CGAL 5.1.2 - 2D and Surface Function Interpolation
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#include <CGAL/Voronoi_intersection_2_traits_3.h>
K.
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.
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... | |
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.
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 , |
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const K & | k = K() |
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) |
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.