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cgal/Packages/Polyhedron/include/CGAL/Polyhedron_old/Polyhedron_3.h

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// ============================================================================
//
// Copyright (c) 1997 The CGAL Consortium
//
// This software and related documentation is part of an INTERNAL release
// of the Computational Geometry Algorithms Library (CGAL). It is not
// intended for general use.
//
// ----------------------------------------------------------------------------
//
// release : $CGAL_Revision: $
// release_date : $CGAL_Date: $
//
// file : include/CGAL/Polyhedron_old/Polyhedron_3.h
// package : Polyhedron 2.9 (13 Sep 2000)
// chapter : 3D-Polyhedral Surfaces
//
// revision : $Revision$
// revision_date : $Date$
//
// author(s) : Lutz Kettner <kettner@mpi-sb.mpg.de>)
// maintainer :
// coordinator : MPI Saarbruecken
//
// Polyhedral Surfaces.
// ============================================================================
#ifndef CGAL_POLYHEDRON_OLD_POLYHEDRON_3_H
#define CGAL_POLYHEDRON_OLD_POLYHEDRON_3_H 1
#include <CGAL/Halfedge_data_structure_polyhedron_default_3.h>
#include <CGAL/Halfedge_data_structure_decorator.h>
#ifdef CGAL_REP_CLASS_DEFINED
#include <CGAL/Polyhedron_default_traits_3.h>
#endif // CGAL_REP_CLASS_DEFINED
#include <CGAL/Polyhedron_iterator_3.h>
#include <CGAL/Iterator_project.h>
#include <CGAL/function_objects.h>
#include <CGAL/N_step_adaptor_derived.h>
#include <CGAL/Modifier_base.h>
#include <CGAL/IO/Verbose_ostream.h>
CGAL_BEGIN_NAMESPACE
// Forward declaration of the three element classes.
template <class HDS> class _Polyhedron_vertex;
template <class HDS> class _Polyhedron_halfedge;
template <class HDS> class _Polyhedron_facet;
// 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 HDS>
class _Polyhedron_halfedge : public HDS::Halfedge {
public:
typedef HDS Halfedge_data_structure;
protected:
typedef typename HDS::Vertex V;
typedef typename HDS::Halfedge H;
typedef typename HDS::Facet F;
public:
typedef _Polyhedron_vertex<HDS> Vertex_;
typedef _Polyhedron_halfedge<HDS> Halfedge_;
typedef _Polyhedron_facet<HDS> Facet_;
typedef typename HDS::Size Size;
typedef typename HDS::Difference Difference;
// The following types denotes the (optionally) associated geometry. If
// the specific item is not supported the type is `void*'.
typedef typename HDS::Point Point;
typedef typename HDS::Point Point_3;
typedef typename F::Vector_3 Vector_3;
typedef typename F::Plane_3 Plane_3;
// The following types are equal to either `Tag_true' or
// `Tag_false', dependant whether the named feature is
// supported or not.
typedef typename HDS::Supports_vertex_halfedge
Supports_vertex_halfedge;
typedef typename HDS::Supports_halfedge_prev
Supports_halfedge_prev;
typedef typename HDS::Supports_halfedge_vertex
Supports_halfedge_vertex;
typedef typename HDS::Supports_halfedge_facet
Supports_halfedge_facet;
typedef typename HDS::Supports_facet_halfedge
Supports_facet_halfedge;
typedef typename HDS::Supports_vertex_point Supports_vertex_point;
typedef typename HDS::Supports_facet_plane Supports_facet_plane;
typedef typename HDS::Supports_facet_normal Supports_facet_normal;
typedef typename HDS::Supports_removal Supports_removal;
// The iterator/circulator categories.
typedef typename HDS::iterator_category iterator_category;
typedef Polyhedron_circulator_traits<Supports_halfedge_prev>
Circ_traits;
typedef typename Circ_traits::iterator_category
circulator_category;
protected:
// These extra (internal) typedefs are necessary to make
// SunPro CC 4.2 happy. (And they are used.)
typedef typename HDS::Vertex_iterator TR_VI;
typedef typename HDS::Vertex_const_iterator TR_C_VI;
typedef typename HDS::Halfedge_iterator TR_HI;
typedef typename HDS::Halfedge_const_iterator TR_C_HI;
typedef typename HDS::Edge_iterator TR_EI;
typedef typename HDS::Edge_const_iterator TR_C_EI;
typedef typename HDS::Facet_iterator TR_FI;
typedef typename HDS::Facet_const_iterator TR_C_FI;
public:
typedef _Polyhedron_iterator<
TR_VI,
Vertex_,
Difference, iterator_category> Vertex_iterator;
typedef _Polyhedron_const_iterator<
TR_C_VI, TR_VI,
Vertex_,
Difference, iterator_category> Vertex_const_iterator;
typedef _Polyhedron_iterator<
TR_HI,
Halfedge_,
Difference, iterator_category> Halfedge_iterator;
typedef _Polyhedron_const_iterator<
TR_C_HI, TR_HI,
Halfedge_,
Difference, iterator_category> Halfedge_const_iterator;
typedef _Polyhedron_iterator<
TR_FI,
Facet_,
Difference, iterator_category> Facet_iterator;
typedef _Polyhedron_const_iterator<
TR_C_FI, TR_FI,
Facet_,
Difference, iterator_category> Facet_const_iterator;
// The circulators around a vertex or around a facet.
typedef _Polyhedron_facet_circ<
Halfedge_,
Halfedge_iterator,
circulator_category> Halfedge_around_facet_circulator;
typedef _Polyhedron_vertex_circ<
Halfedge_,
Halfedge_iterator,
circulator_category> Halfedge_around_vertex_circulator;
typedef _Polyhedron_facet_const_circ<
Halfedge_,
Halfedge_const_iterator,
circulator_category> Halfedge_around_facet_const_circulator;
typedef _Polyhedron_vertex_const_circ<
Halfedge_,
Halfedge_const_iterator,
circulator_category> Halfedge_around_vertex_const_circulator;
// The handles. They are currently only simple typedef's.
typedef Vertex_iterator Vertex_handle;
typedef Vertex_const_iterator Vertex_const_handle;
typedef Halfedge_iterator Halfedge_handle;
typedef Halfedge_const_iterator Halfedge_const_handle;
typedef Facet_iterator Facet_handle;
typedef Facet_const_iterator Facet_const_handle;
// Edge iterator.
typedef N_step_adaptor_derived<Halfedge_iterator, 2>
Edge_iterator;
typedef N_step_adaptor_derived<Halfedge_const_iterator, 2>
Edge_const_iterator;
public:
typedef _Polyhedron_vertex<HDS> Vertex;
typedef _Polyhedron_facet<HDS> Facet;
_Polyhedron_halfedge() {}
_Polyhedron_halfedge( const H& h) : H(h) {}
Halfedge_handle opposite() { return TR_HI( H::opposite());}
Halfedge_handle next() { return TR_HI( H::next());}
Halfedge_handle prev() {
// returns the halfedge previous to this. Uses the `prev()'
// method if available or performs a search around the facet.
Halfedge_data_structure_decorator<HDS> decorator;
return TR_HI(decorator.find_prev((H*)(this)));
}
Vertex_handle vertex() { return TR_VI( H::vertex());}
Facet_handle facet() { return TR_FI( H::facet());}
Halfedge_const_handle opposite() const {
return TR_C_HI( H::opposite());
}
Halfedge_const_handle next() const {
return TR_C_HI( H::next());
}
Halfedge_const_handle prev() const {
Halfedge_data_structure_decorator<HDS> D;
return TR_C_HI( D.find_prev(this));
}
Vertex_const_handle vertex() const {
return TR_C_VI( H::vertex());
}
Facet_const_handle facet() const {
return TR_C_FI(H::facet());
}
// Derived Access Functions (not present in H).
