The class Regular_triangulation_euclidean_traits_3<K,Weight> is designed as a default traits class for the class Regular_triangulation_3<RegularTriangulationTraits_3,TriangulationDataStructure_3>. It provides Weighted_point_3, a class for weighted points, which derives from the three dimensional point class K::Point_3.
The first argument K must be a model of the Kernel concept.
The second argument Weight of the class Regular_triangulation_euclidean_traits_3<K,Weight> is in fact optional: if is it not provided, K::RT will be used.
The class is a model of the concept RegularTriangulationTraits_3 but it also contains predicates and constructors on weighted points that are not required in the concept RegularTriangulationTraits_3.
Note that filtered predicates are automatically used if the boolean Has_filtered_predicates in the kernel provided as template parameter of that class is set to true.
#include <CGAL/Regular_triangulation_euclidean_traits_3.h>
typedef K::Point_3 | Bare_point; | The type for point p of a weighted point p(w)=(p,wp). |
typedef Weighted_point <Bare_point, Weight> | ||
Weighted_point_3; | The type for weighted points. |
Regular_triangulation_euclidean_traits_3<K,Weight>::Power_test_3 | |
A predicate type for power test. Belongs to the
RegularTriangulationTraits_3 concept.
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Regular_triangulation_euclidean_traits_3<K,Weight>::Compare_power_distance_3 | |
A predicate type to compare power distance. Belongs to the
RegularTriangulationTraits_3 concept.
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Regular_triangulation_euclidean_traits_3<K,Weight>::Compare_weighted_squared_radius_3 | |
A predicate type. The operator() takes weighted point(s) as arguments,
together with one weight. It compares the weight of the smallest sphere
orthogonal to the weighted points with the input weight. Comparison_result operator()( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, Weighted_point_3 s, FT w) ; Comparison_result operator()( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, FT w) ; Comparison_result operator()( Weighted_point_3 p, Weighted_point_3 q, FT w) ; Comparison_result operator()( Weighted_point_3 p, FT w) ;
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Regular_triangulation_euclidean_traits_3<K,Weight>::In_smallest_orthogonal_sphere_3 | |
A predicate type. The operator() takes weighted points as arguments
and returns the sign of the power distance of the last one
with respect to the smallest sphere orthogonal to the others. Sign operator()( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, Weighted_point_3 s, Weighted_point_3 t) ; Sign operator()( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, Weighted_point_3 s) ; Sign operator()( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r) ; Sign operator()( Weighted_point_3 p, Weighted_point_3 q) ;
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Regular_triangulation_euclidean_traits_3<K,Weight>::Side_of_bounded_orthogonal_sphere_3 | |
A predicate type. The operator() is similar to the operator() of
In_smallest_orthogonal_sphere_3
except that the returned type is not a Sign
but belongs to the enum Bounded_side
(A NEGATIVE, ZERO and POSITIVE)
corresponding respectively to
ON_BOUNDED_SIDE, ON_BOUNDARY and ON_UNBOUNDED_SIDE)). Bounded_side operator() ( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, Weighted_point_3 s, Weighted_point_3 t) ; Bounded_side operator() ( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, Weighted_point_3 s) ; Bounded_side operator() ( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r) ;
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Regular_triangulation_euclidean_traits_3<K,Weight>::Does_simplex_intersect_dual_support_3 | |
A predicate type. The operator()
takes weighted points as arguments,
considers the subspace of points with equal power distance
with respect to its arguments
and the intersection of this subspace with the affine hull of the bare
points associated to the arguments.
The operator() returns ON_BOUNDED_SIDE,
ON_BOUNDARY or ON_UNBOUNDED_SIDE
according to the position of this intersection
with respect to the simplex formed by the bare
points.
This predicate is useful for flow computations. Bounded_side operator()( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, Weighted_point_3 s) ; Bounded_side operator()( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r) ; Bounded_side operator()( Weighted_point_3 p, Weighted_point_3 q) ;
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