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

CGAL 4.8 - 2D Conforming Triangulations and Meshes

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ConformingDelaunayTriangulationTraits_2 Concept Reference
Concepts

## Definition

The concept `ConformingDelaunayTriangulationTraits_2` refines the concept `ConstrainedDelaunayTriangulationTraits_2` by providing a numeric field type `FT`, a type `Vector_2` and several constructors on `Vector_2`, `Point_2`, and a predicate on angles. The field type has to be a model of the concept `FieldWithSqrt`. This field type and the constructors are used by the conforming algorithm to compute Steiner points on constrained edges.

Refines:
  `DelaunayTriangulationTraits_2`

Has Models:

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

  `Projection_traits_xy_3<K>`

## Types
typedef unspecified_type | FT
| The field type. More...
typedef unspecified_type | Vector_2
| The vector type.
typedef unspecified_type | Construct_vector_2
| Constructor object. More...
typedef unspecified_type | Construct_scaled_vector_2
| Constructor object. More...
typedef unspecified_type | Construct_translated_point_2
| Constructor object. More...
typedef unspecified_type | Construct_midpoint_2
| Constructor object. More...
typedef unspecified_type | Compute_squared_distance_2
| Constructor object. More...
typedef unspecified_type | Angle_2
| Predicate object. More...

## Access to predicate and constructor objects
Construct_vector_2 | construct_vector_2_object ()
Construct_scaled_vector_2 | construct_scaled_vector_2_object ()
Construct_translated_point_2 | construct_translated_point_2_object ()
Construct_midpoint_2 | construct_midpoint_2_object ()
Compute_squared_distance_2 | compute_squared_distance_2_object ()
Angle_2 | angle_2_object ()

## Member Typedef Documentation

typedef unspecified_type ConformingDelaunayTriangulationTraits_2::Angle_2

Predicate object.

Must provide the operator `CGAL::Angle operator()(Point_2 p, Point_2 q, Point_2 r)` that returns OBTUSE, RIGHT or ACUTE depending on the angle formed by the three points `p`, `q`, `r` (`q` being the vertex of the angle).

typedef unspecified_type ConformingDelaunayTriangulationTraits_2::Compute_squared_distance_2

Constructor object.

Must provide the operator `FT operator()(Point_2 a, Point_2 b)` that computes the squared distance between `a` and `b`.

typedef unspecified_type ConformingDelaunayTriangulationTraits_2::Construct_midpoint_2

Constructor object.

Must provide the operator `Point_2 operator()(Point_2 a, Point_2 b)` that computes the midpoint of the segment \( ab\).

typedef unspecified_type ConformingDelaunayTriangulationTraits_2::Construct_scaled_vector_2

Constructor object.

Must provide the operator `Vector_2 operator()(Vector_2 v, FT scale)` that computes the vector `scale` \(\cdot\) `v`.

typedef unspecified_type ConformingDelaunayTriangulationTraits_2::Construct_translated_point_2

Constructor object.

Must provide the operator `Point_2 operator()(Point_2 p, Vector_2 v)` that computes the point `p+v`.

typedef unspecified_type ConformingDelaunayTriangulationTraits_2::Construct_vector_2

Constructor object.

Must provide the operator `Vector_2 operator()(Point a, Point b)` that computes the vector `b-a`.

typedef unspecified_type ConformingDelaunayTriangulationTraits_2::FT

The field type.

It must be a model of `FieldWithSqrt`, that is must be a number type supporting the operations \( +\), \( -\), \( *\), \( /\), and \( \sqrt{\cdot}\).