CGAL::Spherical_kernel_3< Kernel, AlgebraicKernelForSpheres > Struct Template Reference

#include <CGAL/Spherical_kernel_3.h>

Inherits from

Kernel.

Definition

Is Model Of:

SphericalKernel

Parameters

The first parameter of the spherical kernel must be instantiated with a model of the Kernel concept. The Spherical_kernel_3 class template derives from this first parameter, in order to reuse all needed functionalities on basic objects provided by a model of the Kernel concept.

The second parameter, AlgebraicKernelForSpheres, is meant to provide the spherical kernel with all the algebraic functionalities required for the manipulation of algebraic curves.

See also

Kernel

AlgebraicKernelForSpheres

CGAL::Exact_spherical_kernel_3

Types
The spherical kernel uses basic number types of the algebraic kernel: In fact, the two number types AlgebraicKernelForSpheres::RT and Kernel::RT must refer to the same type, as well as AlgebraicKernelForSpheres::FT and Kernel::FT.
typedef AlgebraicKernelForSpheres::RT	RT
	Ring number type.
typedef AlgebraicKernelForSpheres::FT	FT
	Field number type.
The following types are available, as well as all the functionality on them described in the SphericalKernel concept. Polynomials_for_circle_3 is implemented as a std::pair< Polynomial_for_spheres_2_3, Polynomial_1_3 > and is a model of AlgebraicKernelForSpheres::PolynomialsForCircles_3.
typedef Line_arc_3< Spherical_kernel_3 >	Line_arc_3
typedef Circular_arc_3< Spherical_kernel_3 >	Circular_arc_3
typedef Circular_arc_point_3< Spherical_kernel_3 >	Circular_arc_point_3

