\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.11.2 - 3D Spherical Geometry Kernel
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CGAL Namespace Reference

Namespaces

 Scale_space_reconstruction_3
 
 Shape_detection_3
 
 Surface_mesh_parameterization
 

Classes

class  Algebraic_kernel_for_circles_2_2
 
class  Circular_arc_2
 
class  Circular_arc_point_2
 
class  Circular_kernel_2
 
class  Exact_circular_kernel_2
 
class  Line_arc_2
 
class  Polynomial_1_2
 
class  Polynomial_for_circles_2_2
 
class  Root_for_circles_2_2
 
class  Aff_transformation_2
 
class  Aff_transformation_3
 
class  Identity_transformation
 
class  Reflection
 
class  Rotation
 
class  Scaling
 
class  Translation
 
class  Bbox_2
 
class  Bbox_3
 
class  Cartesian
 
class  Cartesian_converter
 
class  Circle_2
 
class  Circle_3
 
class  Ambient_dimension
 
class  Dimension_tag
 
class  Dynamic_dimension_tag
 
class  Feature_dimension
 
class  Direction_2
 
class  Direction_3
 
class  Exact_predicates_exact_constructions_kernel
 
class  Exact_predicates_exact_constructions_kernel_with_kth_root
 
class  Exact_predicates_exact_constructions_kernel_with_root_of
 
class  Exact_predicates_exact_constructions_kernel_with_sqrt
 
class  Exact_predicates_inexact_constructions_kernel
 
class  Filtered_kernel_adaptor
 
class  Filtered_kernel
 
class  Filtered_predicate
 
class  Homogeneous
 
class  Homogeneous_converter
 
class  Iso_cuboid_3
 
class  Iso_rectangle_2
 
class  Kernel_traits
 
class  Line_2
 
class  Line_3
 
class  Null_vector
 
class  Origin
 
class  Plane_3
 
class  Point_2
 
class  Point_3
 
class  Projection_traits_xy_3
 
class  Projection_traits_xz_3
 
class  Projection_traits_yz_3
 
class  Ray_2
 
class  Ray_3
 
class  Segment_2
 
class  Segment_3
 
class  Simple_cartesian
 
class  Simple_homogeneous
 
class  Sphere_3
 
class  Tetrahedron_3
 
class  Triangle_2
 
class  Triangle_3
 
class  Vector_2
 
class  Vector_3
 
class  Weighted_point_2
 
class  Weighted_point_3
 
class  Protect_FPU_rounding
 
class  Set_ieee_double_precision
 
class  Gmpfi
 
class  Gmpfr
 
class  Gmpq
 
class  Gmpz
 
class  Gmpzf
 
class  Interval_nt
 
class  Lazy_exact_nt
 
class  MP_Float
 
class  Mpzf
 
class  NT_converter
 
class  Number_type_checker
 
class  Quotient
 
class  Rational_traits
 
class  Root_of_traits
 
class  Sqrt_extension
 
class  Is_valid
 
class  Max
 
class  Min
 
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...