3D Spherical Geometry Kernel Reference

Pedro Machado Manhães de Castro, Frédéric Cazals, Sébastien Loriot, and Monique Teillaud

This package is an extension of the linear CGAL Kernel. It offers functionalities on spheres, circles, circular arcs and line segments, in the 3D space or restricted on a reference sphere.

Introduced in: CGAL 3.4
BibTeX: cgal:cclt-sgk3-17b
License: GPL

Classified Reference Pages

Geometric Concepts

• SphericalKernel

Object types

• SphericalKernel::CircularArc_3
• SphericalKernel::CircularArcPoint_3
• SphericalKernel::LineArc_3

Functors

• SphericalKernel::ConstructPlane_3
• SphericalKernel::ConstructSphere_3
• SphericalKernel::ConstructLine_3
• SphericalKernel::ConstructCircle_3
• SphericalKernel::ConstructCircularArcPoint_3
• SphericalKernel::ConstructLineArc_3
• SphericalKernel::ConstructCircularArc_3
• SphericalKernel::ConstructCircularMinVertex_3
• SphericalKernel::ConstructCircularMaxVertex_3
• SphericalKernel::ConstructCircularSourceVertex_3
• SphericalKernel::ConstructCircularTargetVertex_3
• SphericalKernel::ConstructBbox_3
• SphericalKernel::CompareX_3
• SphericalKernel::CompareY_3
• SphericalKernel::CompareZ_3
• SphericalKernel::CompareXY_3
• SphericalKernel::CompareXYZ_3
• SphericalKernel::CompareTheta_3
• SphericalKernel::CompareThetaZ_3
• SphericalKernel::CompareZAtTheta_3
• SphericalKernel::CompareZToRight_3
• SphericalKernel::Equal_3
• SphericalKernel::HasOn_3
• SphericalKernel::DoOverlap_3
• SphericalKernel::DoIntersect_3
• SphericalKernel::IsThetaMonotone_3
• SphericalKernel::BoundedSide_3
• SphericalKernel::HasOnBoundedSide_3
• SphericalKernel::HasOnUnboundedSide_3
• SphericalKernel::Intersect_3
• SphericalKernel::Split_3
• SphericalKernel::MakeThetaMonotone_3
• SphericalKernel::ComputeCircularX_3
• SphericalKernel::ComputeCircularY_3
• SphericalKernel::ComputeCircularZ_3
• SphericalKernel::ComputeApproximateSquaredLength_3
• SphericalKernel::ComputeApproximateAngle_3
• SphericalKernel::GetEquation

Geometric Kernels and Classes

Kernels

• CGAL::Spherical_kernel_3<Kernel,AlgebraicKernelForSpheres>
• CGAL::Exact_spherical_kernel_3

Points

• CGAL::Circular_arc_point_3<SphericalKernel>

Arcs

• CGAL::Line_arc_3<SphericalKernel>
• CGAL::Circular_arc_3<SphericalKernel>

Constants and Enumerations

• CGAL::Circle_type

Geometric Global Functions

• CGAL::compare_x()
• CGAL::compare_y()
• CGAL::compare_z()
• CGAL::compare_xy()
• CGAL::compare_xyz()
• CGAL::compare_theta()
• CGAL::compare_theta_z()
• CGAL::is_theta_monotone()
• CGAL::classify()
• CGAL::x_extremal_point()
• CGAL::y_extremal_point()
• CGAL::z_extremal_point()
• CGAL::theta_extremal_point()
• CGAL::x_extremal_points()
• CGAL::y_extremal_points()
• CGAL::z_extremal_points()
• CGAL::theta_extremal_points()
• CGAL::do_intersect()
• CGAL::intersection()

Algebraic Concepts

• AlgebraicKernelForSpheres

Functors

• AlgebraicKernelForSpheres::ConstructPolynomial_1_3
• AlgebraicKernelForSpheres::ConstructPolynomialForSpheres_2_3
• AlgebraicKernelForSpheres::ConstructPolynomialsForLines_3
• AlgebraicKernelForSpheres::CompareX
• AlgebraicKernelForSpheres::CompareY
• AlgebraicKernelForSpheres::CompareZ
• AlgebraicKernelForSpheres::CompareXY
• AlgebraicKernelForSpheres::CompareXYZ
• AlgebraicKernelForSpheres::SignAt
• AlgebraicKernelForSpheres::XCriticalPoints
• AlgebraicKernelForSpheres::YCriticalPoints
• AlgebraicKernelForSpheres::ZCriticalPoints
• AlgebraicKernelForSpheres::Solve

Algebraic Kernel and Classes

Kernel

• CGAL::Algebraic_kernel_for_spheres_2_3<RT>

Polynomials

• CGAL::Polynomial_1_3<RT>
• CGAL::Polynomial_for_spheres_2_3<FT>
• CGAL::Polynomials_for_lines_3<FT>

Roots of Polynomials

• CGAL::Sqrt_extension<NT,ROOT>
• CGAL::Root_for_spheres_2_3<RT>
• CGAL::Root_of_traits<RT>

Modules
	Algebraic Concepts
	Algebraic Kernel and Classes
	Geometric Concepts
	Geometric Global Functions
	Geometric Kernel and Classes