CGAL 4.7 - 3D Spherical Geometry Kernel: CGAL::Spherical_kernel_3< Kernel, AlgebraicKernelForSpheres > Class Template Reference

\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.7 - 3D Spherical Geometry Kernel

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CGAL::Spherical_kernel_3< Kernel, AlgebraicKernelForSpheres > Class Template Reference
Geometric Kernel and Classes

`#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 | 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_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_max_vertex_2
typedef unspecified_type | Construct_midpoint_2
typedef unspecified_type | Construct_equidistant_line_3
typedef unspecified_type | Construct_min_vertex_2
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_bisector_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_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_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_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_square_distance_2
typedef unspecified_type | Compare_angle_with_x_axis_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 | 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 | 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_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_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_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_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_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 | 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_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_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 | 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 | 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