) ||
D.get_face(h1) != D.get_face(h5));
CGAL_assertion( ! check_tag( Supports_halfedge_face()) ||
D.get_face(h1) != D.get_face(h6));
CGAL_assertion( ! check_tag( Supports_halfedge_face()) ||
D.get_face(h4) != D.get_face(h5));
CGAL_assertion( ! check_tag( Supports_halfedge_face()) ||
D.get_face(h4) != D.get_face(h6));
CGAL_assertion( ! check_tag( Supports_halfedge_face()) ||
D.get_face(h5) != D.get_face(h6));
return true;
}
// Euler Operators (Combinatorial Modifications)
//
// The following Euler operations modify consistently the combinatorial
// structure of the polyhedral surface. The geometry remains unchanged.
Halfedge_handle split_facet( Halfedge_handle h, Halfedge_handle g) {
// split the facet incident to `h' and `g' into two facets with
// new diagonal between the two vertices denoted by `h' and `g'
// respectively. The second (new) facet is a copy of the first
// facet. It returns the new diagonal. The time is proportional to
// the distance from `h' to `g' around the facet. Precondition:
// `h' and `g' are incident to the same facet. `h != g' (no
// loops). `h->next() != g' and `g->next() != h' (no multi-edges).
reserve( size_of_vertices(),
2 + size_of_halfedges(),
1 + size_of_facets());
HalfedgeDS_decorator<HDS> D(hds);
CGAL_precondition( D.get_face(h) == D.get_face(g));
CGAL_precondition( h != g);
CGAL_precondition( h != g->next());
CGAL_precondition( h->next() != g);
return D.split_face( h, g);
}
Halfedge_handle join_facet( Halfedge_handle h) {
// join the two facets incident to h. The facet incident to
// `h->opposite()' gets removed. Both facets might be holes.
// Returns the predecessor of h. The invariant `join_facet(
// split_facet( h, g))' returns h and keeps the polyhedron
// unchanged. The time is proportional to the size of the facet
// removed and the time to compute `h.prev()'. Precondition:
// `HDS' supports removal of facets. The degree of both
// vertices incident to h is at least three (no antennas).
HalfedgeDS_decorator<HDS> D(hds);
CGAL_precondition( circulator_size(h->vertex_begin())
>= size_type(3));
CGAL_precondition( circulator_size(h->opposite()->vertex_begin())
>= size_type(3));
return D.join_face(h);
}
Halfedge_handle split_vertex( Halfedge_handle h, Halfedge_handle g) {
// split the vertex incident to `h' and `g' into two vertices and
// connects them with a new edge. The second (new) vertex is a
// copy of the first vertex. It returns the new edge. The time is
// proportional to the distance from `h' to `g' around the vertex.
// Precondition: `h' and `g' are incident to the same vertex. `h
// != g' (no antennas). `h->next() != g' and `g->next() != h'.
reserve( 1 + size_of_vertices(),
2 + size_of_halfedges(),
size_of_facets());
HalfedgeDS_decorator<HDS> D(hds);
CGAL_precondition( D.get_vertex(h) == D.get_vertex(g));
CGAL_precondition( h != g);
return D.split_vertex( h, g);
}
Halfedge_handle join_vertex( Halfedge_handle h) {
// join the two vertices incident to h. The vertex denoted by
// `h->opposite()' gets removed. Returns the predecessor of h. The
// invariant `join_vertex( split_vertex( h, g))' returns h and
// keeps the polyhedron unchanged. The time is proportional to
// the degree of the vertex removed and the time to compute
// `h.prev()'.
// Precondition: `HDS' supports removal of vertices. The size of
// both facets incident to h is at least four (no multi-edges)
HalfedgeDS_decorator<HDS> D(hds);
CGAL_precondition( circulator_size( h->facet_begin())
>= size_type(4));
CGAL_precondition( circulator_size( h->opposite()->facet_begin())
>= size_type(4));
return D.join_vertex(h);
}
Halfedge_handle split_edge( Halfedge_handle h) {
return split_vertex( h->prev(), h->opposite())->opposite();
}
Halfedge_handle flip_edge( Halfedge_handle h) {
HalfedgeDS_items_decorator<HDS> D;
return D.flip_edge(h);
}
Halfedge_handle create_center_vertex( Halfedge_handle h) {
HalfedgeDS_decorator<HDS> D(hds);
CGAL_assertion( circulator_size( h->facet_begin())
>= size_type(3));
return D.create_center_vertex(h);
}
Halfedge_handle erase_center_vertex( Halfedge_handle h) {
HalfedgeDS_decorator<HDS> D(hds);
return D.erase_center_vertex(h);
}
// Euler Operators Modifying Genus
Halfedge_handle split_loop( Halfedge_handle h,
Halfedge_handle i,
Halfedge_handle j) {
// cut the polyhedron into two parts along the cycle (h,i,j).