Halfedge_handle next_on_vertex() {
return next()->opposite();
}
Halfedge_const_handle next_on_vertex() const {
return next()->opposite();
}
// the next halfedge around the vertex (clockwise). Is equal to
// `h.next()->opposite()'.
Halfedge_handle prev_on_vertex() {
return opposite()->prev();
}
Halfedge_const_handle prev_on_vertex() const {
return opposite()->prev();
}
// the previous halfedge around the vertex (counterclockwise). Is
// equal to `h.opposite()->prev()'.
bool is_border_edge() const {
// is true if `h' or `h.opposite()' is a border halfedge.
return (opposite()->is_border() || is_border());
}
Halfedge_around_vertex_circulator vertex_begin() {
// a circulator of halfedges around the vertex (clockwise).
return Halfedge_around_vertex_circulator(TR_HI(this));
}
Halfedge_around_vertex_const_circulator vertex_begin() const {
// a circulator of halfedges around the vertex (clockwise).
return Halfedge_around_vertex_const_circulator(TR_C_HI(this));
}
Halfedge_around_facet_circulator facet_begin() {
// a circulator of halfedges around the facet (counterclockwise).
return Halfedge_around_facet_circulator(TR_HI(this));
}
Halfedge_around_facet_const_circulator facet_begin() const {
// a circulator of halfedges around the facet (counterclockwise).
return Halfedge_around_facet_const_circulator(TR_C_HI(this));
}
private:
// Hide some other functions of H.
void set_next( Halfedge_* h) { H::set_next(h);}
void set_prev( Halfedge_* h) { H::set_prev(h);}
void set_vertex( Vertex* v) { H::set_vertex(v);}
void set_facet( Facet* f) { H::set_facet(f);}
};
template <class HDS>
class _Polyhedron_vertex : public HDS::Vertex {
public:
typedef HDS Halfedge_data_structure;
protected:
typedef typename HDS::Vertex V;
typedef typename HDS::Halfedge H;
typedef typename HDS::Facet F;
public:
typedef _Polyhedron_vertex<HDS> Vertex_;
typedef _Polyhedron_halfedge<HDS> Halfedge_;
typedef _Polyhedron_facet<HDS> Facet_;
typedef typename HDS::Size Size;
typedef typename HDS::Difference Difference;
// The following types denotes the (optionally) associated geometry. If
// the specific item is not supported the type is `void*'.
typedef typename HDS::Point Point;
typedef typename HDS::Point Point_3;
typedef typename F::Vector_3 Vector_3;
typedef typename F::Plane_3 Plane_3;
// The following types are equal to either `Tag_true' or
// `Tag_false', dependant whether the named feature is
// supported or not.
typedef typename HDS::Supports_vertex_halfedge
Supports_vertex_halfedge;
typedef typename HDS::Supports_halfedge_prev
Supports_halfedge_prev;
typedef typename HDS::Supports_halfedge_vertex
Supports_halfedge_vertex;
typedef typename HDS::Supports_halfedge_facet
Supports_halfedge_facet;
typedef typename HDS::Supports_facet_halfedge
Supports_facet_halfedge;
typedef typename HDS::Supports_vertex_point Supports_vertex_point;
typedef typename HDS::Supports_facet_plane Supports_facet_plane;
typedef typename HDS::Supports_facet_normal Supports_facet_normal;
typedef typename HDS::Supports_removal Supports_removal;
// The iterator/circulator categories.
typedef typename HDS::iterator_category iterator_category;
typedef Polyhedron_circulator_traits<Supports_halfedge_prev>
Circ_traits;
typedef typename Circ_traits::iterator_category
circulator_category;
protected:
// These extra (internal) typedefs are necessary to make
// SunPro CC 4.2 happy. (And they are used.)
typedef typename HDS::Vertex_iterator TR_VI;
typedef typename HDS::Vertex_const_iterator TR_C_VI;
typedef typename HDS::Halfedge_iterator TR_HI;
typedef typename HDS::Halfedge_const_iterator TR_C_HI;
typedef typename HDS::Edge_iterator TR_EI;
typedef typename HDS::Edge_const_iterator TR_C_EI;
typedef typename HDS::Facet_iterator TR_FI;
typedef typename HDS::Facet_const_iterator TR_C_FI;
public:
typedef _Polyhedron_iterator<
TR_VI,
Vertex_,
Difference, iterator_category> Vertex_iterator;
typedef _Polyhedron_const_iterator<
TR_C_VI, TR_VI,
Vertex_,
Difference, iterator_category> Vertex_const_iterator;
typedef _Polyhedron_iterator<
TR_HI,
Halfedge_,
Difference, iterator_category> Halfedge_iterator;
typedef _Polyhedron_const_iterator<
TR_C_HI, TR_HI,
Halfedge_,
Difference, iterator_category> Halfedge_const_iterator;
typedef _Polyhedron_iterator<
TR_FI,
Facet_,
Difference, iterator_category> Facet_iterator;
typedef _Polyhedron_const_iterator<
TR_C_FI, TR_FI,
Facet_,
Difference, iterator_category> Facet_const_iterator;
// The circulators around a vertex or around a facet.
typedef _Polyhedron_facet_circ<
Halfedge_,
Halfedge_iterator,
circulator_category> Halfedge_around_facet_circulator;
typedef _Polyhedron_vertex_circ<
Halfedge_,
Halfedge_iterator,
circulator_category> Halfedge_around_vertex_circulator;
typedef _Polyhedron_facet_const_circ<
Halfedge_,
Halfedge_const_iterator,
circulator_category> Halfedge_around_facet_const_circulator;
typedef _Polyhedron_vertex_const_circ<
Halfedge_,
Halfedge_const_iterator,
circulator_category> Halfedge_around_vertex_const_circulator;
// The handles. They are currently only simple typedef's.
typedef Vertex_iterator Vertex_handle;
typedef Vertex_const_iterator Vertex_const_handle;
typedef Halfedge_iterator Halfedge_handle;
typedef Halfedge_const_iterator Halfedge_const_handle;
typedef Facet_iterator Facet_handle;
typedef Facet_const_iterator Facet_const_handle;
// Edge iterator.
typedef N_step_adaptor_derived<Halfedge_iterator, 2>
Edge_iterator;
typedef N_step_adaptor_derived<Halfedge_const_iterator, 2>
Edge_const_iterator;
public:
typedef _Polyhedron_halfedge<HDS> Halfedge;
typedef _Polyhedron_facet<HDS> Facet;
_Polyhedron_vertex() {}
_Polyhedron_vertex( const V& v) : V(v) {}
Halfedge_handle halfedge() {return TR_HI( V::halfedge());}
Halfedge_const_handle halfedge() const {
return TR_C_HI( V::halfedge());
}
// Avoids unnecessary matchings with base class. (g++ bug)
Point& point() { return V::point();}
const Point& point() const { return V::point();}
// Derived Access Functions (not present in V).
