CGAL::Voronoi_intersection_2_traits_3< K > Class Template Reference

#include <CGAL/Voronoi_intersection_2_traits_3.h>

Inherits from

K.

Definition

Voronoi_intersection_2_traits_3 is a model for the concept RegularTriangulationTraits_2.

It can be used to instantiate the geometric traits class of a two-dimensional regular triangulation. A three-dimensional plane is defined by a point and a vector that are members of the traits class. The triangulation is defined on 3D points. It is the regular triangulation of the input points projected onto the plane and each weighted with the negative squared distance of the input point to the plane. It can be shown that it is dual to the power diagram obtained by intersecting the three-dimensional Voronoi diagram of the input points with the plane. All predicates and constructions used in the computation of the regular triangulation are formulated on the three dimensional points without explicitly constructing the projected points and the weights. This reduces the arithmetic demands. The traits class is templated by a kernel class K and inherits from it.

Is Model Of:

RegularTriangulationTraits_2

See Also

CGAL::Regular_triangulation_2<Gt, Tds>

CGAL::regular_neighbor_coordinates_2()

3D Surface Neighbor Coordinates Functions

3D types camouflaged as 2D types
typedef K::Point_3	Point_2
typedef K::Weighted_point_3	Weighted_point_2
typedef K::Segment_3	Segment_2
typedef K::Triangle_3	Triangle_2
typedef K::Line_3	Line_2
typedef K::Ray_3	Ray_2
typedef K::Vector_3	Vector_2
typedef K::Circle_3	Circle_2
typedef K::Construct_point_3	Construct_point_2
typedef K::Construct_weighted_point_3	Construct_weighted_point_2
typedef K::Construct_segment_3	Construct_segment_2
typedef K::Construct_vector_3	Construct_vector_2
typedef K::Construct_ray_3	Construct_ray_2
typedef K::Construct_triangle_3	Construct_triangle_2
typedef K::Compare_distance_3	Compare_distance_2
typedef K::Less_distance_to_point_3	Less_distance_to_point_2
	Necessary for certificated coordinates / neighbors computation.
typedef K::Compute_squared_distance_3	Compute_squared_distance_2
	Necessary for certificated coordinates / neighbors computation.
typedef K::Equal_3	Equal_2
typedef K::Construct_circumcenter_3	Construct_circumcenter_2

Custom predicates and constructions
typedef Compute_area_3< K >	Compute_area_2
	An instance of this function object class computes the square root of the result of K::Compute_squared_area_3. More...
typedef Orientation_with_normal_plane_2_3 < K >	Orientation_2
typedef Side_of_plane_centered_sphere_2_3 < K >	Power_side_of_oriented_power_circle_2
typedef Construct_plane_centered_circumcenter_3 < K >	Construct_weighted_circumcenter_2
typedef Construct_plane_intersected_bisector_3 < Point_2 >	Construct_radical_axis_2
typedef Compare_first_projection_3< K >	Compare_x_2
typedef Compare_second_projection_3< K >	Compare_y_2
typedef Compare_to_less < Compare_x_2 >	Compare_x_2
typedef Compare_to_less < Compare_y_2 >	Compare_y_2

Creation
	Voronoi_intersection_2_traits_3 (const typename K::Point_3 &point=typename K::Point_3(), const typename K::Vector_3 &normal=NULL_VECTOR, const K &k=K())
	The plane associated to the traits class contains point and has as normal vector normal. More...

Member Typedef Documentation

template<typename K >

typedef Compute_area_3<K> CGAL::Voronoi_intersection_2_traits_3< K >::Compute_area_2

An instance of this function object class computes the square root of the result of K::Compute_squared_area_3.

If the number type FT does not support the square root operation, the result is cast to double before computing the square root.

Constructor & Destructor Documentation

template<typename K >

CGAL::Voronoi_intersection_2_traits_3< K >::Voronoi_intersection_2_traits_3	(	const typename K::Point_3 &	point = typename K::Point_3(),
		const typename K::Vector_3 &	normal = NULL_VECTOR,
		const K &	k = K()
	)

The plane associated to the traits class contains point and has as normal vector normal.

The optional kernel parameter k is the base class of the traits class.