3D Polyhedral Surface Reference

Lutz Kettner

Polyhedral surfaces in three dimensions are composed of vertices, edges, facets and an incidence relationship on them. The organization beneath is a halfedge data structure, which restricts the class of representable surfaces to orientable 2-manifolds - with and without boundary. If the surface is closed we call it a polyhedron.

Introduced in: CGAL 1.0
Depends on: Halfedge Data Structures
BibTeX: cgal:k-ps-18b
License: GPL
Windows Demo: Polyhedron demo
Common Demo Dlls: dlls

Polyhedral surfaces in three dimensions are composed of vertices, edges, facets and an incidence relationship on them. The organization beneath is a halfedge data structure, which restricts the class of representable surfaces to orientable 2-manifolds - with and without boundary. If the surface is closed we call it a polyhedron.

The polyhedral surface is realized as a container class managing vertices, halfedges, facets with their incidences, and maintaining the combinatorial integrity of them. Its local types for the vertices, halfedges and facets are documented separately. A default traits class, a default items class and an incremental builder conclude the references. The polyhedral surface is based on the highly flexible design of the halfedge data structure, see the reference for HalfedgeDS in Chapter Halfedge Data Structures or [3], but the default instantiation of the polyhedral surface can be used without knowing the halfedge data structure.

Classified Reference Pages

Concepts

• PolyhedronTraits_3
• PolyhedronItems_3

Classes

• CGAL::Polyhedron_3<Traits>
• CGAL::Polyhedron_3<Traits>::Vertex
• CGAL::Polyhedron_3<Traits>::Halfedge
• CGAL::Polyhedron_3<Traits>::Facet
• CGAL::Polyhedron_traits_3<Kernel>
• CGAL::Polyhedron_traits_with_normals_3<Kernel>
• CGAL::Polyhedron_items_3
• CGAL::Polyhedron_min_items_3
• CGAL::Polyhedron_incremental_builder_3<HDS>

Functions

• CGAL::operator<<()
• CGAL::operator>>()
• write_off()
• read_off()

Modules
	Concepts
	I/O Functions

Classes
class	CGAL::Polyhedron_3< Traits >::Halfedge
	A halfedge is an oriented edge between two vertices. More...
class	CGAL::Polyhedron_3< Traits >::Facet
	A facet optionally stores a plane equation, and a reference to an incident halfedge that points to the facet. More...
class	CGAL::Polyhedron_3< Traits >::Vertex
	A vertex optionally stores a point and a reference to an incident halfedge that points to the vertex. More...
class	CGAL::Polyhedron_3< Traits >
	A polyhedral surface Polyhedron_3 consists of vertices V, edges E, facets F and an incidence relation on them. More...
class	CGAL::Polyhedron_incremental_builder_3< HDS >
	The auxiliary class Polyhedron_incremental_builder_3 supports the incremental construction of polyhedral surfaces, which is for example convenient when constructing polyhedral surfaces from file formats, such as the Object File Format (OFF) [5], OpenInventor [7] or VRML [1], [6]. More...
class	CGAL::Polyhedron_items_3
	The class Polyhedron_items_3 is a model of the PolyhedronItems_3 concept. More...
class	CGAL::Polyhedron_min_items_3
	The class Polyhedron_min_items_3 is a minimal model of the PolyhedronItems_3 concept. More...
class	CGAL::Polyhedron_traits_3< Kernel >
	The class Polyhedron_traits_3 is a model of the PolyhedronTraits_3 concept. More...
class	CGAL::Polyhedron_traits_with_normals_3< Kernel >
	The class Polyhedron_traits_with_normals_3 is a model of the PolyhedronTraits_3 concept. More...