Halfedge_around_vertex_circulator vertex_begin() {
// a circulator of halfedges around the vertex (clockwise).
return Halfedge_around_vertex_circulator( TR_HI(halfedge().ptr()));
}
Halfedge_around_vertex_const_circulator vertex_begin() const {
// a circulator of halfedges around the vertex (clockwise).
return Halfedge_around_vertex_const_circulator(
TR_C_HI(halfedge().ptr()));
}
private:
// Hide some other functions of V.
void set_halfedge( Halfedge* h) { V::set_halfedge(h);}
};
template <class HDS>
class _Polyhedron_facet : public HDS::Facet {
public:
typedef HDS Halfedge_data_structure;
protected:
typedef typename HDS::Vertex V;
typedef typename HDS::Halfedge H;
typedef typename HDS::Facet F;
public:
typedef _Polyhedron_vertex<HDS> Vertex_;
typedef _Polyhedron_halfedge<HDS> Halfedge_;
typedef _Polyhedron_facet<HDS> Facet_;
typedef typename HDS::Size Size;
typedef typename HDS::Difference Difference;
// The following types denotes the (optionally) associated geometry. If
// the specific item is not supported the type is `void*'.
typedef typename HDS::Point Point;
typedef typename HDS::Point Point_3;
typedef typename F::Vector_3 Vector_3;
typedef typename F::Plane_3 Plane_3;
// The following types are equal to either `Tag_true' or
// `Tag_false', dependant whether the named feature is
// supported or not.
typedef typename HDS::Supports_vertex_halfedge
Supports_vertex_halfedge;
typedef typename HDS::Supports_halfedge_prev
Supports_halfedge_prev;
typedef typename HDS::Supports_halfedge_vertex
Supports_halfedge_vertex;
typedef typename HDS::Supports_halfedge_facet
Supports_halfedge_facet;
typedef typename HDS::Supports_facet_halfedge
Supports_facet_halfedge;
typedef typename HDS::Supports_vertex_point Supports_vertex_point;
typedef typename HDS::Supports_facet_plane Supports_facet_plane;
typedef typename HDS::Supports_facet_normal Supports_facet_normal;
typedef typename HDS::Supports_removal Supports_removal;
// The iterator/circulator categories.
typedef typename HDS::iterator_category iterator_category;
typedef Polyhedron_circulator_traits<Supports_halfedge_prev>
Circ_traits;
typedef typename Circ_traits::iterator_category
circulator_category;
protected:
// These extra (internal) typedefs are necessary to make
// SunPro CC 4.2 happy. (And they are used.)
typedef typename HDS::Vertex_iterator TR_VI;
typedef typename HDS::Vertex_const_iterator TR_C_VI;
typedef typename HDS::Halfedge_iterator TR_HI;
typedef typename HDS::Halfedge_const_iterator TR_C_HI;
typedef typename HDS::Edge_iterator TR_EI;
typedef typename HDS::Edge_const_iterator TR_C_EI;
typedef typename HDS::Facet_iterator TR_FI;
typedef typename HDS::Facet_const_iterator TR_C_FI;
public:
typedef _Polyhedron_iterator<
TR_VI,
Vertex_,
Difference, iterator_category> Vertex_iterator;
typedef _Polyhedron_const_iterator<
TR_C_VI, TR_VI,
Vertex_,
Difference, iterator_category> Vertex_const_iterator;
typedef _Polyhedron_iterator<
TR_HI,
Halfedge_,
Difference, iterator_category> Halfedge_iterator;
typedef _Polyhedron_const_iterator<
TR_C_HI, TR_HI,
Halfedge_,
Difference, iterator_category> Halfedge_const_iterator;
typedef _Polyhedron_iterator<
TR_FI,
Facet_,
Difference, iterator_category> Facet_iterator;
typedef _Polyhedron_const_iterator<
TR_C_FI, TR_FI,
Facet_,
Difference, iterator_category> Facet_const_iterator;
// The circulators around a vertex or around a facet.
typedef _Polyhedron_facet_circ<
Halfedge_,
Halfedge_iterator,
circulator_category> Halfedge_around_facet_circulator;
typedef _Polyhedron_vertex_circ<
Halfedge_,
Halfedge_iterator,
circulator_category> Halfedge_around_vertex_circulator;
typedef _Polyhedron_facet_const_circ<
Halfedge_,
Halfedge_const_iterator,
circulator_category> Halfedge_around_facet_const_circulator;
typedef _Polyhedron_vertex_const_circ<
Halfedge_,
Halfedge_const_iterator,
circulator_category> Halfedge_around_vertex_const_circulator;
// The handles. They are currently only simple typedef's.
typedef Vertex_iterator Vertex_handle;
typedef Vertex_const_iterator Vertex_const_handle;
typedef Halfedge_iterator Halfedge_handle;
typedef Halfedge_const_iterator Halfedge_const_handle;
typedef Facet_iterator Facet_handle;
typedef Facet_const_iterator Facet_const_handle;
// Edge iterator.
typedef N_step_adaptor_derived<Halfedge_iterator, 2>
Edge_iterator;
typedef N_step_adaptor_derived<Halfedge_const_iterator, 2>
Edge_const_iterator;
public:
typedef _Polyhedron_vertex<HDS> Vertex;
typedef _Polyhedron_halfedge<HDS> Halfedge;
_Polyhedron_facet() {}
_Polyhedron_facet( const F& f) : F(f) {}
Halfedge_handle halfedge() {return TR_HI( F::halfedge());}
Halfedge_const_handle halfedge() const {
return TR_C_HI( F::halfedge());
}
// Avoids unnecessary matchings with base class. (g++ bug)
Vector_3 normal() const { return F::normal();}
Plane_3& plane() { return F::plane();}
const Plane_3& plane() const { return F::plane();}
// Derived Access Functions (not present in F).
Halfedge_around_facet_circulator facet_begin() {
// a circulator of halfedges around the facet (counterclockwise).
return Halfedge_around_facet_circulator( TR_HI(halfedge().ptr()));
}
Halfedge_around_facet_const_circulator facet_begin() const {
// a circulator of halfedges around the facet (counterclockwise).
return Halfedge_around_facet_const_circulator(
TR_C_HI(halfedge().ptr()));
}
private:
// Hide some other functions of F.
void set_halfedge( Halfedge* h) { F::set_halfedge(h);}
};
template < class TR, class HDS
= CGAL::Halfedge_data_structure_polyhedron_default_3< TR> >
class Polyhedron_3 {
//
// DEFINITION
//
// The boundary representation of a 3d-polyhedron P of the type
// Polyhedron<HDS> 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<HDS> 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 HDS Halfedge_data_structure;
typedef HDS HalfedgeDS;
protected:
typedef typename HDS::Vertex V;
typedef typename HDS::Halfedge H;
typedef typename HDS::Facet F;
public:
typedef _Polyhedron_vertex<HDS> Vertex_;
typedef _Polyhedron_halfedge<HDS> Halfedge_;
typedef _Polyhedron_facet<HDS> Facet_;
typedef typename HDS::Size Size;
typedef typename HDS::Difference Difference;
// The following types denotes the (optionally) associated geometry. If
// the specific item is not supported the type is `void*'.
typedef typename HDS::Point Point;
typedef typename HDS::Point Point_3;
typedef typename F::Vector_3 Vector_3;
typedef typename F::Plane_3 Plane_3;
// The following types are equal to either `Tag_true' or
// `Tag_false', dependant whether the named feature is
// supported or not.
typedef typename HDS::Supports_vertex_halfedge
Supports_vertex_halfedge;
typedef typename HDS::Supports_halfedge_prev
Supports_halfedge_prev;
typedef typename HDS::Supports_halfedge_vertex
Supports_halfedge_vertex;
typedef typename HDS::Supports_halfedge_facet
Supports_halfedge_facet;
typedef typename HDS::Supports_facet_halfedge
Supports_facet_halfedge;
typedef typename HDS::Supports_vertex_point Supports_vertex_point;
typedef typename HDS::Supports_facet_plane Supports_facet_plane;
typedef typename HDS::Supports_facet_normal Supports_facet_normal;
typedef typename HDS::Supports_removal Supports_removal;
// The iterator/circulator categories.
