CGAL 4.11.2 - 3D Spherical Geometry Kernel
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Namespaces | |
Scale_space_reconstruction_3 | |
Shape_detection_3 | |
Surface_mesh_parameterization | |
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... | |