2D Conforming Triangulations and Meshes Reference

Laurent Rineau

This package implements a Delaunay refinement algorithm to construct conforming triangulations and 2D meshes. Conforming Delaunay triangulations are obtained from constrained Delaunay triangulations by refining constrained edges until they are Delaunay edges. Conforming Gabriel triangulations are obtained by further refining constrained edges until they become Gabriel edges. The package provides also a 2D mesh generator that refines triangles and constrained edges until user defined size and shape criteria on triangles are satisfied. The generated meshes can be optimized using the Lloyd algorithm, also provided in this package. The package can handle intersecting input constraints and set no restriction on the angle formed by two constraints sharing an endpoint.

Introduced in: CGAL 3.1
Depends on: 2D Triangulations
BibTeX: cgal:r-ctm2-24b
License: GPL
Windows Demo: 2D Mesh Generator
Common Demo Dlls: dlls

Classified Reference Pages

Concepts

• ConformingDelaunayTriangulationTraits_2
• DelaunayMeshTraits_2
• MeshingCriteria_2
• DelaunayMeshFaceBase_2
• DelaunayMeshVertexBase_2

Classes

• CGAL::Triangulation_conformer_2<CDT>
• CGAL::Delaunay_mesher_2<CDT, Criteria>
• CGAL::Delaunay_mesh_face_base_2<Traits, Fb>
• CGAL::Delaunay_mesh_vertex_base_2<Traits, Vb>
• CGAL::Delaunay_mesh_criteria_2<CDT>
• CGAL::Delaunay_mesh_size_criteria_2<CDT>
• CGAL::Mesh_2::Face_badness

Global Functions

• CGAL::make_conforming_Delaunay_2
• CGAL::make_conforming_Gabriel_2
• CGAL::refine_Delaunay_mesh_2
• CGAL::lloyd_optimize_mesh_2

I/O Functions

• CGAL::IO::write_VTU()

Enumerations

• CGAL::Mesh_optimization_return_code

Modules
	Concepts
	Mesh Generation Functions
	The main function to generate a mesh is refine_Delaunay_mesh_2().
	Enumerations
	I/O Functions
	In addition to the stream extraction and insertion operators for CGAL 2D triangulations, the following functions can be used.

Classes
class	CGAL::Delaunay_mesh_criteria_2< CDT >
	The class Delaunay_mesh_criteria_2 is a model for the MeshingCriteria_2 concept. More...
class	CGAL::Delaunay_mesh_face_base_2< Traits, Fb >
	The class Delaunay_mesh_face_base_2 is a model for the concept DelaunayMeshFaceBase_2. More...
class	CGAL::Delaunay_mesh_size_criteria_2< CDT >
	The class Delaunay_mesh_size_criteria_2 is a model for the MeshingCriteria_2 concept. More...
class	CGAL::Delaunay_mesh_vertex_base_2< Traits, Vb >
	The class Delaunay_mesh_vertex_base_2 is a model for the concept DelaunayMeshVertexBase_2. More...
class	CGAL::Delaunay_mesher_2< CDT, Criteria >
	This class implements a 2D mesh generator. More...
class	CGAL::Triangulation_conformer_2< CDT >
	The class Triangulation_conformer_2 is an auxiliary class of Delaunay_mesher_2<CDT>. More...

Enumerations
enum	CGAL::Mesh_2::Face_badness { CGAL::Mesh_2::NOT_BAD, CGAL::Mesh_2::BAD, CGAL::Mesh_2::IMPERATIVELY_BAD }

Enumeration Type Documentation

Face_badness

enum CGAL::Mesh_2::Face_badness

#include <CGAL/Mesh_2/Face_badness.h>

Enumerator
NOT_BAD
BAD
IMPERATIVELY_BAD