3D Boolean Operations on Nef Polyhedra Reference

Todo:

check generated documentation

Peter Hachenberger and Lutz Kettner

3D Nef polyhedra, are a boundary representation for cell-complexes bounded by halfspaces that supports Boolean operations and topological operations in full generality including unbounded cells, mixed dimensional cells (e.g., isolated vertices and antennas). Nef polyhedra distinguish between open and closed sets and can represent non-manifold geometry.

Introduced in: CGAL 3.1
Depends on: 2D Boolean Operations on Nef Polygons, 2D Boolean Operations on Nef Polygons Embedded on the Sphere
BibTeX: cgal:hk-bonp3-15a
License: GPL
Windows Demo: Operations on Polyhedra
Common Demo Dlls: dlls

A Nef polyhedron is any point set generated from a finite number of open halfspaces by set complement and set intersection operations. In our implementation of Nef polyhedra in 3-dimensional space, we offer a B-rep data structures that is closed under boolean operations and with all their generality. Starting from halfspaces (and also directly from oriented 2-manifolds), we can work with set union, set intersection, set difference, set complement, interior, exterior, boundary, closure, and regularization operations. In essence, we can evaluate a CSG-tree with halfspaces as primitives and convert it into a B-rep representation.

In fact, we work with two data structures; one that represents the local neighborhoods of vertices, which is in itself already a complete description, and a data structure that connects these neighborhoods up to a global data structure with edges, facets, and volumes. We offer a rich interface to investigate these data structures, their different elements and their connectivity. We provide affine (rigid) tranformations and a point location query operation. We have a custom file format for storing and reading Nef polyhedra from files. We offer a simple OpenGL visualization for debugging and illustrations.

Classified Reference Pages

Classes

• CGAL::Nef_polyhedron_3<Traits>
• CGAL::Nef_polyhedron_3<Traits>::Vertex
• CGAL::Nef_polyhedron_3<Traits>::Halfedge
• CGAL::Nef_polyhedron_3<Traits>::Halffacet
• CGAL::Nef_polyhedron_3<Traits>::Volume
• CGAL::Nef_polyhedron_3<Traits>::SHalfedge
• CGAL::Nef_polyhedron_3<Traits>::SHalfloop
• CGAL::Nef_polyhedron_3<Traits>::SFace
• CGAL::Nef_polyhedron_3<Traits>::SFace_cycle_iterator

Functions

• CGAL::OFF_to_nef_3()
• CGAL::operator<<()
• CGAL::operator>>()

Modules
	I/O Functions

Classes
class	CGAL::Qt_widget_Nef_3< Nef_polyhedron_3 >
	The class Qt_widget_Nef_3 uses the OpenGL interface of Qt to display a Nef_polyhedron_3. More...
class	CGAL::Nef_nary_union_3< Nef_polyhedron_3 >
	This class helps to perform the union of a set of 3D Nef polyhedra efficiently. More...
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >
	A 3D Nef polyhedron is a subset of the 3-dimensional space that is the result of forming complements and intersections starting from a finite set H of 3-dimensional halfspaces. More...
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halfedge
	A Halfedge has a double meaning. More...
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halffacet_cycle_iterator
	The type Halffacet_cycle_iterator iterates over a list of Object_handles. More...
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halffacet
	A halffacet is an oriented, rectilinear bounded part of a plane. More...
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SFace_cycle_iterator
	The type SFace_cycle_iterator iterates over a list of Object_handles. More...
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SFace
	An sface is described by its boundaries. More...
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfedge
	A shalfedge is a great arc on a sphere map. More...
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop
	A shalfloop is a great circle on a sphere map. More...
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Vertex
	A vertex is a point in the 3-dimensional space. More...
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Volume
	A volume is a full-dimensional connected point set in \( \mathbb{R}^3\). More...

