SphericalKernel Concept Reference

Definition

Refines

Kernel

Has Models:

CGAL::Spherical_kernel_3<Kernel,AlgebraicKernelForSpheres>

CGAL::Exact_spherical_kernel_3

See also

Kernel

Concepts
concept	BoundedSide_3
concept	CircularArc_3
	Concept for arcs of circles. More...
concept	CircularArcPoint_3
	Concept for points on spheres, circles, circular arcs or line arcs. More...
concept	CompareTheta_3
concept	CompareThetaZ_3
concept	CompareX_3
concept	CompareXY_3
concept	CompareXYZ_3
concept	CompareY_3
concept	CompareZ_3
concept	CompareZAtTheta_3
concept	CompareZToRight_3
concept	ComputeApproximateAngle_3
concept	ComputeApproximateSquaredLength_3
concept	ComputeCircularX_3
concept	ComputeCircularY_3
concept	ComputeCircularZ_3
concept	ConstructBbox_3
concept	ConstructCircle_3
concept	ConstructCircularArc_3
	The circular arc constructed from a circle, a source, and a target, is defined as the set of points of the circle that lie between the source p1 and the target p2, when traversing the circle counterclockwise seen from the side of the plane of the circle pointed by its positive normal vectors. More...
concept	ConstructCircularArcPoint_3
concept	ConstructCircularMaxVertex_3
concept	ConstructCircularMinVertex_3
concept	ConstructCircularSourceVertex_3
concept	ConstructCircularTargetVertex_3
concept	ConstructLine_3
concept	ConstructLineArc_3
concept	ConstructPlane_3
concept	ConstructSphere_3
concept	DoIntersect_3
	Testing whether two curves or surfaces intersect. More...
concept	DoOverlap_3
concept	Equal_3
	Testing equality between objects. More...
concept	GetEquation
concept	HasOn_3
concept	HasOnBoundedSide_3
concept	HasOnUnboundedSide_3
concept	Intersect_3
concept	IsThetaMonotone_3
concept	LineArc_3
	Concept for line segments supported by a line that is a model of Kernel::Line_3, and whose endpoints are models of the SphericalKernel::CircularArcPoint_3 concept. More...
concept	MakeThetaMonotone_3
concept	Split_3

Types
A model of SphericalKernel must provide some basic types
typedef unspecified_type	Linear_kernel
	Model of Kernel.
typedef unspecified_type	Algebraic_kernel
	Model of AlgebraicKernelForSpheres.
typedef unspecified_type	Root_of_2
	Model of RootOf_2.
typedef unspecified_type	Root_for_spheres_2_3
	Model of AlgebraicKernelForSpheres::RootForSpheres_2_3.
typedef unspecified_type	Polynomial_1_3
	Model of AlgebraicKernelForSpheres::Polynomial_1_3.
typedef unspecified_type	Polynomials_for_line_3
	Model of AlgebraicKernelForSpheres::PolynomialsForLines_3.
typedef unspecified_type	Polynomial_for_spheres_2_3
	Model of AlgebraicKernelForSpheres::PolynomialForSpheres_2_3.
typedef unspecified_type	Polynomials_for_circle_3
	Model of AlgebraicKernelForSpheres::PolynomialsForCircles_3.
and to define the following geometric objects
typedef unspecified_type	Point_3
	Model of Kernel::Point_3.
typedef unspecified_type	Vector_3
	Model of Kernel::Vector_3.
typedef unspecified_type	Line_3
	Model of Kernel::Line_3.
typedef unspecified_type	Plane_3
	Model of Kernel::Plane_3.
typedef unspecified_type	Sphere_3
	Model of Kernel::Sphere_3.
typedef unspecified_type	Circle_3
	Model of Kernel::Circle_3.
typedef unspecified_type	Line_arc_3
	Model of SphericalKernel::LineArc_3.
typedef unspecified_type	Circular_arc_3
	Model of SphericalKernel::CircularArc_3.
typedef unspecified_type	Circular_arc_point_3
	Model of SphericalKernel::CircularArcPoint_3.

