\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.3 - 3D Spherical Geometry Kernel
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AlgebraicKernelForSpheres Concept Reference
Algebraic Concepts

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
See Also
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.