// Three copies of the vertices and two new triangles will be
// created. h,i,j will be incident to the first new triangle. The
// returnvalue will be an halfedge iterator denoting the new
// halfegdes of the second new triangle which was h beforehand.
// Precondition: h,i,j are distinct, consecutive vertices of the
// polyhedron and form a cycle: i.e. `h->vertex() == i->opposite()
// ->vertex()', ..., `j->vertex() == h->opposite()->vertex()'. The
// six facets incident to h,i,j are all distinct.
reserve( 3 + size_of_vertices(),
6 + size_of_halfedges(),
2 + size_of_facets());
HalfedgeDS_decorator<HDS> D(hds);
CGAL_precondition( h != i);
CGAL_precondition( h != j);
CGAL_precondition( i != j);
CGAL_precondition( D.get_vertex(h) == D.get_vertex(i->opposite()));
CGAL_precondition( D.get_vertex(i) == D.get_vertex(j->opposite()));
CGAL_precondition( D.get_vertex(j) == D.get_vertex(h->opposite()));
CGAL_precondition( D.get_face(h) == Facet_handle() ||
D.get_face(h) != D.get_face(i));
CGAL_precondition( D.get_face(h) == Facet_handle() ||
D.get_face(h) != D.get_face(j));
CGAL_precondition( D.get_face(i) == Facet_handle() ||
D.get_face(i) != D.get_face(j));
CGAL_precondition( D.get_face(h) == Facet_handle() ||
D.get_face(h) != D.get_face(h->opposite()));
CGAL_precondition( D.get_face(h) == Facet_handle() ||
D.get_face(h) != D.get_face(i->opposite()));
CGAL_precondition( D.get_face(h) == Facet_handle() ||
D.get_face(h) != D.get_face(j->opposite()));
CGAL_precondition( D.get_face(i) == Facet_handle() ||
D.get_face(i) != D.get_face(h->opposite()));
CGAL_precondition( D.get_face(i) == Facet_handle() ||
D.get_face(i) != D.get_face(i->opposite()));
CGAL_precondition( D.get_face(i) == Facet_handle() ||
D.get_face(i) != D.get_face(j->opposite()));
CGAL_precondition( D.get_face(j) == Facet_handle() ||
D.get_face(j) != D.get_face(h->opposite()));
CGAL_precondition( D.get_face(j) == Facet_handle() ||
D.get_face(j) != D.get_face(i->opposite()));
CGAL_precondition( D.get_face(j) == Facet_handle() ||
D.get_face(j) != D.get_face(j->opposite()));
CGAL_precondition( D.get_face(h->opposite()) == Facet_handle() ||
D.get_face(h->opposite()) != D.get_face(i->opposite()));
CGAL_precondition( D.get_face(h->opposite()) == Facet_handle() ||
D.get_face(h->opposite()) != D.get_face(j->opposite()));
CGAL_precondition( D.get_face(i->opposite()) == Facet_handle() ||
D.get_face(i->opposite()) != D.get_face(j->opposite()));
return D.split_loop( h, i, j);
}
Halfedge_handle join_loop( Halfedge_handle h, Halfedge_handle g) {
// glues the boundary of two facets together. Both facets and the
// vertices of g gets removed. Returns an halfedge iterator for h.
// The invariant `join_loop( h, split_loop( h, i, j))' returns h
// and keeps the polyhedron unchanged. Precondition: `HDS'
// supports removal of vertices and facets. The facets denoted by
// h and g have equal size.
