CGAL 5.1.3 - 3D Polyhedral Surface
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-21a
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.

## Concepts

• PolyhedronTraits_3
• PolyhedronItems_3

## Modules

Concepts

I/O Functions

Draw a Polyhedron 3

## 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...