typedef typename HDS::iterator_category iterator_category;
typedef Polyhedron_circulator_traits<Supports_halfedge_prev>
Circ_traits;
typedef typename Circ_traits::iterator_category
circulator_category;
protected:
// These extra (internal) typedefs are necessary to make
// SunPro CC 4.2 happy. (And they are used.)
typedef typename HDS::Vertex_iterator TR_VI;
typedef typename HDS::Vertex_const_iterator TR_C_VI;
typedef typename HDS::Halfedge_iterator TR_HI;
typedef typename HDS::Halfedge_const_iterator TR_C_HI;
typedef typename HDS::Edge_iterator TR_EI;
typedef typename HDS::Edge_const_iterator TR_C_EI;
typedef typename HDS::Facet_iterator TR_FI;
typedef typename HDS::Facet_const_iterator TR_C_FI;
public:
typedef _Polyhedron_iterator<
TR_VI,
Vertex_,
Difference, iterator_category> Vertex_iterator;
typedef _Polyhedron_const_iterator<
TR_C_VI, TR_VI,
Vertex_,
Difference, iterator_category> Vertex_const_iterator;
typedef _Polyhedron_iterator<
TR_HI,
Halfedge_,
Difference, iterator_category> Halfedge_iterator;
typedef _Polyhedron_const_iterator<
TR_C_HI, TR_HI,
Halfedge_,
Difference, iterator_category> Halfedge_const_iterator;
typedef _Polyhedron_iterator<
TR_FI,
Facet_,
Difference, iterator_category> Facet_iterator;
typedef _Polyhedron_const_iterator<
TR_C_FI, TR_FI,
Facet_,
Difference, iterator_category> Facet_const_iterator;
// The circulators around a vertex or around a facet.
typedef _Polyhedron_facet_circ<
Halfedge_,
Halfedge_iterator,
circulator_category> Halfedge_around_facet_circulator;
typedef _Polyhedron_vertex_circ<
Halfedge_,
Halfedge_iterator,
circulator_category> Halfedge_around_vertex_circulator;
typedef _Polyhedron_facet_const_circ<
Halfedge_,
Halfedge_const_iterator,
circulator_category> Halfedge_around_facet_const_circulator;
typedef _Polyhedron_vertex_const_circ<
Halfedge_,
Halfedge_const_iterator,
circulator_category> Halfedge_around_vertex_const_circulator;
// The handles. They are currently only simple typedef's.
typedef Vertex_iterator Vertex_handle;
typedef Vertex_const_iterator Vertex_const_handle;
typedef Halfedge_iterator Halfedge_handle;
typedef Halfedge_const_iterator Halfedge_const_handle;
typedef Facet_iterator Facet_handle;
typedef Facet_const_iterator Facet_const_handle;
// Edge iterator.
typedef N_step_adaptor_derived<Halfedge_iterator, 2>
Edge_iterator;
typedef N_step_adaptor_derived<Halfedge_const_iterator, 2>
Edge_const_iterator;
typedef TR Traits;
public:
typedef _Polyhedron_vertex<HDS> Vertex;
typedef _Polyhedron_halfedge<HDS> Halfedge;
typedef _Polyhedron_facet<HDS> Facet;
protected:
HDS hds; // the boundary representation.
TR m_traits;
public:
typedef Polyhedron_3<TR,HDS> Self;
// CREATION
Polyhedron_3( const Traits& traits = Traits())
: m_traits(traits) {
// the empty polyhedron `P'.
typedef typename Traits::Point_3 Traits_point;
assert_equal_types( Point(), Traits_point());
}
Polyhedron_3( Size v, Size h, Size 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.
typedef typename Traits::Point_3 Traits_point;
assert_equal_types( Point(), Traits_point());
}
//Polyhedron_3( const Self& p);
// copy constructor.
//Self& operator= ( const Self& p);
// assignment operator.
// Explicit implementation to help EGCS in compiling ...
Self& operator= ( const Self& p) {
hds = p.hds;
m_traits = p.m_traits;
return *this;
}
void reserve( Size v, Size h, Size f) { hds.reserve(v,h,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.
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
protected:
Halfedge_handle make_tetrahedron( V* v1, V* v2, V* v3, V* v4);
Halfedge_handle make_triangle( V* v1, V* v2, V* v3);
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.
Halfedge_handle make_tetrahedron(const Point& p1,
const Point& p2,
const Point& p3,
const Point& 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.
Halfedge_handle make_triangle(const Point& p1,
const Point& p2,
const Point& 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.
#endif // CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS //
// Access Member Functions
Size size_of_vertices() const { return hds.size_of_vertices();}
// number of vertices.
Size size_of_halfedges() const { return hds.size_of_halfedges();}
// number of all halfedges (including border halfedges).
Size size_of_facets() const { return hds.size_of_facets();}
// number of facets.
Size capacity_of_vertices() const {return hds.capacity_of_vertices();}
// space reserved for vertices.
Size capacity_of_halfedges() const {
// space reserved for halfedges.
return hds.capacity_of_halfedges();
}
Size capacity_of_facets() const { return hds.capacity_of_facets();}
// space reserved for facets.
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.facets_begin();}
// iterator over all facets
Facet_iterator facets_end() { return hds.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.
// 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.facets_begin();}
Facet_const_iterator facets_end() const {return hds.facets_end();}
Edge_const_iterator edges_begin() const {return halfedges_begin();}
Edge_const_iterator edges_end() const {return halfedges_end();}
const Traits& traits() const { return m_traits; }
// Geometric Predicates
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
bool is_triangle( Halfedge_const_handle h) const;
// returns whether the connected component containing h is a
// single triangle.
bool is_tetrahedron( Halfedge_const_handle h) const;
// returns whether the connected component containing h is a
// single tetrahedron.
// 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).
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).
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'.
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)}
//
// 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.
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.
#endif // CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS //
// 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()'.
Halfedge_data_structure_decorator<HDS> D;
return TR_HI( D.make_hole( hds, h.ptr()));
}
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()'.
Halfedge_data_structure_decorator<HDS> D;
return TR_HI( D.fill_hole( hds, h.ptr()));
}
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);
Halfedge_data_structure_decorator<HDS> D;
H* hh = D.add_facet_to_border( hds, h.ptr(), g.ptr());
CGAL_assertion( hh == &*(g.ptr()->next()));
D.split_vertex( hds, g.ptr(), 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);
Halfedge_data_structure_decorator<HDS> D;
return TR_HI( D.add_facet_to_border( hds, h.ptr(), g.ptr()));
}
// 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.
Halfedge_data_structure_decorator<HDS> D;
D.erase_facet( hds, h.ptr());
}
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.
Halfedge_data_structure_decorator<HDS> D;
D.erase_connected_component( hds, h.ptr());
}
void clear() {
// removes all vertices, halfedges, and facets.
hds.delete_all();
}
void erase_all() {
// equivalent to `clear()'. Depricated.
clear();
}
// 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_postcondition( is_valid());
}
// Operations with Border Halfedges
Size 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 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();
}
Edge_iterator border_edges_begin() { return border_halfedges_begin();}
// ... trial to make Edge_iterator obsolete.
Halfedge_const_iterator border_halfedges_begin() const {
return hds.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.
