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: PkgNef2, PkgNefS2
BibTeX: cgal:hk-bonp3-21b
License: GPL
Windows Demo: Polyhedron demo
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::convert_nef_polyhedron_to_polygon_mesh()
• CGAL::convert_nef_polyhedron_to_polygon_soup()
• CGAL::operator<<()
• CGAL::operator>>()

Draw a Nef Polyhedron

• CGAL::draw<Nef3>()

Modules
	I/O Functions
	Draw a Nef Polyhedron
	Draw.

Classes
class	CGAL::Nef_nary_union_3< Nef_polyhedron_3 >
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halfedge
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halffacet_cycle_iterator
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halffacet
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SFace_cycle_iterator
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SFace
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfedge
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Vertex
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Volume
class	CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >