CGAL 4.14 - 3D Spherical Geometry Kernel
|
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. More... | |
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 . More... | |
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 . More... | |
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 . More... | |
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 . More... | |
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. More... | |
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 ). More... | |
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 . More... | |
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. More... | |
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. More... | |
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. More... | |
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. More... | |
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. More... | |
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. More... | |
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. More... | |
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. More... | |
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. More... | |
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::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.
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.
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::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.
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.
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::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.
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.