Types
enum	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Boundary { CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::EXCLUDED, CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::INCLUDED }
	construction selection. More...
enum	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Content { CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::EMPTY, CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::COMPLETE }
	construction selection. More...
enum	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Intersection_mode { CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::CLOSED_HALFSPACE, CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::OPEN_HALFSPACE, CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::PLANE_ONLY }
	intersection selection. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Mark
	All object (vertices, edges, etc.) are attributed by a Mark. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::size_type
	size type of Nef_polyhedron_3. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Vertex_const_handle
	non-mutable handle to a vertex. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halfedge_const_handle
	non-mutable handle to a halfedge. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halffacet_const_handle
	non-mutable handle to a halffacet. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Volume_const_handle
	non-mutable handle to a volume. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SVertex_const_handle
	non-mutable handle to a svertex. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfedge_const_handle
	non-mutable handle to a shalfedge. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop_const_handle
	non-mutable handle to a shalfloop. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SFace_const_handle
	non-mutable handle to a sface. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Vertex_const_iterator
	non-mutable iterator over all vertices. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halfedge_const_iterator
	non-mutable iterator over all halfeges. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halffacet_const_iterator
	non-mutable iterator over all halffacets. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Volume_const_iterator
	non-mutable iterator over all volumes. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SVertex_const_iterator
	non-mutable iterator over all svertices. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfedge_const_iterator
	non-mutable iterator over all shalfedges. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop_const_iterator
	non-mutable iterator over all shalfloops. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SFace_const_iterator
	non-mutable iterator over all sfaces. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfedge_around_svertex_const_circulator
	non-mutable circulator of shalfedges around a svertex (cw). More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfedge_around_sface_const_circulator
	non-mutable circulator of shalfedges around a sface (ccw). More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfedge_around_facet_const_circulator
	non-mutable circulator of shalfedges around a halffacet (ccw). More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SFace_cycle_const_iterator
	non-mutable iterator over the cylces of a sface. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halffacet_cycle_const_iterator
	non-mutable iterator over the cylces of a halffacet. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Shell_entry_const_iterator
	non-mutable iterator providing an entry to each shell. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Object_handle
	a generic handle to an object. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Point_3
	location of vertices. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Segment_3
	segment represented by a halfedge. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Vector_3
	direction of a halfedge. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Plane_3
	plane of a halffacet lies in. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Aff_transformation_3
	affine transformation. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Polylines_tag
	tag for calling polyline constructor. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Nef_polyhedron_S2
	a sphere map. More...
typedef unspecified_type	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Polyhedron
	a polyhedral surface. More...

Typedef Documentation

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Aff_transformation_3

affine transformation.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halfedge_const_handle

non-mutable handle to a halfedge.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halfedge_const_iterator

non-mutable iterator over all halfeges.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halffacet_const_handle

non-mutable handle to a halffacet.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halffacet_const_iterator

non-mutable iterator over all halffacets.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halffacet_cycle_const_iterator

non-mutable iterator over the cylces of a halffacet.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Mark

All object (vertices, edges, etc.) are attributed by a Mark.

Mark equals bool.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Nef_polyhedron_S2

a sphere map.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Object_handle

a generic handle to an object.

The kind of object (vertex, halfedge, halffacet, volume, svertex, shalfedge, shalfloop, sface) can be determined and the object can be assigned to a corresponding constant handle by one of the following functions:

bool assign(Vertex_const_handle& h, Object_handle)

bool assign(Halfedge_const_handle& h, Object_handle)

bool assign(Halffacet_const_handle& h, Object_handle)

bool assign(Volume_const_handle& h, Object_handle)

bool assign(SVertex_const_handle& h, Object_handle)

bool assign(SHalfedge_const_handle& h, Object_handle)

bool assign(SHalfloop_const_handle& h, Object_handle)

bool assign(SFace_const_handle& h, Object_handle)

where each function returns true iff the assignment to h could be accomplished.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Plane_3

plane of a halffacet lies in.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Point_3

location of vertices.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Polyhedron

a polyhedral surface.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Polylines_tag

tag for calling polyline constructor.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Segment_3

segment represented by a halfedge.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SFace_const_handle

non-mutable handle to a sface.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SFace_const_iterator

non-mutable iterator over all sfaces.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SFace_cycle_const_iterator

non-mutable iterator over the cylces of a sface.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfedge_around_facet_const_circulator

non-mutable circulator of shalfedges around a halffacet (ccw).

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfedge_around_sface_const_circulator

non-mutable circulator of shalfedges around a sface (ccw).

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfedge_around_svertex_const_circulator

non-mutable circulator of shalfedges around a svertex (cw).

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfedge_const_handle

non-mutable handle to a shalfedge.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfedge_const_iterator

non-mutable iterator over all shalfedges.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop_const_handle

non-mutable handle to a shalfloop.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop_const_iterator

non-mutable iterator over all shalfloops.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Shell_entry_const_iterator

non-mutable iterator providing an entry to each shell.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::size_type

size type of Nef_polyhedron_3.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SVertex_const_handle

non-mutable handle to a svertex.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SVertex_const_iterator

non-mutable iterator over all svertices.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Vector_3

direction of a halfedge.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Vertex_const_handle

non-mutable handle to a vertex.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Vertex_const_iterator

non-mutable iterator over all vertices.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Volume_const_handle

non-mutable handle to a volume.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Volume_const_iterator

non-mutable iterator over all volumes.

Enumeration Type Documentation

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

enum CGAL::Nef_polyhedron_3::Boundary

construction selection.

Enumerator
EXCLUDED
INCLUDED

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

enum CGAL::Nef_polyhedron_3::Content

construction selection.

Enumerator
EMPTY
COMPLETE

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>

enum CGAL::Nef_polyhedron_3::Intersection_mode

intersection selection.

Enumerator
CLOSED_HALFSPACE
OPEN_HALFSPACE
PLANE_ONLY