HalfedgeDS_decorator<HDS> D(hds);
CGAL_precondition( D.get_face(h) == Facet_handle() ||
D.get_face(h) != D.get_face(g));
CGAL_precondition( circulator_size( h->facet_begin())
>= size_type(3));
CGAL_precondition( circulator_size( h->facet_begin())
== circulator_size( g->facet_begin()));
return D.join_loop( h, g);
}
// Modifying Facets and Holes
Halfedge_handle make_hole( Halfedge_handle h) {
// removes incident facet and makes all halfedges incident to the
// facet to border edges. Returns h. Precondition: `HDS'
// supports removal of facets. `! h.is_border()'.
HalfedgeDS_decorator<HDS> D(hds);
return D.make_hole(h);
}
Halfedge_handle fill_hole( Halfedge_handle h) {
// fill a hole with a new created facet. Makes all border
// halfedges of the hole denoted by h incident to the new facet.
// Returns h. Precondition: `h.is_border()'.
reserve( size_of_vertices(),
size_of_halfedges(),
1 + size_of_facets());
HalfedgeDS_decorator<HDS> D(hds);
return D.fill_hole(h);
}
Halfedge_handle add_vertex_and_facet_to_border( Halfedge_handle h,
Halfedge_handle g) {
// creates a new facet within the hole incident to h and g by
// connecting the tip of g with the tip of h with two new
// halfedges and a new vertex and filling this separated part of
// the hole with a new facet. Returns the new halfedge incident to
// the new facet and the new vertex. Precondition: `h->is_border(
// )', `g->is_border()', `h != g', and g can be reached along the
// same hole starting with h.
CGAL_precondition( h != g);
reserve( 1 + size_of_vertices(),
4 + size_of_halfedges(),
1 + size_of_facets());
HalfedgeDS_decorator<HDS> D(hds);
Halfedge_handle hh = D.add_face_to_border( h, g);
CGAL_assertion( hh == g->next());
D.split_vertex( g, hh->opposite());
return g->next();
}
Halfedge_handle add_facet_to_border( Halfedge_handle h,
Halfedge_handle g) {
// creates a new facet within the hole incident to h and g by
// connecting the tip of g with the tip of h with a new halfedge
// and filling this separated part of the hole with a new facet.
// Returns the new halfedge incident to the new facet.
// Precondition: `h->is_border()', `g->is_border()', `h != g',
// `h->next() != g', and g can be reached along the same hole
// starting with h.
CGAL_precondition( h != g);
CGAL_precondition( h->next() != g);
reserve( size_of_vertices(),
2 + size_of_halfedges(),
1 + size_of_facets());
HalfedgeDS_decorator<HDS> D(hds);
return D.add_face_to_border( h, g);
}
// Erasing
void erase_facet( Halfedge_handle h) {
// removes the incident facet of h and changes all halfedges
// incident to the facet into border edges or removes them from
// the polyhedral surface if they were already border edges. See
// `make_hole(h)' for a more specialized variant. Precondition:
// `Traits' supports removal.
HalfedgeDS_decorator<HDS> D(hds);
D.erase_face(h);
}
void erase_connected_component( Halfedge_handle h) {
// removes the vertices, halfedges, and facets that belong to the
// connected component of h. Precondition: `Traits' supports
// removal.
HalfedgeDS_decorator<HDS> D(hds);
D.erase_connected_component(h);
}
/// Erases the small connected components and the isolated vertices.
///
/// @commentheading Preconditions:
/// supports vertices, halfedges, and removal operation.
///
/// @commentheading Template Parameters:
/// @param nb_components_to_keep the number of large connected components to keep.
///
/// @return the number of connected components erased (ignoring isolated vertices).
unsigned int keep_largest_connected_components(unsigned int nb_components_to_keep)
{
HalfedgeDS_decorator<HDS> D(hds);
return D.keep_largest_connected_components(nb_components_to_keep);
}
void clear() { hds.clear(); }
// removes all vertices, halfedges, and facets.
void erase_all() { clear(); }
// equivalent to `clear()'. Depricated.
// Special Operations on Polyhedral Surfaces
void delegate( Modifier_base<HDS>& modifier) {
// calls the `operator()' of the `modifier'. Precondition: The
// `modifier' returns a consistent representation.
modifier( hds);
CGAL_expensive_postcondition( is_valid());
}
// Operations with Border Halfedges
size_type size_of_border_halfedges() const {
// number of border halfedges. An edge with no incident facet
// counts as two border halfedges. Precondition: `normalize_border
// ()' has been called and no halfedge insertion or removal and no
// change in border status of the halfedges have occured since
// then.
return hds.size_of_border_halfedges();
}
size_type size_of_border_edges() const {
// number of border edges. If `size_of_border_edges() ==
// size_of_border_halfedges()' all border edges are incident to a
// facet on one side and to a hole on the other side.