Halfedge_data_structure_decorator<HDS> decorator;
bool valid = decorator.normalized_border_is_valid( hds, 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: normals, planes
void inside_out_geometry( Tag_false, Tag_false) {}
void inside_out_geometry( Tag_true, Tag_false);
void inside_out_geometry( Tag_true, Tag_true);
void inside_out_geometry( Tag_false, Tag_true) {
inside_out_geometry( Tag_true(), Tag_true());
}
public:
void inside_out() {
// reverse facet orientation.
Halfedge_data_structure_decorator<HDS> decorator;
decorator.inside_out( hds);
inside_out_geometry( Supports_facet_normal(),
Supports_facet_plane());
}
bool is_valid( bool verb = false, int level = 0) const;
// checks the combinatorial consistency.
#ifdef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
make_triangle( V* v1, V* v2, V* v3) {
Halfedge_data_structure_decorator<HDS> decorator;
H* h = hds.new_edge();
h->set_next( hds.new_edge());
h->next()->set_next( hds.new_edge());
h->next()->next()->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()->set_next( h->next()->next()->opposite());
h->next()->opposite()->set_next( h->opposite());
h->next()->next()->opposite()->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
F* f = decorator.new_facet( hds);
decorator.set_facet( h, f);
decorator.set_facet( h->next(), f);
decorator.set_facet( h->next()->next(), f);
decorator.set_facet_halfedge( h);
return TR_HI(h);
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
make_triangle() {
Halfedge_data_structure_decorator<HDS> decorator;
return make_triangle( decorator.new_vertex( hds),
decorator.new_vertex( hds),
decorator.new_vertex( hds));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
make_triangle(const Point& p1, const Point& p2, const Point& p3) {
Halfedge_data_structure_decorator<HDS> decorator;
return make_triangle( decorator.new_vertex( hds, p1),
decorator.new_vertex( hds, p2),
decorator.new_vertex( hds, p3));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
make_tetrahedron( V* v1, V* v2, V* v3, V* v4) {
Halfedge_data_structure_decorator<HDS> decorator;
H* h = make_triangle(v1,v2,v3).ptr();
// The remaining tip.
H* g = hds.new_edge();
decorator.insert_tip( g->opposite(), h->opposite());
decorator.close_tip( g);
decorator.set_vertex( g, v4);
H* e = hds.new_edge();
H* d = hds.new_edge();
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
F* f = decorator.new_facet( hds);
decorator.set_facet( h->opposite(), f);
decorator.set_facet( g, f);
decorator.set_facet( e->opposite(), f);
decorator.set_facet_halfedge( g);
f = decorator.new_facet( hds);
decorator.set_facet( h->next()->opposite(), f);
decorator.set_facet( e, f);
decorator.set_facet( d->opposite(), f);
decorator.set_facet_halfedge( e);
f = decorator.new_facet( hds);
decorator.set_facet( h->next()->next()->opposite(), f);
decorator.set_facet( d, f);
decorator.set_facet( g->opposite(), f);
decorator.set_facet_halfedge( d);
return TR_HI(h);
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
make_tetrahedron() {
Halfedge_data_structure_decorator<HDS> decorator;
return make_tetrahedron( decorator.new_vertex( hds),
decorator.new_vertex( hds),
decorator.new_vertex( hds),
decorator.new_vertex( hds));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
make_tetrahedron(const Point& p1,
const Point& p2,
const Point& p3,
const Point& p4){
Halfedge_data_structure_decorator<HDS> decorator;
return make_tetrahedron( decorator.new_vertex( hds, p1),
decorator.new_vertex( hds, p2),
decorator.new_vertex( hds, p3),
decorator.new_vertex( hds, p4));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
bool
Polyhedron_3<TR,HDS>::
#else
bool
#endif
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_facet())
&& ! 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( Halfedge_data_structure_decorator<HDS>
decorator;)
CGAL_assertion( decorator.get_prev( h1.ptr()) == NULL ||
decorator.get_prev( h1.ptr()) == h3.ptr());
CGAL_assertion( decorator.get_prev( h2.ptr()) == NULL ||
decorator.get_prev( h2.ptr()) == h1.ptr());
CGAL_assertion( decorator.get_prev( h3.ptr()) == NULL ||
decorator.get_prev( h3.ptr()) == h2.ptr());
// check vertices.
CGAL_assertion( decorator.get_vertex( h1.ptr()) ==
decorator.get_vertex( h2->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h2.ptr()) ==
decorator.get_vertex( h3->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h3.ptr()) ==
decorator.get_vertex( h1->opposite().ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_vertex( h1.ptr()) !=
decorator.get_vertex( h2.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_vertex( h1.ptr()) !=
decorator.get_vertex( h3.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_vertex( h2.ptr()) !=
decorator.get_vertex( h3.ptr()));
// check facets.
CGAL_assertion( decorator.get_facet( h1.ptr()) ==
decorator.get_facet( h2.ptr()));
CGAL_assertion( decorator.get_facet( h1.ptr()) ==
decorator.get_facet( h3.ptr()));
return true;
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
bool
Polyhedron_3<TR,HDS>::
#else
bool
#endif
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( Halfedge_data_structure_decorator<HDS>
decorator;)
CGAL_assertion( decorator.get_prev( h1.ptr()) == NULL ||
decorator.get_prev( h1.ptr()) == h3.ptr());
CGAL_assertion( decorator.get_prev( h2.ptr()) == NULL ||
decorator.get_prev( h2.ptr()) == h1.ptr());
CGAL_assertion( decorator.get_prev( h3.ptr()) == NULL ||
decorator.get_prev( h3.ptr()) == h2.ptr());
CGAL_assertion( decorator.get_prev( h4.ptr()) == NULL ||
decorator.get_prev( h4.ptr()) == h1->opposite().ptr());
CGAL_assertion( decorator.get_prev( h5.ptr()) == NULL ||
decorator.get_prev( h5.ptr()) == h2->opposite().ptr());
CGAL_assertion( decorator.get_prev( h6.ptr()) == NULL ||
decorator.get_prev( h6.ptr()) == h3->opposite().ptr());
// check vertices.
CGAL_assertion( decorator.get_vertex( h1.ptr()) ==
decorator.get_vertex( h2->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h1.ptr()) ==
decorator.get_vertex( h5->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h2.ptr()) ==
decorator.get_vertex( h3->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h2.ptr()) ==
decorator.get_vertex( h6->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h3.ptr()) ==
decorator.get_vertex( h1->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h3.ptr()) ==
decorator.get_vertex( h4->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h4.ptr()) ==
decorator.get_vertex( h5.ptr()));
CGAL_assertion( decorator.get_vertex( h4.ptr()) ==
decorator.get_vertex( h6.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
decorator.get_vertex( h1.ptr()) !=
decorator.get_vertex( h2.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
decorator.get_vertex( h1.ptr()) !=
decorator.get_vertex( h3.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
decorator.get_vertex( h1.ptr()) !=
decorator.get_vertex( h4.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
decorator.get_vertex( h2.ptr()) !=
decorator.get_vertex( h3.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
decorator.get_vertex( h2.ptr()) !=
decorator.get_vertex( h4.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
decorator.get_vertex( h3.ptr()) !=
decorator.get_vertex( h4.ptr()));
// check facets.
