CGAL::Delaunay_mesh_size_criteria_2< CDT > Class Template Reference

#include <CGAL/Delaunay_mesh_size_criteria_2.h>

Definition

template<typename CDT>
class CGAL::Delaunay_mesh_size_criteria_2< CDT >

The class Delaunay_mesh_size_criteria_2 is a model for the MeshingCriteria_2 concept.

The shape criterion on triangles is given by a bound \( B\) such that for good triangles \( \frac{r}{l} \le B\) where \( l\) is the shortest edge length and \( r\) is the circumradius of the triangle. By default, \( B=\sqrt{2}\), which is the best bound one can use with the guarantee that the refinement algorithm will terminate. The upper bound \( B\) is related to a lower bound \( \alpha_{min}\) on the minimum angle in the triangle:

\[ \sin{ \alpha_{min} } = \frac{1}{2 B} \]

so \( B=\sqrt{2}\) corresponds to \( \alpha_{min} \ge 20.7\) degrees.

This traits class defines also a size criteria: all segments of all triangles must be shorter than a bound \( S\).

Template Parameters

CDT	must be a 2D constrained Delaunay triangulation.

Is model of

MeshingCriteria_2

Examples

Mesh_2/mesh_class.cpp, Mesh_2/mesh_global.cpp, and Mesh_2/mesh_optimization.cpp.

Creation
	Delaunay_mesh_size_criteria_2 ()
	Default constructor with \( B=\sqrt{2}\).
	Delaunay_mesh_size_criteria_2 (double b=0.125, double S=0)
	Construct a traits class with bound \( B=\sqrt{\frac{1}{4 b}}\).

Constructor & Destructor Documentation

Delaunay_mesh_size_criteria_2() [1/2]

template<typename CDT >

CGAL::Delaunay_mesh_size_criteria_2< CDT >::Delaunay_mesh_size_criteria_2

(

)

Default constructor with \( B=\sqrt{2}\).

No bound on size.

Delaunay_mesh_size_criteria_2() [2/2]

template<typename CDT >

CGAL::Delaunay_mesh_size_criteria_2< CDT >::Delaunay_mesh_size_criteria_2	(	double	b = 0.125,
		double	S = 0
	)

Construct a traits class with bound \( B=\sqrt{\frac{1}{4 b}}\).

If \( S \neq0\), the size bound is \( S\). If \( S = 0\), there is no bound on size.