CGAL::Projection_on_sphere_traits_3< LK, SK > Class Template Reference

#include <CGAL/Projection_on_sphere_traits_3.h>

Definition

template<typename LK, typename SK = CGAL::Spherical_kernel_3< LK, CGAL::Algebraic_kernel_for_spheres_2_3<typename LK::FT> >>
class CGAL::Projection_on_sphere_traits_3< LK, SK >

The class Projection_on_sphere_traits_3 is a model of the concept DelaunayTriangulationOnSphereTraits_2.

It implements the Point_on_sphere_2 type as a custom point type which represents the projection of a point living in the 3D Euclidean space onto the sphere along the segment between said point and the center of the sphere.

Template Parameters

LK	a linear kernel type; must be a model of Kernel.
SK	a spherical kernel type; must be a model of SphericalKernel.

Is Model Of:

DelaunayTriangulationOnSphereTraits_2

See also

CGAL::Delaunay_triangulation_on_sphere_traits_2

Examples:

Triangulation_on_sphere_2/triang_on_sphere_exact.cpp, Triangulation_on_sphere_2/triang_on_sphere_proj.cpp, and Triangulation_on_sphere_2/triang_on_sphere_range.cpp.

Public Types
typedef LK::FT	FT
	The field number type.
typedef unspecified_type	Point_on_sphere_2
	The point on the sphere type.
typedef SK::Circular_arc_3	Arc_on_sphere_2
typedef LK::Point_3	Point_3
typedef LK::Segment_3	Segment_3
typedef LK::Triangle_3	Triangle_3

Predicates
typedef unspecified_type	Equal_on_sphere_2
	Points are equal if they have the same projection onto the sphere.

Precision predicates
bool	is_on_sphere (const Point_on_sphere_2 &p) const
	Due to the chosen point representation, any point is theoretically on the sphere, and this function always returns true. More...
bool	are_points_too_close (const Point_on_sphere_2 &p, const Point_on_sphere_2 &q) const
	returns false if LK can represent algebraic coordinates, or whether the distance between p and q is lower than \( 2 \sqrt{R\delta} \) otherwise (see the traits class CGAL::Delaunay_triangulation_on_sphere_traits_2). More...

Member Function Documentation

are_points_too_close()

template<typename LK , typename SK = CGAL::Spherical_kernel_3< LK, CGAL::Algebraic_kernel_for_spheres_2_3<typename LK::FT> >>

bool CGAL::Projection_on_sphere_traits_3< LK, SK >::are_points_too_close	(	const Point_on_sphere_2 &	p,
		const Point_on_sphere_2 &	q
	)		const

returns false if LK can represent algebraic coordinates, or whether the distance between p and q is lower than \( 2 \sqrt{R\delta} \) otherwise (see the traits class CGAL::Delaunay_triangulation_on_sphere_traits_2).

is_on_sphere()

template<typename LK , typename SK = CGAL::Spherical_kernel_3< LK, CGAL::Algebraic_kernel_for_spheres_2_3<typename LK::FT> >>

bool CGAL::Projection_on_sphere_traits_3< LK, SK >::is_on_sphere

(

const Point_on_sphere_2 &

p

)

const

Due to the chosen point representation, any point is theoretically on the sphere, and this function always returns true.