Additional Inherited Members
Public Types inherited from Kernel
typedef unspecified_type	FT
typedef unspecified_type	RT
typedef unspecified_type	Boolean
typedef unspecified_type	Sign
typedef unspecified_type	Comparison_result
typedef unspecified_type	Orientation
typedef unspecified_type	Oriented_side
typedef unspecified_type	Bounded_side
typedef unspecified_type	Angle
typedef unspecified_type	Cartesian_const_iterator_2
typedef unspecified_type	Point_2
typedef unspecified_type	Weighted_point_2
typedef unspecified_type	Vector_2
typedef unspecified_type	Direction_2
typedef unspecified_type	Line_2
typedef unspecified_type	Ray_2
typedef unspecified_type	Segment_2
typedef unspecified_type	Triangle_2
typedef unspecified_type	Iso_rectangle_2
typedef unspecified_type	Circle_2
typedef unspecified_type	Object_2
typedef unspecified_type	Construct_point_2
typedef unspecified_type	Construct_weighted_point_2
typedef unspecified_type	Construct_vector_2
typedef unspecified_type	Construct_direction_2
typedef unspecified_type	Construct_segment_2
typedef unspecified_type	Construct_line_2
typedef unspecified_type	Construct_ray_2
typedef unspecified_type	Construct_circle_2
typedef unspecified_type	Construct_triangle_2
typedef unspecified_type	Construct_iso_rectangle_2
typedef unspecified_type	Construct_object_2
typedef unspecified_type	Construct_scaled_vector_2
typedef unspecified_type	Construct_difference_of_vectors_2
typedef unspecified_type	Construct_sum_of_vectors_2
typedef unspecified_type	Construct_divided_vector_2
typedef unspecified_type	Construct_translated_point_2
typedef unspecified_type	Construct_point_on_2
typedef unspecified_type	Construct_projected_point_2
typedef unspecified_type	Construct_projected_xy_point_2
typedef unspecified_type	Construct_second_point_2
typedef unspecified_type	Construct_cartesian_const_iterator_2
typedef unspecified_type	Construct_vertex_2
typedef unspecified_type	Construct_bbox_2
typedef unspecified_type	Construct_perpendicular_vector_2
typedef unspecified_type	Construct_perpendicular_direction_2
typedef unspecified_type	Construct_perpendicular_line_2
typedef unspecified_type	Construct_midpoint_2
typedef unspecified_type	Construct_equidistant_line_3
typedef unspecified_type	Construct_center_2
typedef unspecified_type	Construct_centroid_2
typedef unspecified_type	Construct_barycenter_2
typedef unspecified_type	Construct_circumcenter_2
typedef unspecified_type	Construct_weighted_circumcenter_2
typedef unspecified_type	Construct_bisector_2
typedef unspecified_type	Construct_radical_axis_2
typedef unspecified_type	Construct_radical_line_2
typedef unspecified_type	Construct_opposite_direction_2
typedef unspecified_type	Construct_opposite_segment_2
typedef unspecified_type	Construct_opposite_ray_2
typedef unspecified_type	Construct_opposite_line_2
typedef unspecified_type	Construct_opposite_triangle_2
typedef unspecified_type	Construct_opposite_circle_2
typedef unspecified_type	Construct_opposite_vector_2
typedef unspecified_type	Construct_source_2
typedef unspecified_type	Construct_target_2
typedef unspecified_type	Construct_max_vertex_2
typedef unspecified_type	Construct_min_vertex_2
typedef unspecified_type	Intersect_2
typedef unspecified_type	Assign_2
typedef unspecified_type	Compute_weight_2
typedef unspecified_type	Compute_x_2
typedef unspecified_type	Compute_y_2
typedef unspecified_type	Compute_a_2
typedef unspecified_type	Compute_b_2
typedef unspecified_type	ComputeC_2
typedef unspecified_type	Compute_dx_2
typedef unspecified_type	Compute_dy_2
typedef unspecified_type	Compute_hx_2
typedef unspecified_type	Compute_hy_2
typedef unspecified_type	Compute_hw_2
typedef unspecified_type	Compute_L_infinity_distance_2
typedef unspecified_type	Compute_xmax_2
typedef unspecified_type	Compute_xmin_2
typedef unspecified_type	Compute_ymax_2
typedef unspecified_type	Compute_ymin_2
typedef unspecified_type	Compute_y_at_x_2
typedef unspecified_type	Compute_squared_distance_2
typedef unspecified_type	Compute_squared_length_2
typedef unspecified_type	Compute_squared_radius_2
typedef unspecified_type	Compute_squared_radius_smallest_orthogonal_circle_2
typedef unspecified_type	Compute_power_product_2
typedef unspecified_type	Compute_area_2
typedef unspecified_type	Compute_determinant_2
typedef unspecified_type	Compute_scalar_product_2
typedef unspecified_type	Angle_2
typedef unspecified_type	Equal_2
typedef unspecified_type	Equal_x_2
typedef unspecified_type	Equal_y_2
typedef unspecified_type	Less_x_2
typedef unspecified_type	Less_y_2
typedef unspecified_type	Less_xy_2
typedef unspecified_type	Less_yx_2
typedef unspecified_type	Compare_x_2
