CGAL::Delaunay_mesh_size_criteria_2< CDT > Class Template Reference

#include <CGAL/Delaunay_mesh_size_criteria_2.h>

Definition

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, Mesh_2/mesh_optimization.cpp, and Mesh_2/mesh_with_seeds.cpp.

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

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.