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CGAL 6.0 - 3D Spherical Geometry Kernel
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Functions | |
| template<class SphericalKernel > | |
| CGAL::Circle_type | CGAL::classify (const CGAL::Circle_3< SphericalKernel > &c, const CGAL::Sphere_3< SphericalKernel > &sphere) |
Classify a circle according to sphere, as defined in Section Spherical Kernel Objects. | |
| template<class SphericalKernel > | |
| Comparison_result | CGAL::compare_theta (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q, const CGAL::Sphere_3< SphericalKernel > &sphere) |
Compares the \( \theta\)-coordinates of p and q relatively to sphere. | |
| template<class SphericalKernel > | |
| Comparison_result | CGAL::compare_theta (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Vector_3< SphericalKernel > &m, const CGAL::Sphere_3< SphericalKernel > &sphere) |
Compares the \( \theta\)-coordinates of p and of the meridian defined by m (see Section Spherical Kernel Objects) in the cylindrical coordinate system relative to sphere. | |
| template<class SphericalKernel > | |
| Comparison_result | CGAL::compare_theta (const CGAL::Vector_3< SphericalKernel > &m, const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Sphere_3< SphericalKernel > &sphere) |
Compares the \( \theta\)-coordinates of the meridian defined by m and of p (see Section Spherical Kernel Objects) in the cylindrical coordinate system relative to sphere. | |
| template<class SphericalKernel > | |
| bool | CGAL::compare_theta_z (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q, const CGAL::Sphere_3< SphericalKernel > &sphere) |
Compares p and q according to the lexicographic ordering on \( \theta\) and \( z\)-coordinates in the cylindrical coordinate system relative to sphere. | |
| template<class SphericalKernel > | |
| bool | CGAL::is_theta_monotone (const CGAL::Circular_arc_3< SphericalKernel > &a, const CGAL::Sphere_3< SphericalKernel > &sphere) |
Tests whether the arc a is \( \theta\)-monotone, i.e. the intersection of any meridian anchored at the poles sphere and the arc a is reduced to at most one point in general, and two points if a pole of sphere is an endpoint of the arc. | |
| template<class SphericalKernel > | |
| CGAL::Circular_arc_point_3< SphericalKernel > | CGAL::theta_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, const CGAL::Sphere_3< SphericalKernel > sphere, bool b) |
Returns the point on the circle that is extremal in \( \theta\) using the cylindrical coordinate system relative to sphere, and that has the smallest (resp. largest) \( \theta\)-coordinate of the two points if b is true (resp. false). | |
| template<class SphericalKernel , class OutputIterator > | |
| OutputIterator | CGAL::theta_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, const CGAL::Sphere_3< SphericalKernel > &sphere, OutputIterator res) |
Copies in the output iterator the \( \theta\)-extremal points of the circle relatively to sphere. | |
| template<class SphericalKernel > | |
| CGAL::Circular_arc_point_3< SphericalKernel > | CGAL::x_extremal_point (const CGAL::Sphere_3< SphericalKernel > &c, bool b) |
Returns the point on the sphere that is extremal in the \( x\)-direction, and that is the smallest (resp. largest) of the two \( x\)-extremal points for the lexicographic order if b is true (resp. false). | |
| template<class SphericalKernel > | |
| CGAL::Circular_arc_point_3< SphericalKernel > | CGAL::x_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, bool b) |
| Same for a circle. | |
| template<class SphericalKernel , class OutputIterator > | |
| OutputIterator | CGAL::x_extremal_points (const CGAL::Sphere_3< SphericalKernel > &c, OutputIterator res) |
| Copies in the output iterator the \( x\)-extremal points of the sphere. | |
| template<class SphericalKernel , class OutputIterator > | |
| OutputIterator | CGAL::x_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, OutputIterator res) |
| Copies in the output iterator the \( x\)-extremal points of the circle. | |
| template<class SphericalKernel > | |
| CGAL::Circular_arc_point_3< SphericalKernel > | CGAL::y_extremal_point (const CGAL::Sphere_3< SphericalKernel > &c, bool b) |
Returns the point on the sphere that is extremal in the \( y\)-direction, and that is the smallest (resp. largest) of the two \( y\)-extremal points for the lexicographic order if b is true (resp. false). | |
| template<class SphericalKernel > | |
