CGAL 4.8.2 - 3D Triangulations
|
#include <CGAL/Regular_triangulation_euclidean_traits_3.h>
K.
The class Regular_triangulation_euclidean_traits_3
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
.
K | must be a model of the Kernel concept. |
Weight | is 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
.
Operations
The following functions give access to the predicate and constructor functors.
Types | |
typedef K::Point_3 | Bare_point |
The type for point \( p\) of a weighted point \( {p}^{(w)}=(p,w_p)\). | |
typedef Weighted_point < Bare_point, Weight > | Weighted_point_3 |
The type for weighted points. | |
typedef Weighted_point < Bare_point, Weight > | Point_3 |
The type for points. | |
Types for Predicate Functors | |
typedef unspecified_type | Power_test_3 |
A predicate type for power test. More... | |
typedef unspecified_type | Compare_power_distance_3 |
A predicate type to compare power distance. More... | |
typedef unspecified_type | Compare_weighted_squared_radius_3 |
A predicate type. More... | |
typedef unspecified_type | In_smallest_orthogonal_sphere_3 |
A predicate type. More... | |
typedef unspecified_type | Side_of_bounded_orthogonal_sphere_3 |
A predicate type. More... | |
typedef unspecified_type | Does_simplex_intersect_dual_support_3 |
A predicate type. More... | |
Types for Constructor Functors | |
typedef unspecified_type | Construct_weighted_circumcenter_3 |
A constructor type. More... | |
typedef unspecified_type | Compute_power_product_3 |
A functor type. More... | |
typedef unspecified_type | Compute_squared_radius_smallest_orthogonal_sphere_3 |
A functor type. More... | |
typedef unspecified_type | Compute_critical_squared_radius_3 |
A functor type. More... | |
typedef unspecified_type CGAL::Regular_triangulation_euclidean_traits_3< K, Weight >::Compare_power_distance_3 |
A predicate type to compare power distance.
Belongs to the RegularTriangulationTraits_3
concept.
typedef unspecified_type CGAL::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) ;
typedef unspecified_type CGAL::Regular_triangulation_euclidean_traits_3< K, Weight >::Compute_critical_squared_radius_3 |
A functor type.
The operator() takes weighted points as arguments and computes the squared radius of the sphere centered in the last point and orthogonal to the other weighted points. The last argument is a weighted point but its weight does not matter. This construction is ad hoc for pumping slivers. For robustness issue, a predicate to compare critical squared radii for a given last point should be needed.
FT operator() ( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, Weighted_point_3 s, Weighted_point_3 t);
typedef unspecified_type CGAL::Regular_triangulation_euclidean_traits_3< K, Weight >::Compute_power_product_3 |
A functor type.
The operator() computes the power distance between its arguments.
FT operator() ( Weighted_point_3 p, Weighted_point_3 q) ;
typedef unspecified_type CGAL::Regular_triangulation_euclidean_traits_3< K, Weight >::Compute_squared_radius_smallest_orthogonal_sphere_3 |
A functor type.
The operator() computes the squared radius of the smallest sphere orthogonal to the argument(s).
FT operator() ( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, Weighted_point_3 s);
FT operator() ( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r);
FT operator() ( Weighted_point_3 p, Weighted_point_3 q);
FT operator() ( Weighted_point_3 p);
typedef unspecified_type CGAL::Regular_triangulation_euclidean_traits_3< K, Weight >::Construct_weighted_circumcenter_3 |
A constructor type.
The operator() constructs the bare point which is the center of the smallest orthogonal sphere to the input weighted points.
Bare_point operator() ( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, Weighted_point_3 s);
Bare_point operator() ( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r);
Bare_point operator() ( Weighted_point_3 p, Weighted_point_3 q);
typedef unspecified_type CGAL::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) ;
typedef unspecified_type CGAL::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) ;
typedef unspecified_type CGAL::Regular_triangulation_euclidean_traits_3< K, Weight >::Power_test_3 |
A predicate type for power test.
Belongs to the RegularTriangulationTraits_3
concept.
typedef unspecified_type CGAL::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) ;