CGAL 5.3 - 2D Triangulations on the Sphere
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
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...

## ◆ 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.