dD Triangulations Reference

Olivier Devillers, Samuel Hornus, and Clément Jamin

This package provides classes for manipulating triangulations (pure simplicial complexes) in Euclidean spaces whose dimension can be specified at compile-time or at run-time. Specifically, it provides a data structure to store the triangulations, and two classes to handle triangulations and Delaunay triangulations of point sets. Point location and point insertion are supported. The Delaunay triangulation also supports point removal.

Introduced in: CGAL 4.6
BibTeX: cgal:hdj-t-23a
License: GPL

A triangulation is a pure manifold simplicial complex. Its faces are simplices such that two of them either do not intersect or share a common face.

The triangulation classes of CGAL are designed to represent triangulations of a set of points \( A\) in \( \mathbb{R}^d\). It can be viewed as a partition of the convex hull of \( A\) into simplices whose vertices are the points of \( A\).

See the User Manual for more details.

Classified Reference Pages

Concepts

Triangulation Data Structure

• TriangulationDataStructure
• TriangulationDataStructure::FullCell
• TriangulationDataStructure::Vertex
• TriangulationDSVertex
• TriangulationDSFullCell
• TriangulationDSFace
• FullCellData

Triangulations

• TriangulationTraits
• DelaunayTriangulationTraits
• RegularTriangulationTraits
• TriangulationVertex
• TriangulationFullCell

The latter two concepts are also abbreviated respectively as TrVertex and TrFullCell.

Classes

Triangulation Data Structure

• CGAL::Triangulation_data_structure<Dimensionality, TriangulationDSVertex_, TriangulationDSFullCell_>
• CGAL::Triangulation_ds_vertex<TriangulationDataStructure_>
• CGAL::Triangulation_ds_full_cell<TriangulationDataStructure_, TriangulationDSFullCellStoragePolicy>
• CGAL::Triangulation_face<TriangulationDataStructure_>

(Geometric) Triangulations

• CGAL::Triangulation<TriangulationTraits_, TriangulationDataStructure_>
• CGAL::Delaunay_triangulation<DelaunayTriangulationTraits_, TriangulationDataStructure_>
• CGAL::Regular_triangulation<RegularTriangulationTraits_, TriangulationDataStructure_>
• CGAL::Triangulation_vertex<TriangulationTraits_, Data, TriangulationDSVertex_>
• CGAL::Triangulation_full_cell<TriangulationTraits_, Data, TriangulationDSFullCell_>

Traits Classes

• CGAL::Regular_triangulation_traits_adapter<K>

Enums

• CGAL::Triangulation::Locate_type

Modules
	Concepts
	Triangulation Classes
	Traits Classes
	Vertex, Face and Cell Classes