Definition

template<typename Kernel, typename AlgebraicKernelForSpheres>
struct CGAL::Spherical_kernel_3< Kernel, AlgebraicKernelForSpheres >

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. More...

typedef AlgebraicKernelForSpheres::FT	FT
	Field number type. More...

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	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