Classify a circle according to sphere, as defined in Section Spherical Kernel Objects.

Precondition

c lies on sphere.

See Also

CGAL::Circle_type

#include <CGAL/global_functions_spherical_kernel_3.h>

Compares the $\theta$-coordinates of p and q relatively to sphere.

Precondition

p and q lie on sphere, but do not coincide with the poles of sphere.

See Also

CGAL::compare_x()

CGAL::compare_xy()

CGAL::compare_xy()

CGAL::compare_x_at_y()

CGAL::compare_y()

CGAL::compare_yx()

CGAL::compare_y_at_x()

CGAL::compare_z()

CGAL::compare_theta_z()

#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.

Precondition

p lies on sphere, but does not coincide with its poles. m $\neq(0,0,0)$ and the $z$-coordinate of m is $0$.

See Also

CGAL::compare_x()

CGAL::compare_xy()

CGAL::compare_xy()

CGAL::compare_x_at_y()

CGAL::compare_y()

CGAL::compare_yx()

CGAL::compare_y_at_x()

CGAL::compare_z()

CGAL::compare_theta_z()

#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.

Precondition

p lies on sphere, but does not coincide with its poles. m $\neq(0,0,0)$ and the $z$-coordinate of m is $0$.

See Also

CGAL::compare_x()

CGAL::compare_xy()

CGAL::compare_x_at_y()

CGAL::compare_y()

CGAL::compare_yx()

CGAL::compare_y_at_x()

CGAL::compare_z()

CGAL::compare_theta_z()

#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.

Precondition

p and q lie on sphere, but do not coincide with the poles of sphere.

See Also

CGAL::compare_x()

CGAL::compare_xy()

CGAL::compare_xy()

CGAL::compare_x_at_y()

CGAL::compare_y()

CGAL::compare_yx()

CGAL::compare_y_at_x()

CGAL::compare_z()

CGAL::compare_theta()

#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.

Precondition

a lies on sphere, and the supporting circle of a is not bipolar.

#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.

Precondition

c lies on sphere and is a normal circle.

#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.

Precondition

c lies on sphere and is a normal circle.

#include <CGAL/global_functions_spherical_kernel_3.h>

Examples:

Circular_kernel_3/functor_compare_theta_3.cpp.

Same for a circle.

Precondition

The circle is not contained in a plane orthogonal to the $x$-axis.

#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.

#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.

Precondition

The circle is not contained in a plane orthogonal to the $x$-axis.

#include <CGAL/global_functions_spherical_kernel_3.h>

Same for a circle.

Precondition

The circle is not contained in a plane orthogonal to the $y$-axis.

#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.

#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.

Precondition

The circle is not contained in a plane orthogonal to the $y$-axis.

#include <CGAL/global_functions_spherical_kernel_3.h>

Same for a circle.

Precondition

The circle is not contained in a plane orthogonal to the $z$-axis.

#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.

#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.

Precondition

The circle is not contained in a plane orthogonal to the $z$-axis.

#include <CGAL/global_functions_spherical_kernel_3.h>