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

All models of the CGAL concept Kernel

CGAL::Projection_traits_xy_3<K>

Types
typedef unspecified_type	FT
	The field type.
typedef unspecified_type	Vector_2
	The vector type.
typedef unspecified_type	Construct_vector_2
	Constructor object.
typedef unspecified_type	Construct_scaled_vector_2
	Constructor object.
typedef unspecified_type	Construct_translated_point_2
	Constructor object.
typedef unspecified_type	Construct_midpoint_2
	Constructor object.
typedef unspecified_type	Compute_squared_distance_2
	Constructor object.
typedef unspecified_type	Angle_2
	Predicate object.
typedef unspecified_type	Oriented_side_2
	Predicate object.

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

Angle_2

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).

Compute_squared_distance_2

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.

Construct_midpoint_2

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 \( ab\).

Construct_scaled_vector_2

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.

Construct_translated_point_2

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.

Construct_vector_2

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.

FT

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 \( \sqrt{\cdot}\).

Oriented_side_2

typedef unspecified_type ConformingDelaunayTriangulationTraits_2::Oriented_side_2

Predicate object.

Must provide the operator CGAL::Oriented_side operator()(Segment_2 s, Triangle_2 t) that returns CGAL::ON_ORIENTED_BOUNDARY, CGAL::ON_NEGATIVE_SIDE, or CGAL::ON_POSITIVE_SIDE, depending on the position of the circumcenter of t relative to the oriented supporting line of s. The orientation of the supporting line is the same as the orientation of s.