RegularTriangulationTraits_2 Concept Reference

Definition

The concept RegularTriangulationTraits_2 describe the requirements for the traits class of regular triangulations. It refines the concept TriangulationTraits_2 requiring the type CGAL::Weighted_point and the power test predicate on those weighted points. A weighted point is basically a point augmented with a scalar weight. It can be seen as a circle when the weight is interpreted as a square radius. The power test on weighted points is the fundamental test to build regular triangulations as the side_of_oriented_circle test is the fundamental test of Delaunay triangulations.

Refines:

TriangulationTraits_2

Has Models:

CGAL::Regular_triangulation_euclidean_traits_2<K,Weight>

CGAL::Regular_triangulation_filtered_traits_2<FK>

See Also

TriangulationTraits_2

CGAL::Regular_triangulation_2<Traits,Tds>

Types
typedef unspecified_type	Bare_point
	Another name for the point type.
typedef unspecified_type	Weighted_point_2
	The weighted point type. More...
typedef unspecified_type	Power_test_2
	A function object which must provide operators for the power test applied to two, three, and four points. More...

Optional Types
The following type/predicate is required for a call to nearest_power_vertex:
typedef unspecified_type	Compare_power_distance_2
	A function object for computing two power distances. More...
typedef unspecified_type	Construct_weighted_circumcenter_2
	A function object which constructs the weighted circumcenter of three weighted points. More...
typedef unspecified_type	Construct_radical_axis_2
	A function object constructs the radical axis of two weighted points. More...

Creation
	RegularTriangulationTraits_2 ()
	Default constructor.
	RegularTriangulationTraits_2 (const RegularTriangulatioTraits_2 &)
	Copy constructor.
RegularTriangulationTraits_2 &	operator= (const RegularTriangulationTraits_2 &)
	Assignment operator.

Access to Predicate and Constructors Objects
Power_test_2	power_test_2_object ()
Compare_power_distance_2	compare_power_distance_2_object ()
Construct_weighted_circumcenter_2	construct_weighted_circumcenter_2_object ()
Construct_radical_axis_2	construct_radical_axis_2_object ()

Member Typedef Documentation

typedef unspecified_type RegularTriangulationTraits_2::Compare_power_distance_2

A function object for computing two power distances.

Must provide the operator:

Comparison_result operator()(Bare_point p, Weighted_point_2 q, Weighted_point_2 r), which compares the power distance between p and q to the power distance between p and r.

typedef unspecified_type RegularTriangulationTraits_2::Construct_radical_axis_2

A function object constructs the radical axis of two weighted points.

Must provide the operator:

Line_2 operator() ( Weighted_point_2 p, Weighted_point_2 q);

typedef unspecified_type RegularTriangulationTraits_2::Construct_weighted_circumcenter_2

A function object which constructs the weighted circumcenter of three weighted points.

Must provide the operator:

Bare_point operator() ( Weighted_point_2 p, Weighted_point_2 q, Weighted_point_2 r);

typedef unspecified_type RegularTriangulationTraits_2::Power_test_2

A function object which must provide operators for the power test applied to two, three, and four points.

Must provide the operators:

• Oriented_side operator() ( Weighted_point_2 p, Weighted_point_2 q, Weighted_point_2 r, Weighted_point_2 s) which is the power test for points p, q, r and s.

  Precondition

  the bare points corresponding to p, q, r are not collinear.

• Oriented_side operator() ( Weighted_point_2 p, Weighted_point_2 q, Weighted_point_2 r) which is the degenerated power test for collinear points p, q, r.

  Precondition

  the bare points corresponding to p, q, r are collinear and p != q.

• Oriented_side operator() ( Weighted_point_2 p, Weighted_point_2 q) which is the degenerated power test for weighted points p and q whose corresponding bare-points are identical.

  Precondition

  the bare points corresponding to p and q are identical.

typedef unspecified_type RegularTriangulationTraits_2::Weighted_point_2

The weighted point type.

It has to be a model of the concept WeightedPoint.