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

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.
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.