typedef unspecified_type	Compare_x_at_y_2
typedef unspecified_type	Compare_y_2
typedef unspecified_type	Compare_xy_2
typedef unspecified_type	Compare_yx_2
typedef unspecified_type	Compare_y_at_x_2
typedef unspecified_type	Compare_distance_2
typedef unspecified_type	Compare_power_distance_2
typedef unspecified_type	Compare_square_distance_2
typedef unspecified_type	Compare_angle_with_x_axis_2
typedef unspecified_type	Compare_signed_distance_to_line_2
typedef unspecified_type	Compare_slope_2
typedef unspecified_type	Less_distance_to_point_2
typedef unspecified_type	Less_signed_distance_to_line_2
typedef unspecified_type	Less_rotate_ccw_2
typedef unspecified_type	Left_turn_2
typedef unspecified_type	Collinear_2
typedef unspecified_type	Orientation_2
typedef unspecified_type	Side_of_oriented_circle_2
typedef unspecified_type	Side_of_bounded_circle_2
typedef unspecified_type	Power_side_of_oriented_power_circle_2
typedef unspecified_type	Power_side_of_bounded_power_circle_2
typedef unspecified_type	Is_horizontal_2
typedef unspecified_type	Is_vertical_2
typedef unspecified_type	Is_degenerate_2
typedef unspecified_type	Has_on_2
typedef unspecified_type	Collinear_has_on_2
typedef unspecified_type	Has_on_bounded_side_2
typedef unspecified_type	Has_on_unbounded_side_2
typedef unspecified_type	Has_on_boundary_2
typedef unspecified_type	Has_on_positive_side_2
typedef unspecified_type	Has_on_negative_side_2
typedef unspecified_type	Oriented_side_2
typedef unspecified_type	Bounded_side_2
typedef unspecified_type	Are_parallel_2
typedef unspecified_type	Are_ordered_along_line_2
typedef unspecified_type	Are_strictly_ordered_along_line_2
typedef unspecified_type	Collinear_are_ordered_along_line_2
typedef unspecified_type	Collinear_are_strictly_ordered_along_line_2
typedef unspecified_type	Counterclockwise_in_between_2
typedef unspecified_type	Do_intersect_2
typedef unspecified_type	Cartesian_const_iterator_3
typedef unspecified_type	Point_3
typedef unspecified_type	Weighted_point_3
typedef unspecified_type	Vector_3
typedef unspecified_type	Direction_3
typedef unspecified_type	Iso_cuboid_3
typedef unspecified_type	Line_3
typedef unspecified_type	Ray_3
typedef unspecified_type	Circle_3
typedef unspecified_type	Sphere_3
typedef unspecified_type	Segment_3
typedef unspecified_type	Plane_3
typedef unspecified_type	Triangle_3
typedef unspecified_type	Tetrahedron_3
typedef unspecified_type	Object_3
typedef unspecified_type	Construct_point_3
typedef unspecified_type	Construct_weighted_point_3
typedef unspecified_type	Construct_vector_3
typedef unspecified_type	Construct_direction_3
typedef unspecified_type	Construct_plane_3
typedef unspecified_type	Construct_iso_cuboid_3
typedef unspecified_type	Construct_line_3
typedef unspecified_type	Construct_ray_3
typedef unspecified_type	Construct_sphere_3
typedef unspecified_type	Construct_segment_3
typedef unspecified_type	Construct_triangle_3
typedef unspecified_type	Construct_tetrahedron_3
typedef unspecified_type	Construct_circle_3
typedef unspecified_type	Construct_object_3
typedef unspecified_type	Construct_scaled_vector_3
typedef unspecified_type	Construct_translated_point_3
typedef unspecified_type	Construct_point_on_3
typedef unspecified_type	Construct_projected_point_3
typedef unspecified_type	Construct_lifted_point_3
typedef unspecified_type	Construct_cartesian_const_iterator_3
typedef unspecified_type	Construct_vertex_3
typedef unspecified_type	Construct_source_3
typedef unspecified_type	Construct_target_3
typedef unspecified_type	Construct_max_vertex_3
typedef unspecified_type	Construct_min_vertex_3
typedef unspecified_type	Construct_bbox_3
typedef unspecified_type	Construct_supporting_plane_3
typedef unspecified_type	Construct_orthogonal_vector_3
typedef unspecified_type	Construct_base_vector_3
typedef unspecified_type	Construct_difference_of_vectors_3
typedef unspecified_type	Construct_sum_of_vectors_3
typedef unspecified_type	Construct_divided_vector_3
typedef unspecified_type	Construct_normal_3
typedef unspecified_type	Construct_perpendicular_plane_3
typedef unspecified_type	Construct_radical_plane_3
typedef unspecified_type	Construct_perpendicular_line_3
typedef unspecified_type	Construct_midpoint_3
typedef unspecified_type	Construct_center_3
typedef unspecified_type	Construct_centroid_3
typedef unspecified_type	Construct_circumcenter_3
typedef unspecified_type	Construct_weighted_circumcenter_3
typedef unspecified_type	Construct_bisector_3
typedef unspecified_type	Construct_cross_product_vector_3
typedef unspecified_type	Construct_barycenter_3
typedef unspecified_type	Construct_second_point_3
