CGAL 4.7 - 3D Spherical Geometry Kernel: CGAL Namespace Reference

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CGAL 4.7 - 3D Spherical Geometry Kernel

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Classes | Enumerations | Functions
CGAL Namespace Reference

## Classes

class | Algebraic_kernel_for_spheres_2_3
class | Circular_arc_3
class | Circular_arc_point_3
class | Exact_spherical_kernel_3
| A typedef to a spherical kernel that provides both exact geometric predicates and exact geometric constructions. More...
class | Line_arc_3
class | Polynomial_1_3
class | Polynomial_for_spheres_2_3
class | Polynomials_for_lines_3
class | Root_for_spheres_2_3
class | Spherical_kernel_3

## Enumerations

enum | Circle_type { NORMAL, THREADED, POLAR, BIPOLAR }
| The enum `Circle_type` is used to classify an object of type `Circle_3`, so as to specify its type (normal,polar,bipolar or threaded), as defined in Section Spherical Kernel Objects. More...

## Functions

template<class SphericalKernel >
CGAL::Circle_type | 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 | 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 | 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 | 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 | 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 | 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 > | 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 | 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 > | 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 > | x_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, bool b)
| Same for a circle. More...
template<class SphericalKernel , class OutputIterator >
OutputIterator | 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 | 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 > | 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 > | y_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, bool b)
| Same for a circle. More...
template<class SphericalKernel class OutputIterator>
OutputIterator | 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 | 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 > | 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 > | z_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, bool b)
| Same for a circle. More...
template<class SphericalKernel , class OutputIterator >
OutputIterator | 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 | z_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, OutputIterator res)
| Copies in the output iterator the \( z\)-extremal points of the circle. More...