// Precondition: `normalize_border()' has been called and no
// halfedge insertion or removal and no change in border status of
// the halfedges have occured since then.
return hds.size_of_border_edges();
}
Halfedge_iterator border_halfedges_begin() {
// halfedge iterator starting with the border edges. The range [
// `halfedges_begin(), border_halfedges_begin()') denotes all
// non-border edges. The range [`border_halfedges_begin(),
// halfedges_end()') denotes all border edges. Precondition:
// `normalize_border()' has been called and no halfedge insertion
// or removal and no change in border status of the halfedges have
// occured since then.
return hds.border_halfedges_begin();
}
Halfedge_const_iterator border_halfedges_begin() const {
return hds.border_halfedges_begin();
}
// Convenient edge iterator
Edge_iterator border_edges_begin() { return border_halfedges_begin(); }
Edge_const_iterator border_edges_begin() const {
return border_halfedges_begin();
}
bool normalized_border_is_valid( bool verbose = false) const {
// checks whether all non-border edges precedes the border edges.
HalfedgeDS_const_decorator<HDS> decorator(hds);
bool valid = decorator.normalized_border_is_valid( verbose);
for ( Halfedge_const_iterator i = border_halfedges_begin();
valid && (i != halfedges_end()); (++i, ++i)) {
if ( i->is_border()) {
Verbose_ostream verr(verbose);
verr << " both halfedges of an edge are border "
"halfedges." << std::endl;
valid = false;
}
}
return valid;
}
void normalize_border() {
// sorts halfedges such that the non-border edges precedes the
// border edges.
hds.normalize_border();
CGAL_postcondition( normalized_border_is_valid());
}
protected: // Supports_face_plane
void inside_out_geometry( Tag_false) {}
void inside_out_geometry( Tag_true) {
typename Traits::Construct_opposite_plane_3 opp
= traits().construct_opposite_plane_3_object();
std::transform( planes_begin(), planes_end(), planes_begin(), opp);
}
public:
void inside_out() {
// reverse facet orientation.
HalfedgeDS_decorator<HDS> decorator(hds);
decorator.inside_out();
inside_out_geometry( Supports_face_plane());
}
bool is_valid( bool verb = false, int level = 0) const {
// checks the combinatorial consistency.
Verbose_ostream verr(verb);
verr << "begin CGAL::Polyhedron_3<...>::is_valid( verb=true, "
"level = " << level << "):" << std::endl;
HalfedgeDS_const_decorator<HDS> D(hds);
bool valid = D.is_valid( verb, level + 3);
// All halfedges.
Halfedge_const_iterator i = halfedges_begin();
Halfedge_const_iterator end = halfedges_end();
size_type n = 0;
for( ; valid && (i != end); ++i) {
verr << "halfedge " << n << std::endl;
// At least triangular facets and distinct geometry.
valid = valid && ( i->next() != i);
valid = valid && ( i->next()->next() != i);
valid = valid && ( ! check_tag( Supports_halfedge_vertex()) ||
D.get_vertex(i) != D.get_vertex(i->opposite()));
valid = valid && ( ! check_tag( Supports_halfedge_vertex()) ||
D.get_vertex(i) != D.get_vertex(i->next()));
valid = valid && ( ! check_tag( Supports_halfedge_vertex()) ||
D.get_vertex(i) != D.get_vertex(i->next()->next()));
if ( ! valid) {
verr << " incident facet is not at least a triangle."
<< std::endl;
break;
}
// Distinct facets on each side of an halfegde.
valid = valid && ( ! check_tag( Supports_halfedge_face()) ||
D.get_face(i) != D.get_face(i->opposite()));
if ( ! valid) {
verr << " both incident facets are equal." << std::endl;
break;
}
++n;
}
valid = valid && (n == size_of_halfedges());
if ( n != size_of_halfedges())
verr << "counting halfedges failed." << std::endl;
verr << "end of CGAL::Polyhedron_3<...>::is_valid(): structure is "
<< ( valid ? "valid." : "NOT VALID.") << std::endl;
return valid;
}
};
} //namespace CGAL
#endif // CGAL_POLYHEDRON_3_H //
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