CGAL 4.12.1 - 2D Conforming Triangulations and Meshes
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...

## ◆ 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.