| CGAL::Circular_arc_point_3< SphericalKernel > | CGAL::y_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, bool b) |
| Same for a circle. | |
| template<class SphericalKernel class OutputIterator> | |
| OutputIterator | CGAL::y_extremal_points (const CGAL::Sphere_3< SphericalKernel > &c, OutputIterator res) |
| Copies in the output iterator the \( y\)-extremal points of the sphere. | |
| template<class SphericalKernel , class OutputIterator > | |
| OutputIterator | CGAL::y_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, OutputIterator res) |
| Copies in the output iterator the \( y\)-extremal points of the circle. | |
| template<class SphericalKernel > | |
| CGAL::Circular_arc_point_3< SphericalKernel > | CGAL::z_extremal_point (const CGAL::Sphere_3< SphericalKernel > &c, bool b) |
Returns the point on the sphere that is extremal in the \( z\)-direction, and that is the smallest (resp. largest) of the two \( z\)-extremal points for the lexicographic order if b is true (resp. false). | |
| template<class SphericalKernel > | |
| CGAL::Circular_arc_point_3< SphericalKernel > | CGAL::z_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, bool b) |
| Same for a circle. | |
| template<class SphericalKernel , class OutputIterator > | |
| OutputIterator | CGAL::z_extremal_points (const CGAL::Sphere_3< SphericalKernel > &c, OutputIterator res) |
| Copies in the output iterator the \( z\)-extremal points of the sphere. | |
| template<class SphericalKernel , class OutputIterator > | |
| OutputIterator | CGAL::z_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, OutputIterator res) |
| Copies in the output iterator the \( z\)-extremal points of the circle. | |
| CGAL::Circle_type CGAL::classify | ( | const CGAL::Circle_3< SphericalKernel > & | c, |
| const CGAL::Sphere_3< SphericalKernel > & | sphere | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Classify a circle according to sphere, as defined in Section Spherical Kernel Objects.
c lies on sphere.CGAL::Circle_type | Comparison_result CGAL::compare_theta | ( | const CGAL::Circular_arc_point_3< SphericalKernel > & | p, |
| const CGAL::Circular_arc_point_3< SphericalKernel > & | q, | ||
| const CGAL::Sphere_3< SphericalKernel > & | sphere | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Compares the \( \theta\)-coordinates of p and q relatively to sphere.
p and q lie on sphere, but do not coincide with the poles of sphere.| Comparison_result CGAL::compare_theta | ( | const CGAL::Circular_arc_point_3< SphericalKernel > & | p, |
| const CGAL::Vector_3< SphericalKernel > & | m, | ||
| const CGAL::Sphere_3< SphericalKernel > & | sphere | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Compares the \( \theta\)-coordinates of p and of the meridian defined by m (see Section Spherical Kernel Objects) in the cylindrical coordinate system relative to sphere.
p lies on sphere, but does not coincide with its poles. m \( \neq(0,0,0)\) and the \( z\)-coordinate of m is \( 0\).| Comparison_result CGAL::compare_theta | ( | const CGAL::Vector_3< SphericalKernel > & | m, |
| const CGAL::Circular_arc_point_3< SphericalKernel > & | p, | ||
| const CGAL::Sphere_3< SphericalKernel > & | sphere | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Compares the \( \theta\)-coordinates of the meridian defined by m and of p (see Section Spherical Kernel Objects) in the cylindrical coordinate system relative to sphere.
p lies on sphere, but does not coincide with its poles. m \( \neq(0,0,0)\) and the \( z\)-coordinate of m is \( 0\).| bool CGAL::compare_theta_z | ( | const CGAL::Circular_arc_point_3< SphericalKernel > & | p, |
| const CGAL::Circular_arc_point_3< SphericalKernel > & | q, | ||
| const CGAL::Sphere_3< SphericalKernel > & | sphere | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Compares p and q according to the lexicographic ordering on \( \theta\) and \( z\)-coordinates in the cylindrical coordinate system relative to sphere.
p and q lie on sphere, but do not coincide with the poles of sphere.| bool CGAL::is_theta_monotone | ( | const CGAL::Circular_arc_3< SphericalKernel > & | a, |
| const CGAL::Sphere_3< SphericalKernel > & | sphere | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Tests whether the arc a is \( \theta\)-monotone, i.e. the intersection of any meridian anchored at the poles sphere and the arc a is reduced to at most one point in general, and two points if a pole of sphere is an endpoint of the arc.
