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
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.

Definition

Concepts

Types

Definition

Concepts

Types