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

CGAL 4.8 - 3D Spherical Geometry Kernel

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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-sgk3-16a
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