Note that a bipolar circle has no such arcs.
a lies on sphere, and the supporting circle of a is not bipolar. | CGAL::Circular_arc_point_3< SphericalKernel > CGAL::theta_extremal_point | ( | const CGAL::Circle_3< SphericalKernel > & | c, |
| const CGAL::Sphere_3< SphericalKernel > | sphere, | ||
| bool | b | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Returns the point on the circle that is extremal in \( \theta\) using the cylindrical coordinate system relative to sphere, and that has the smallest (resp. largest) \( \theta\)-coordinate of the two points if b is true (resp. false).
See Section Spherical Kernel Objects for definitions.
c lies on sphere and is a normal circle. | OutputIterator CGAL::theta_extremal_points | ( | const CGAL::Circle_3< SphericalKernel > & | c, |
| const CGAL::Sphere_3< SphericalKernel > & | sphere, | ||
| OutputIterator | res | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Copies in the output iterator the \( \theta\)-extremal points of the circle relatively to sphere.
res iterates on elements of type Circular_arc_point_3<SphericalKernel>, lexicographically sorted in the cylindrical coordinate system relative to sphere. See Section Spherical Kernel Objects for definitions.
c lies on sphere and is a normal circle. | CGAL::Circular_arc_point_3< SphericalKernel > CGAL::x_extremal_point | ( | const CGAL::Circle_3< SphericalKernel > & | c, |
| bool | b | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Same for a circle.
| OutputIterator CGAL::x_extremal_points | ( | const CGAL::Circle_3< SphericalKernel > & | c, |
| OutputIterator | res | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Copies in the output iterator the \( x\)-extremal points of the circle.
res iterates on elements of type Circular_arc_point_3<SphericalKernel>, lexicographically sorted.
| OutputIterator CGAL::x_extremal_points | ( | const CGAL::Sphere_3< SphericalKernel > & | c, |
| OutputIterator | res | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Copies in the output iterator the \( x\)-extremal points of the sphere.
res iterates on elements of type Circular_arc_point_3<SphericalKernel>, lexicographically sorted.
| CGAL::Circular_arc_point_3< SphericalKernel > CGAL::y_extremal_point | ( | const CGAL::Circle_3< SphericalKernel > & | c, |
| bool | b | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Same for a circle.
| OutputIterator CGAL::y_extremal_points | ( | const CGAL::Circle_3< SphericalKernel > & | c, |
| OutputIterator | res | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Copies in the output iterator the \( y\)-extremal points of the circle.
res iterates on elements of type Circular_arc_point_3<SphericalKernel>, lexicographically sorted.
| OutputIterator CGAL::y_extremal_points | ( | const CGAL::Sphere_3< SphericalKernel > & | c, |
| OutputIterator | res | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Copies in the output iterator the \( y\)-extremal points of the sphere.
res iterates on elements of type Circular_arc_point_3<SphericalKernel>, lexicographically sorted.
| CGAL::Circular_arc_point_3< SphericalKernel > CGAL::z_extremal_point | ( | const CGAL::Circle_3< SphericalKernel > & | c, |
| bool | b | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Same for a circle.
| OutputIterator CGAL::z_extremal_points | ( | const CGAL::Circle_3< SphericalKernel > & | c, |
| OutputIterator | res | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Copies in the output iterator the \( z\)-extremal points of the circle.
res iterates on elements of type Circular_arc_point_3<SphericalKernel>, lexicographically sorted.
| OutputIterator CGAL::z_extremal_points | ( | const CGAL::Sphere_3< SphericalKernel > & | c, |
| OutputIterator | res | ||
| ) |
#include <CGAL/global_functions_spherical_kernel_3.h>
Copies in the output iterator the \( z\)-extremal points of the sphere.
res iterates on elements of type Circular_arc_point_3<SphericalKernel>, lexicographically sorted.