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

CGAL 4.8 - 2D Conforming Triangulations and Meshes

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DelaunayMeshTraits_2 Concept Reference
Concepts

## Definition

The concept `DelaunayMeshTraits_2` refines the concept `ConformingDelaunayTriangulationTraits_2`. It provides a construction object `Construct_circumcenter_2`.

Refines:
  `ConformingDelaunayTriangulationTraits_2`

Has Models:

  Any model of the `Kernel` concept. In particular, all CGAL kernels

  `CGAL::Projection_traits_xy_3<K>`

## Types
typedef unspecified_type | Construct_circumcenter_2
| Constructor object. More...
typedef unspecified_type | Compute_area_2
| Constructor object. More...

## Access to predicate and constructor objects
Construct_circumcenter_2 | construct_circumcenter_2_object ()
Compute_area_2 | compute_area_2_object ()

## Member Typedef Documentation

typedef unspecified_type DelaunayMeshTraits_2::Compute_area_2

Constructor object.

Must provide an operator `FT operator()(Point_2 p, Point_2 q, Point_2 r);` that computes the signed area of the triangle defined by the points `p`, `q`, and `r`.

typedef unspecified_type DelaunayMeshTraits_2::Construct_circumcenter_2

Constructor object.

Must provide an operator `Point_2 operator()(Point_2 p, Point_2 q, Point_2 r);` that constructs the center of the circle passing through the points `p`, `q`, and `r`.

Precondition
  `p`, `q`, and `r` are not collinear.