#include <Concepts/AlgebraicKernelForSpheres.h>

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>

Classes
class	CompareX

class	CompareXY

class	CompareXYZ

class	CompareY

class	CompareZ

class	ConstructPolynomial_1_3

class	ConstructPolynomialForSpheres_2_3

class	ConstructPolynomialsForLines_3

class	Polynomial_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...

class	PolynomialForSpheres_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...

class	PolynomialsForCircles_3
	Concept to represent a system of polynomials on `FieldNumberType` capable of storing equations of circles. More...

class	PolynomialsForLines_3
	Concept to represent a system of polynomials on `FieldNumberType` capable of storing equations of lines. More...

class	RootForSpheres_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...

class	SignAt

class	Solve

class	XCriticalPoints

class	YCriticalPoints

class	ZCriticalPoints

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`.