CGAL 4.14 - 2D Conforming Triangulations and Meshes
ConformingDelaunayTriangulationTraits_2 Concept Reference

## 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 ()

## ◆ 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).

## ◆ 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.

## ◆ 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 $$ab$$.

## ◆ 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.

## ◆ 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.

## ◆ Construct_vector_2

Constructor object.

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

## ◆ FT

The field type.

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