\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Conforming Triangulations and Meshes

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CGAL::Delaunay_mesh_size_criteria_2< CDT > Class Template Reference
2D Conforming Triangulations and Meshes 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

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.

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.