Predicates
Moreover, a model of SphericalKernel must provide predicates, constructions and other functionalities.
typedef unspecified_type	Compare_x_3
	Model of SphericalKernel::CompareX_3.
typedef unspecified_type	Compare_y_3
	Model of SphericalKernel::CompareY_3.
typedef unspecified_type	Compare_z_3
	Model of SphericalKernel::CompareZ_3.
typedef unspecified_type	Compare_xy_3
	Model of SphericalKernel::CompareXY_3.
typedef unspecified_type	Compare_xyz_3
	Model of SphericalKernel::CompareXYZ_3.
typedef unspecified_type	Compare_theta_3
	Model of SphericalKernel::CompareTheta_3.
typedef unspecified_type	Compare_theta_z_3
	Model of SphericalKernel::CompareThetaZ_3.
typedef unspecified_type	Compare_z_at_theta_3
	Model of SphericalKernel::CompareZAtTheta_3.
typedef unspecified_type	Compare_z_to_right_3
	Model of SphericalKernel::CompareZToRight_3.
typedef unspecified_type	Equal_3
	Model of SphericalKernel::Equal_3.
typedef unspecified_type	Has_on_3
	Model of SphericalKernel::HasOn_3.
typedef unspecified_type	Do_overlap_3
	Model of SphericalKernel::DoOverlap_3.
typedef unspecified_type	Do_intersect_3
	Model of SphericalKernel::DoIntersect_3.
typedef unspecified_type	Bounded_side_3
	Model of SphericalKernel::BoundedSide_3.
typedef unspecified_type	Has_on_bounded_side_3
	Model of SphericalKernel::HasOnBoundedSide_3.
typedef unspecified_type	Has_on_unbounded_side_3
	Model of SphericalKernel::HasOnUnboundedSide_3.
typedef unspecified_type	Is_theta_monotone_3
	Model of SphericalKernel::IsThetaMonotone_3.

Constructions
typedef unspecified_type	Construct_line_3
	Model of SphericalKernel::ConstructLine_3.
typedef unspecified_type	Construct_plane_3
	Model of SphericalKernel::ConstructPlane_3.
typedef unspecified_type	Construct_sphere_3
	Model of SphericalKernel::ConstructSphere_3.
typedef unspecified_type	Construct_circle_3
	Model of SphericalKernel::ConstructCircle_3.
typedef unspecified_type	Construct_line_arc_3
	Model of SphericalKernel::ConstructLineArc_3.
typedef unspecified_type	Construct_circular_arc_3
	Model of SphericalKernel::ConstructCircularArc_3.
typedef unspecified_type	Construct_circular_arc_point_3
	Model of SphericalKernel::ConstructCircularArcPoint_3.
typedef unspecified_type	Construct_circular_min_vertex_3
	Model of SphericalKernel::ConstructCircularMinVertex_3.
typedef unspecified_type	Construct_circular_max_vertex_3
	Model of SphericalKernel::ConstructCircularMaxVertex_3.
typedef unspecified_type	Construct_circular_source_vertex_3
	Model of SphericalKernel::ConstructCircularSourceVertex_3.
typedef unspecified_type	Construct_circular_target_vertex_3
	Model of SphericalKernel::ConstructCircularTargetVertex_3.
typedef unspecified_type	Construct_bbox_3
	Model of SphericalKernel::ConstructBbox_3.
typedef unspecified_type	Intersect_3
	Model of SphericalKernel::Intersect_3.
typedef unspecified_type	Split_3
	Model of SphericalKernel::Split_3.
typedef unspecified_type	Make_theta_monotone_3
	Model of SphericalKernel::MakeThetaMonotone_3.

Computations
typedef unspecified_type	Compute_circular_x_3
	Model of SphericalKernel::ComputeCircularX_3.
typedef unspecified_type	Compute_circular_y_3
	Model of SphericalKernel::ComputeCircularY_3.
typedef unspecified_type	Compute_circular_z_3
	Model of SphericalKernel::ComputeCircularZ_3.
typedef unspecified_type	Compute_approximate_squared_length_3
	Model of SphericalKernel::ComputeApproximateSquaredLength_3.
typedef unspecified_type	Compute_approximate_angle_3
	Model of SphericalKernel::ComputeApproximateAngle_3.

Link with the algebraic kernel
typedef unspecified_type	Get_equation
	Model of SphericalKernel::GetEquation.

Operations
As in the Kernel concept, for each of the function objects above, there must exist a member function that requires no arguments and returns an instance of that function object. The name of the member function is the uncapitalized name of the type returned with the suffix _object appended. For example, for the function object SphericalKernel::Construct_circular_arc_3 the following member function must exist:
Construct_circular_arc_3	construct_circular_arc_3_object () const

Operations on a given sphere,
A context sphere must be provided to the following functions:
Compare_theta_3	compare_theta_3_object (const Sphere_3 &sphere) const
Compare_theta_z_3	compare_theta_z_3_object (const Sphere_3 &sphere) const
Compare_z_at_theta_3	compare_z_at_theta_3_object (const Sphere_3 &sphere) const
Compare_z_to_right_3	compare_z_to_right_3_object (const Sphere_3 &sphere) const
Make_theta_monotone_3	make_theta_monotone_3_object (const Sphere_3 &sphere) const
Is_theta_monotone_3	is_theta_monotone_3_object (const Sphere_3 &sphere) const