CGAL_assertion( decorator.get_facet(h1.ptr()) ==
decorator.get_facet(h2.ptr()));
CGAL_assertion( decorator.get_facet(h1.ptr()) ==
decorator.get_facet(h3.ptr()));
CGAL_assertion( decorator.get_facet(h4.ptr()) ==
decorator.get_facet(h4->next().ptr()));
CGAL_assertion( decorator.get_facet(h4.ptr()) ==
decorator.get_facet(h1->opposite().ptr()));
CGAL_assertion( decorator.get_facet(h5.ptr()) ==
decorator.get_facet(h5->next().ptr()));
CGAL_assertion( decorator.get_facet(h5.ptr()) ==
decorator.get_facet(h2->opposite().ptr()));
CGAL_assertion( decorator.get_facet(h6.ptr()) ==
decorator.get_facet(h6->next().ptr()));
CGAL_assertion( decorator.get_facet(h6.ptr()) ==
decorator.get_facet(h3->opposite().ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_facet( h1.ptr()) !=
decorator.get_facet( h4.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_facet( h1.ptr()) !=
decorator.get_facet( h5.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_facet( h1.ptr()) !=
decorator.get_facet( h6.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_facet( h4.ptr()) !=
decorator.get_facet( h5.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_facet( h4.ptr()) !=
decorator.get_facet( h6.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_facet( h5.ptr()) !=
decorator.get_facet( h6.ptr()));
return true;
}
// Euler Operations
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
split_facet( Halfedge_handle h, Halfedge_handle g) {
Halfedge_data_structure_decorator<HDS> D;
CGAL_precondition( D.get_facet(h.ptr()) == D.get_facet(g.ptr()));
CGAL_precondition( h != g);
CGAL_precondition( h != g->next());
CGAL_precondition( h->next() != g);
return TR_HI( D.split_facet( hds, h.ptr(), g.ptr()));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
join_facet( Halfedge_handle h) {
Halfedge_data_structure_decorator<HDS> D;
CGAL_precondition( circulator_size(h->vertex_begin()) >= Size(3));
CGAL_precondition( circulator_size(h->opposite()->vertex_begin())
>= Size(3));
return TR_HI( D.join_facet( hds, h.ptr()));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
split_vertex( Halfedge_handle h, Halfedge_handle g) {
Halfedge_data_structure_decorator<HDS> D;
CGAL_precondition( D.get_vertex(h.ptr()) == D.get_vertex(g.ptr()));
CGAL_precondition( h != g);
return TR_HI( D.split_vertex( hds, h.ptr(), g.ptr()));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
join_vertex( Halfedge_handle h) {
Halfedge_data_structure_decorator<HDS> D;
CGAL_precondition( circulator_size( h->facet_begin()) >= Size(4));
CGAL_precondition( circulator_size( h->opposite()->facet_begin())
>= Size(4));
return TR_HI( D.join_vertex( hds, h.ptr()));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
split_loop( Halfedge_handle h,
Halfedge_handle i,
Halfedge_handle j) {
Halfedge_data_structure_decorator<HDS> D;
CGAL_precondition( h != i);
CGAL_precondition( h != j);
CGAL_precondition( i != j);
CGAL_precondition( D.get_vertex(h.ptr())
== D.get_vertex(i->opposite().ptr()));
CGAL_precondition( D.get_vertex(i.ptr())
== D.get_vertex(j->opposite().ptr()));
CGAL_precondition( D.get_vertex(j.ptr())
== D.get_vertex(h->opposite().ptr()));
CGAL_precondition( D.get_facet(h.ptr()) == 0 ||
D.get_facet(h.ptr()) != D.get_facet(i.ptr()));
CGAL_precondition( D.get_facet(h.ptr()) == 0 ||
D.get_facet(h.ptr()) != D.get_facet(j.ptr()));
CGAL_precondition( D.get_facet(i.ptr()) == 0 ||
D.get_facet(i.ptr()) != D.get_facet(j.ptr()));
CGAL_precondition( D.get_facet(h.ptr()) == 0 ||
D.get_facet(h.ptr())
!= D.get_facet(h->opposite().ptr()));
CGAL_precondition( D.get_facet(h.ptr()) == 0 ||
D.get_facet(h.ptr())
!= D.get_facet(i->opposite().ptr()));
CGAL_precondition( D.get_facet(h.ptr()) == 0 ||
D.get_facet(h.ptr())
!= D.get_facet(j->opposite().ptr()));
CGAL_precondition( D.get_facet(i.ptr()) == 0 ||
D.get_facet(i.ptr())
!= D.get_facet(h->opposite().ptr()));
CGAL_precondition( D.get_facet(i.ptr()) == 0 ||
D.get_facet(i.ptr())
!= D.get_facet(i->opposite().ptr()));
CGAL_precondition( D.get_facet(i.ptr()) == 0 ||
D.get_facet(i.ptr())
!= D.get_facet(j->opposite().ptr()));
CGAL_precondition( D.get_facet(j.ptr()) == 0 ||
D.get_facet(j.ptr())
!= D.get_facet(h->opposite().ptr()));
CGAL_precondition( D.get_facet(j.ptr()) == 0 ||
D.get_facet(j.ptr())
!= D.get_facet(i->opposite().ptr()));
CGAL_precondition( D.get_facet(j.ptr()) == 0 ||
D.get_facet(j.ptr())
!= D.get_facet(j->opposite().ptr()));
CGAL_precondition( D.get_facet(h->opposite().ptr()) == 0 ||
D.get_facet(h->opposite().ptr())
!= D.get_facet(i->opposite().ptr()));
CGAL_precondition( D.get_facet(h->opposite().ptr()) == 0 ||
D.get_facet(h->opposite().ptr())
!= D.get_facet(j->opposite().ptr()));
CGAL_precondition( D.get_facet(i->opposite().ptr()) == 0 ||
D.get_facet(i->opposite().ptr())
!= D.get_facet(j->opposite().ptr()));
return TR_HI( D.split_loop( hds, h.ptr(), i.ptr(), j.ptr()));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
join_loop( Halfedge_handle h,
Halfedge_handle g) {
Halfedge_data_structure_decorator<HDS> D;
CGAL_precondition( D.get_facet(h.ptr()) == 0 ||
D.get_facet(h.ptr()) != D.get_facet(g.ptr()));
CGAL_precondition( circulator_size( h->facet_begin()) >= Size(3));
CGAL_precondition( circulator_size( h->facet_begin())
== circulator_size( g->facet_begin()));
return TR_HI( D.join_loop( hds, h.ptr(), g.ptr()));
}
#endif // CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS //
};
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
make_triangle( V* v1, V* v2, V* v3) {
Halfedge_data_structure_decorator<HDS> decorator;
H* h = hds.new_edge();
h->set_next( hds.new_edge());
h->next()->set_next( hds.new_edge());
h->next()->next()->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()->set_next( h->next()->next()->opposite());
h->next()->opposite()->set_next( h->opposite());
h->next()->next()->opposite()->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
F* f = decorator.new_facet( hds);
decorator.set_facet( h, f);
decorator.set_facet( h->next(), f);
decorator.set_facet( h->next()->next(), f);
decorator.set_facet_halfedge( h);
return TR_HI(h);
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
make_triangle() {
Halfedge_data_structure_decorator<HDS> decorator;
return make_triangle( decorator.new_vertex( hds),
decorator.new_vertex( hds),
decorator.new_vertex( hds));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
make_triangle(const Point& p1, const Point& p2, const Point& p3) {
Halfedge_data_structure_decorator<HDS> decorator;
return make_triangle( decorator.new_vertex( hds, p1),
decorator.new_vertex( hds, p2),
decorator.new_vertex( hds, p3));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
make_tetrahedron( V* v1, V* v2, V* v3, V* v4) {
Halfedge_data_structure_decorator<HDS> decorator;
H* h = make_triangle(v1,v2,v3).ptr();
// The remaining tip.
