CGAL 5.5.1 - 3D Spherical Geometry Kernel
AlgebraicKernelForSpheres Concept Reference

## Definition

The AlgebraicKernelForSpheres concept is meant to provide the curved kernel with all the algebraic functionalities required for the manipulation of spheres, circles, and circular arcs in 3D.

Has Models:
CGAL::Algebraic_kernel_for_spheres_2_3
SphericalKernel
CGAL::Spherical_kernel_3<Kernel,AlgebraicKernelForSpheres>

## Concepts

conceptCompareX

conceptCompareXY

conceptCompareXYZ

conceptCompareY

conceptCompareZ

conceptConstructPolynomial_1_3

conceptConstructPolynomialForSpheres_2_3

conceptConstructPolynomialsForLines_3

conceptPolynomial_1_3
Concept to represent trivariate polynomials of degree 1 whose coefficients are of a type that is a model of the concept RingNumberType. More...

conceptPolynomialForSpheres_2_3
Concept to represent trivariate polynomials of degree up to 2 capable of storing equations of spheres, whose center's coordinates, as well as the square of the radius, are of a type that is a model of the concept FieldNumberType. More...

conceptPolynomialsForCircles_3
Concept to represent a system of polynomials on FieldNumberType capable of storing equations of circles. More...

conceptPolynomialsForLines_3
Concept to represent a system of polynomials on FieldNumberType capable of storing equations of lines. More...

conceptRootForSpheres_2_3
Concept to represent the roots of a system of three equations of degree 2 in three variables x, y and z that are models of concept AlgebraicKernelForSpheres::PolynomialForSpheres_2_3. More...

conceptSignAt

conceptSolve

conceptXCriticalPoints

conceptYCriticalPoints

conceptZCriticalPoints

## Types

A model of AlgebraicKernelForSpheres is supposed to provide

typedef unspecified_type RT
A model of RingNumberType.

typedef unspecified_type FT
A model of FieldNumberType<RT>.

typedef unspecified_type Polynomial_1_3
A model of AlgebraicKernelForSpheres::Polynomial_1_3, for trivariate polynomials of degree up to 1.

typedef unspecified_type Polynomial_for_spheres_2_3
A model of AlgebraicKernelForSpheres::PolynomialForSpheres_2_3, for trivariate polynomials of degree up to 2 that can store equations of spheres.

typedef unspecified_type Polynomials_for_lines_3
A model of AlgebraicKernelForSpheres::PolynomialsForLines_3, for systems of polynomials that can store equations of lines in 3D.

typedef unspecified_type Root_of_2
A model of RootOf_2, for algebraic numbers of degree up to 2.

typedef unspecified_type Root_for_spheres_2_3
A model of AlgebraicKernelForSpheres::RootForSpheres_2_3, for solutions of systems of three models of AlgebraicKernelForSpheres::PolynomialForSpheres_2_3.

typedef unspecified_type Construct_polynomial_1_3
A model of AlgebraicKernelForSpheres::ConstructPolynomial_1_3.

typedef unspecified_type Construct_polynomial_for_spheres_2_3
A model of AlgebraicKernelForSpheres::ConstructPolynomialForSpheres_2_3.

typedef unspecified_type Construct_polynomials_for_lines_3
A model of AlgebraicKernelForSpheres::ConstructPolynomialsForLines_3.

typedef unspecified_type Compare_x
A model of the concept AlgebraicKernelForSpheres::CompareX.

typedef unspecified_type Compare_y
A model of the concept AlgebraicKernelForSpheres::CompareY.

typedef unspecified_type Compare_z
A model of the concept AlgebraicKernelForSpheres::CompareZ.

typedef unspecified_type Compare_xy
A model of the concept AlgebraicKernelForSpheres::CompareXY.

typedef unspecified_type Compare_xyz
A model of the concept AlgebraicKernelForSpheres::CompareXYZ.

typedef unspecified_type Sign_at
A model of the concept AlgebraicKernelForSpheres::SignAt.

typedef unspecified_type X_critical_points
A model of the concept AlgebraicKernelForSpheres::XCriticalPoints.

typedef unspecified_type Y_critical_points
A model of the concept AlgebraicKernelForSpheres::YCriticalPoints.

typedef unspecified_type Z_critical_points
A model of the concept AlgebraicKernelForSpheres::ZCriticalPoints.

typedef unspecified_type Solve
A model of the concept AlgebraicKernelForSpheres::Solve.