CGAL::Regular_triangulation_euclidean_traits_3< K, Weight > Class Template Reference

#include <CGAL/Regular_triangulation_euclidean_traits_3.h>

Inherits from

K.

Definition

Deprecated:

The class is deprecated since CGAL 4.10, as the weighted point and the function objects for weighted points are part of the concept Kernel. The class is kept for backward compatibility, but ignores the template parameter Weight.

The class Regular_triangulation_euclidean_traits_3 was the default traits class for the class Regular_triangulation_3<RegularTriangulationTraits_3,TriangulationDataStructure_3> and uses the type K::Weighted_point_3 for weighted points`.

Template Parameters

K	must be a model of the Kernel concept.
Weight	This template parameter is ignored, as Kernel::Weighted_point_3 uses the type Kernel::FT.

The class is a model of the concept RegularTriangulationTraits_3.

It also contains some additional predicates and constructors on weighted points that are not required in the concept RegularTriangulationTraits_3, and hence documented here. They are used by mesh generation packages.

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. This is the case for the predefined kernels Predefined Kernels.

Is Model Of:

RegularTriangulationTraits_3

Types
typedef K::Point_3	Bare_point
	The type for point \( p\) of a weighted point \( {p}^{(w)}=(p,w_p)\).
typedef K::Weighted_point_3	Weighted_point_3
	The type for weighted points.
typedef K::Weighted_point_3	Point_3
	The type for points.

Types for Predicate Functors
typedef unspecified_type	Compare_weighted_squared_radius_3
	A predicate type, model of Kernel::CompareWeightedSquaredRadius_3. More...
typedef unspecified_type	Power_side_of_bounded_power_sphere_3
	A predicate type, model of Kernel::PowerSideOfBoundedPowerSphere_3. More...

Types for Constructor Functors
typedef unspecified_type	Compute_power_product_3
	A functor type, model of Kernel::ComputePowerProduct_3. More...
typedef unspecified_type	Compute_squared_radius_smallest_orthogonal_sphere_3
	A functor type, model of Kernel::ComputeSquaredRadiusSmallestOrthogonalSphere_3. More...
typedef unspecified_type	Compute_power_distance_to_power_sphere_3
	A functor type, model of Kernel::ComputePowerDistanceToPowerSphere_3. More...

Operations
Compare_weighted_squared_radius_3	compare_weighted_squared_radius_3_object ()
Power_side_of_bounded_power_sphere_3	power_side_of_bounded_power_sphere_3_object ()
Compute_power_product_3	compute_power_product_3_object ()
Compute_squared_radius_smallest_orthogonal_sphere_3	compute_squared_radius_smallest_orthogonal_sphere_3_object ()
Compute_power_distance_to_power_sphere_3	compute_power_distance_to_power_sphere_3_object ()

Member Typedef Documentation

template<typename K , typename Weight >

typedef unspecified_type CGAL::Regular_triangulation_euclidean_traits_3< K, Weight >::Compare_weighted_squared_radius_3

A predicate type, model of Kernel::CompareWeightedSquaredRadius_3.

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) ;

template<typename K , typename Weight >

typedef unspecified_type CGAL::Regular_triangulation_euclidean_traits_3< K, Weight >::Compute_power_distance_to_power_sphere_3

A functor type, model of Kernel::ComputePowerDistanceToPowerSphere_3.

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.

FT operator() ( Weighted_point_3 p, Weighted_point_3 q, Weighted_point_3 r, Weighted_point_3 s, Weighted_point_3 t);

template<typename K , typename Weight >

typedef unspecified_type CGAL::Regular_triangulation_euclidean_traits_3< K, Weight >::Compute_power_product_3

A functor type, model of Kernel::ComputePowerProduct_3.

The operator() computes the power distance between its arguments.

FT operator() ( Weighted_point_3 p, Weighted_point_3 q) ;

template<typename K , typename Weight >

typedef unspecified_type CGAL::Regular_triangulation_euclidean_traits_3< K, Weight >::Compute_squared_radius_smallest_orthogonal_sphere_3

A functor type, model of Kernel::ComputeSquaredRadiusSmallestOrthogonalSphere_3.

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);

template<typename K , typename Weight >

typedef unspecified_type CGAL::Regular_triangulation_euclidean_traits_3< K, Weight >::Power_side_of_bounded_power_sphere_3

A predicate type, model of Kernel::PowerSideOfBoundedPowerSphere_3.

The operator() is similar to the operator() of Power_side_of_oriented_power_sphere_3 except that the returned type is not an Oriented_side but belongs to the enum Bounded_side (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) ;