H* g = hds.new_edge();
decorator.insert_tip( g->opposite(), h->opposite());
decorator.close_tip( g);
decorator.set_vertex( g, v4);
H* e = hds.new_edge();
H* d = hds.new_edge();
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
F* f = decorator.new_facet( hds);
decorator.set_facet( h->opposite(), f);
decorator.set_facet( g, f);
decorator.set_facet( e->opposite(), f);
decorator.set_facet_halfedge( g);
f = decorator.new_facet( hds);
decorator.set_facet( h->next()->opposite(), f);
decorator.set_facet( e, f);
decorator.set_facet( d->opposite(), f);
decorator.set_facet_halfedge( e);
f = decorator.new_facet( hds);
decorator.set_facet( h->next()->next()->opposite(), f);
decorator.set_facet( d, f);
decorator.set_facet( g->opposite(), f);
decorator.set_facet_halfedge( d);
return TR_HI(h);
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
make_tetrahedron() {
Halfedge_data_structure_decorator<HDS> decorator;
return make_tetrahedron( decorator.new_vertex( hds),
decorator.new_vertex( hds),
decorator.new_vertex( hds),
decorator.new_vertex( hds));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
make_tetrahedron(const Point& p1,
const Point& p2,
const Point& p3,
const Point& p4){
Halfedge_data_structure_decorator<HDS> decorator;
return make_tetrahedron( decorator.new_vertex( hds, p1),
decorator.new_vertex( hds, p2),
decorator.new_vertex( hds, p3),
decorator.new_vertex( hds, p4));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
bool
Polyhedron_3<TR,HDS>::
#else
bool
#endif
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_facet())
&& ! 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( Halfedge_data_structure_decorator<HDS>
decorator;)
CGAL_assertion( decorator.get_prev( h1.ptr()) == NULL ||
decorator.get_prev( h1.ptr()) == h3.ptr());
CGAL_assertion( decorator.get_prev( h2.ptr()) == NULL ||
decorator.get_prev( h2.ptr()) == h1.ptr());
CGAL_assertion( decorator.get_prev( h3.ptr()) == NULL ||
decorator.get_prev( h3.ptr()) == h2.ptr());
// check vertices.
CGAL_assertion( decorator.get_vertex( h1.ptr()) ==
decorator.get_vertex( h2->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h2.ptr()) ==
decorator.get_vertex( h3->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h3.ptr()) ==
decorator.get_vertex( h1->opposite().ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_vertex( h1.ptr()) !=
decorator.get_vertex( h2.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_vertex( h1.ptr()) !=
decorator.get_vertex( h3.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_vertex( h2.ptr()) !=
decorator.get_vertex( h3.ptr()));
// check facets.
CGAL_assertion( decorator.get_facet( h1.ptr()) ==
decorator.get_facet( h2.ptr()));
CGAL_assertion( decorator.get_facet( h1.ptr()) ==
decorator.get_facet( h3.ptr()));
return true;
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
bool
Polyhedron_3<TR,HDS>::
#else
bool
#endif
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( Halfedge_data_structure_decorator<HDS>
decorator;)
CGAL_assertion( decorator.get_prev( h1.ptr()) == NULL ||
decorator.get_prev( h1.ptr()) == h3.ptr());
CGAL_assertion( decorator.get_prev( h2.ptr()) == NULL ||
decorator.get_prev( h2.ptr()) == h1.ptr());
CGAL_assertion( decorator.get_prev( h3.ptr()) == NULL ||
decorator.get_prev( h3.ptr()) == h2.ptr());
CGAL_assertion( decorator.get_prev( h4.ptr()) == NULL ||
decorator.get_prev( h4.ptr()) == h1->opposite().ptr());
CGAL_assertion( decorator.get_prev( h5.ptr()) == NULL ||
decorator.get_prev( h5.ptr()) == h2->opposite().ptr());
CGAL_assertion( decorator.get_prev( h6.ptr()) == NULL ||
decorator.get_prev( h6.ptr()) == h3->opposite().ptr());
// check vertices.
CGAL_assertion( decorator.get_vertex( h1.ptr()) ==
decorator.get_vertex( h2->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h1.ptr()) ==
decorator.get_vertex( h5->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h2.ptr()) ==
decorator.get_vertex( h3->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h2.ptr()) ==
decorator.get_vertex( h6->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h3.ptr()) ==
decorator.get_vertex( h1->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h3.ptr()) ==
decorator.get_vertex( h4->opposite().ptr()));
CGAL_assertion( decorator.get_vertex( h4.ptr()) ==
decorator.get_vertex( h5.ptr()));
CGAL_assertion( decorator.get_vertex( h4.ptr()) ==
decorator.get_vertex( h6.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
decorator.get_vertex( h1.ptr()) !=
decorator.get_vertex( h2.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
decorator.get_vertex( h1.ptr()) !=
decorator.get_vertex( h3.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
decorator.get_vertex( h1.ptr()) !=
decorator.get_vertex( h4.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
decorator.get_vertex( h2.ptr()) !=
decorator.get_vertex( h3.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
decorator.get_vertex( h2.ptr()) !=
decorator.get_vertex( h4.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_vertex()) ||
decorator.get_vertex( h3.ptr()) !=
decorator.get_vertex( h4.ptr()));
// check facets.
