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
concept	CompareX

concept	CompareXY

concept	CompareXYZ

concept	CompareY

concept	CompareZ

concept	ConstructPolynomial_1_3

concept	ConstructPolynomialForSpheres_2_3

concept	ConstructPolynomialsForLines_3

concept	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...

concept	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...

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

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

concept	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...

concept	SignAt

concept	Solve

concept	XCriticalPoints

concept	YCriticalPoints

concept	ZCriticalPoints

Types
A model of `AlgebraicKernelForSpheres` is supposed to provide
typedef unspecified_type	RT
	A model of `RingNumberType`. More...

typedef unspecified_type	FT
	A model of `FieldNumberType<RT>`. More...

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

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. More...

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. More...

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

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`. More...

typedef unspecified_type	Construct_polynomial_1_3
	A model of `AlgebraicKernelForSpheres::ConstructPolynomial_1_3`. More...

typedef unspecified_type	Construct_polynomial_for_spheres_2_3
	A model of `AlgebraicKernelForSpheres::ConstructPolynomialForSpheres_2_3`. More...

typedef unspecified_type	Construct_polynomials_for_lines_3
	A model of `AlgebraicKernelForSpheres::ConstructPolynomialsForLines_3`. More...

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

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

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

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

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

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

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

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

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

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