typedef unspecified_type	Construct_opposite_direction_3
typedef unspecified_type	Construct_opposite_segment_3
typedef unspecified_type	Construct_opposite_ray_3
typedef unspecified_type	Construct_opposite_line_3
typedef unspecified_type	Construct_opposite_plane_3
typedef unspecified_type	Construct_opposite_sphere_3
typedef unspecified_type	Construct_opposite_vector_3
typedef unspecified_type	Intersect_3
typedef unspecified_type	Assign_3
typedef unspecified_type	Compute_weight_3
typedef unspecified_type	Compute_x_3
typedef unspecified_type	Compute_y_3
typedef unspecified_type	Compute_z_3
typedef unspecified_type	Compute_a_3
typedef unspecified_type	Compute_b_3
typedef unspecified_type	Compute_c_3
typedef unspecified_type	Compute_d_3
typedef unspecified_type	Compute_hx_3
typedef unspecified_type	Compute_hy_3
typedef unspecified_type	Compute_hz_3
typedef unspecified_type	Compute_hw_3
typedef unspecified_type	Compute_L_infinity_distance_3
typedef unspecified_type	Compute_dx_3
typedef unspecified_type	Compute_dy_3
typedef unspecified_type	Compute_dz_3
typedef unspecified_type	Compute_xmax_3
typedef unspecified_type	Compute_xmin_3
typedef unspecified_type	Compute_ymax_3
typedef unspecified_type	Compute_ymin_3
typedef unspecified_type	Compute_zmax_3
typedef unspecified_type	Compute_zmin_3
typedef unspecified_type	Compute_area_3
typedef unspecified_type	Compute_squared_area_3
typedef unspecified_type	Compute_area_divided_by_pi_3
typedef unspecified_type	Compute_approximate_area_3
typedef unspecified_type	Compute_approximate_angle_3
typedef unspecified_type	Compute_approximate_dihedral_angle_3
typedef unspecified_type	Compute_determinant_3
typedef unspecified_type	Compute_scalar_product_3
typedef unspecified_type	Compute_squared_distance_3
typedef unspecified_type	Compute_squared_length_3
typedef unspecified_type	Compute_squared_length_divided_by_pi_square_3
typedef unspecified_type	Compute_approximate_squared_length_3
typedef unspecified_type	Compute_squared_radius_3
typedef unspecified_type	Compute_volume_3
typedef unspecified_type	Compute_power_product_3
typedef unspecified_type	Compute_power_distance_to_power_sphere_3
typedef unspecified_type	Compute_squared_radius_smallest_orthogonal_sphere_3
typedef unspecified_type	Angle_3
typedef unspecified_type	Equal_3
typedef unspecified_type	Equal_x_3
typedef unspecified_type	Equal_y_3
typedef unspecified_type	Equal_z_3
typedef unspecified_type	Equal_xy_3
typedef unspecified_type	Less_x_3
typedef unspecified_type	Less_y_3
typedef unspecified_type	Less_z_3
typedef unspecified_type	Less_xy_3
typedef unspecified_type	Less_xyz_3
typedef unspecified_type	Compare_weighted_squared_radius_3
typedef unspecified_type	Compare_x_3
typedef unspecified_type	Compare_y_3
typedef unspecified_type	Compare_z_3
typedef unspecified_type	Compare_xy_3
typedef unspecified_type	Compare_xyz_3
typedef unspecified_type	Compare_slope_3
typedef unspecified_type	Compare_squared_distance_3
typedef unspecified_type	Less_signed_distance_to_plane_3
typedef unspecified_type	Less_distance_to_point_3
typedef unspecified_type	Compare_dihedral_angle_3
typedef unspecified_type	Compare_distance_3
typedef unspecified_type	Compare_power_distance_3
typedef unspecified_type	Collinear_3
typedef unspecified_type	Coplanar_3
typedef unspecified_type	Orientation_3
typedef unspecified_type	Coplanar_orientation_3
typedef unspecified_type	Coplanar_side_of_bounded_circle_3
typedef unspecified_type	Side_of_oriented_sphere_3
typedef unspecified_type	Side_of_bounded_sphere_3
typedef unspecified_type	Power_side_of_oriented_power_sphere_3
typedef unspecified_type	Power_side_of_bounded_power_sphere_3
typedef unspecified_type	Is_degenerate_3
typedef unspecified_type	Has_on_3
typedef unspecified_type	Has_on_bounded_side_3
typedef unspecified_type	Has_on_unbounded_side_3
typedef unspecified_type	Has_on_boundary_3
typedef unspecified_type	Has_on_positive_side_3
typedef unspecified_type	Has_on_negative_side_3
typedef unspecified_type	Non_zero_coordinate_index_3
typedef unspecified_type	Oriented_side_3
typedef unspecified_type	Bounded_side_3
typedef unspecified_type	Are_parallel_3
typedef unspecified_type	Are_ordered_along_line_3
typedef unspecified_type	Are_strictly_ordered_along_line_3
typedef unspecified_type	Collinear_are_ordered_along_line_3
typedef unspecified_type	Collinear_are_strictly_ordered_along_line_3
typedef unspecified_type	Do_intersect_3
Public Member Functions inherited from Kernel
Kernel::Construct_vector_2	construct_vector_2_object () const
Static Public Attributes inherited from Kernel
static const bool	Has_filtered_predicates