CGAL_assertion( decorator.get_facet(h1.ptr()) ==
decorator.get_facet(h2.ptr()));
CGAL_assertion( decorator.get_facet(h1.ptr()) ==
decorator.get_facet(h3.ptr()));
CGAL_assertion( decorator.get_facet(h4.ptr()) ==
decorator.get_facet(h4->next().ptr()));
CGAL_assertion( decorator.get_facet(h4.ptr()) ==
decorator.get_facet(h1->opposite().ptr()));
CGAL_assertion( decorator.get_facet(h5.ptr()) ==
decorator.get_facet(h5->next().ptr()));
CGAL_assertion( decorator.get_facet(h5.ptr()) ==
decorator.get_facet(h2->opposite().ptr()));
CGAL_assertion( decorator.get_facet(h6.ptr()) ==
decorator.get_facet(h6->next().ptr()));
CGAL_assertion( decorator.get_facet(h6.ptr()) ==
decorator.get_facet(h3->opposite().ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_facet( h1.ptr()) !=
decorator.get_facet( h4.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_facet( h1.ptr()) !=
decorator.get_facet( h5.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_facet( h1.ptr()) !=
decorator.get_facet( h6.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_facet( h4.ptr()) !=
decorator.get_facet( h5.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_facet( h4.ptr()) !=
decorator.get_facet( h6.ptr()));
CGAL_assertion( ! check_tag( Supports_halfedge_facet()) ||
decorator.get_facet( h5.ptr()) !=
decorator.get_facet( h6.ptr()));
return true;
}
// Euler Operations
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
split_facet( Halfedge_handle h, Halfedge_handle g) {
Halfedge_data_structure_decorator<HDS> D;
CGAL_precondition( D.get_facet(h.ptr()) == D.get_facet(g.ptr()));
CGAL_precondition( h != g);
CGAL_precondition( h != g->next());
CGAL_precondition( h->next() != g);
return TR_HI( D.split_facet( hds, h.ptr(), g.ptr()));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
join_facet( Halfedge_handle h) {
Halfedge_data_structure_decorator<HDS> D;
CGAL_precondition( circulator_size(h->vertex_begin()) >= Size(3));
CGAL_precondition( circulator_size(h->opposite()->vertex_begin())
>= Size(3));
return TR_HI( D.join_facet( hds, h.ptr()));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
split_vertex( Halfedge_handle h, Halfedge_handle g) {
Halfedge_data_structure_decorator<HDS> D;
CGAL_precondition( D.get_vertex(h.ptr()) == D.get_vertex(g.ptr()));
CGAL_precondition( h != g);
return TR_HI( D.split_vertex( hds, h.ptr(), g.ptr()));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
join_vertex( Halfedge_handle h) {
Halfedge_data_structure_decorator<HDS> D;
CGAL_precondition( circulator_size( h->facet_begin()) >= Size(4));
CGAL_precondition( circulator_size( h->opposite()->facet_begin())
>= Size(4));
return TR_HI( D.join_vertex( hds, h.ptr()));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
split_loop( Halfedge_handle h,
Halfedge_handle i,
Halfedge_handle j) {
Halfedge_data_structure_decorator<HDS> D;
CGAL_precondition( h != i);
CGAL_precondition( h != j);
CGAL_precondition( i != j);
CGAL_precondition( D.get_vertex(h.ptr())
== D.get_vertex(i->opposite().ptr()));
CGAL_precondition( D.get_vertex(i.ptr())
== D.get_vertex(j->opposite().ptr()));
CGAL_precondition( D.get_vertex(j.ptr())
== D.get_vertex(h->opposite().ptr()));
CGAL_precondition( D.get_facet(h.ptr()) == 0 ||
D.get_facet(h.ptr()) != D.get_facet(i.ptr()));
CGAL_precondition( D.get_facet(h.ptr()) == 0 ||
D.get_facet(h.ptr()) != D.get_facet(j.ptr()));
CGAL_precondition( D.get_facet(i.ptr()) == 0 ||
D.get_facet(i.ptr()) != D.get_facet(j.ptr()));
CGAL_precondition( D.get_facet(h.ptr()) == 0 ||
D.get_facet(h.ptr())
!= D.get_facet(h->opposite().ptr()));
CGAL_precondition( D.get_facet(h.ptr()) == 0 ||
D.get_facet(h.ptr())
!= D.get_facet(i->opposite().ptr()));
CGAL_precondition( D.get_facet(h.ptr()) == 0 ||
D.get_facet(h.ptr())
!= D.get_facet(j->opposite().ptr()));
CGAL_precondition( D.get_facet(i.ptr()) == 0 ||
D.get_facet(i.ptr())
!= D.get_facet(h->opposite().ptr()));
CGAL_precondition( D.get_facet(i.ptr()) == 0 ||
D.get_facet(i.ptr())
!= D.get_facet(i->opposite().ptr()));
CGAL_precondition( D.get_facet(i.ptr()) == 0 ||
D.get_facet(i.ptr())
!= D.get_facet(j->opposite().ptr()));
CGAL_precondition( D.get_facet(j.ptr()) == 0 ||
D.get_facet(j.ptr())
!= D.get_facet(h->opposite().ptr()));
CGAL_precondition( D.get_facet(j.ptr()) == 0 ||
D.get_facet(j.ptr())
!= D.get_facet(i->opposite().ptr()));
CGAL_precondition( D.get_facet(j.ptr()) == 0 ||
D.get_facet(j.ptr())
!= D.get_facet(j->opposite().ptr()));
CGAL_precondition( D.get_facet(h->opposite().ptr()) == 0 ||
D.get_facet(h->opposite().ptr())
!= D.get_facet(i->opposite().ptr()));
CGAL_precondition( D.get_facet(h->opposite().ptr()) == 0 ||
D.get_facet(h->opposite().ptr())
!= D.get_facet(j->opposite().ptr()));
CGAL_precondition( D.get_facet(i->opposite().ptr()) == 0 ||
D.get_facet(i->opposite().ptr())
!= D.get_facet(j->opposite().ptr()));
return TR_HI( D.split_loop( hds, h.ptr(), i.ptr(), j.ptr()));
}
#ifndef CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS
template < class TR, class HDS > CGAL_LARGE_INLINE
typename Polyhedron_3<TR,HDS>::Halfedge_handle
Polyhedron_3<TR,HDS>::
#else
Halfedge_handle
#endif
join_loop( Halfedge_handle h,
Halfedge_handle g) {
Halfedge_data_structure_decorator<HDS> D;
CGAL_precondition( D.get_facet(h.ptr()) == 0 ||
D.get_facet(h.ptr()) != D.get_facet(g.ptr()));
CGAL_precondition( circulator_size( h->facet_begin()) >= Size(3));
CGAL_precondition( circulator_size( h->facet_begin())
== circulator_size( g->facet_begin()));
return TR_HI( D.join_loop( hds, h.ptr(), g.ptr()));
}
#endif // CGAL_CFG_NO_SCOPE_MEMBER_FUNCTION_PARAMETERS //
// Special Operations on Polyhedral Surfaces
template < class TR, class HDS > CGAL_LARGE_INLINE
void // Supports: normals, planes
Polyhedron_3<TR,HDS>::inside_out_geometry(Tag_true,Tag_false) {
typename Traits::Construct_opposite_vector_3 opposite
= traits().construct_opposite_vector_3_object();
for ( Facet_iterator i = facets_begin(); i != facets_end(); ++i)
i->normal() = opposite( i->normal());
}
template < class TR, class HDS > CGAL_LARGE_INLINE
void // Supports: normals, planes
Polyhedron_3<TR,HDS>::inside_out_geometry(Tag_true,Tag_true) {
typename Traits::Construct_opposite_plane_3 opposite
= traits().construct_opposite_plane_3_object();
for ( Facet_iterator i = facets_begin(); i != facets_end(); ++i)
i->plane() = opposite( i->plane());
}
template < class TR, class HDS >
bool
Polyhedron_3<TR,HDS>:: is_valid( bool verb, int level) const {
Verbose_ostream verr(verb);
verr << "begin Polyhedron_3<TR,HDS>::is_valid( verb=true, "
"level = " << level << "):" << std::endl;
Halfedge_data_structure_decorator<HDS> decorator;
bool valid = decorator.is_valid( hds, verb, level + 3);
// All halfedges.
Halfedge_const_iterator begin = halfedges_begin();
Halfedge_const_iterator end = halfedges_end();
Size n = 0;
for( ; valid && (begin != end); begin++) {
verr << "halfedge " << n << std::endl;
// At least triangular facets and distinct geometry.
valid = valid && ( begin->next() != begin);
valid = valid && ( begin->next()->next() != begin);
valid = valid && ( ! check_tag( Supports_halfedge_vertex()) ||
decorator.get_vertex( begin.ptr()) !=
decorator.get_vertex( begin->opposite().ptr()));
valid = valid && ( ! check_tag( Supports_halfedge_vertex()) ||
decorator.get_vertex( begin.ptr()) !=
decorator.get_vertex( begin->next().ptr()));
valid = valid && ( ! check_tag( Supports_halfedge_vertex()) ||
decorator.get_vertex( begin.ptr()) !=
decorator.get_vertex( begin->next()->
next().ptr()));
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_facet()) ||
decorator.get_facet( begin.ptr()) !=
decorator.get_facet( begin->opposite().ptr()));
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 Polyhedron_3<TR,HDS>::is_valid(): structure is "
<< ( valid ? "valid." : "NOT VALID.") << std::endl;
return valid;
}
CGAL_END_NAMESPACE
#endif // CGAL_POLYHEDRON_OLD_POLYHEDRON_3_H //
// EOF //
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