CGAL 5.1 - 2D Circular Geometry Kernel
AlgebraicKernelForCircles Concept Reference

Definition

The AlgebraicKernelForCircles concept is meant to provide the curved kernel with all the algebraic functionalities required for the manipulation of circular arcs.

Has Models:
CGAL::Algebraic_kernel_for_circles_2_2
CircularKernel
CGAL::Circular_kernel_2<Kernel,AlgebraicKernelForCircles>

Concepts

conceptCompareX

conceptCompareXY

conceptCompareY

conceptConstructPolynomial_1_2

conceptConstructPolynomialForCircles_2_2

conceptPolynomial_1_2
Concept to represent bivariate polynomials of degree 1 whose coefficients are of a type that is a model of the concept RingNumberType. More...

conceptPolynomialForCircles_2_2
Concept to represent bivariate polynomials of degree up to 2 capable of storing equations of circles, 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...

conceptRootForCircles_2_2
Concept to represent the roots of a system of two equations of degree 2 in two variables x and y that are models of concept AlgebraicKernelForCircles::PolynomialForCircles_2_2 More...

conceptSignAt

conceptSolve

conceptXCriticalPoints

conceptYCriticalPoints

Types

A model of AlgebraicKernelForCircles 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_2
A model of AlgebraicKernelForCircles::Polynomial_1_2, for bivariate polynomials of degree up to 1.

typedef unspecified_type Polynomial_for_circles_2_2
A model of AlgebraicKernelForCircles::PolynomialForCircles_2_2, for bivariate polynomials of degree up to 2 that can store equations of circles.

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

typedef unspecified_type Root_for_circles_2_2
A model of AlgebraicKernelForCircles::RootForCircles_2_2, for solutions of systems of two models of AlgebraicKernelForCircles::PolynomialForCircles_2_2.

typedef unspecified_type Construct_polynomial_1_2
A model of AlgebraicKernelForCircles::ConstructPolynomial_1_2.

typedef unspecified_type Construct_polynomial_for_circles_2_2
A model of AlgebraicKernelForCircles::ConstructPolynomialForCircles_2_2.

typedef unspecified_type Compare_x
A model of the concept AlgebraicKernelForCircles::CompareX.

typedef unspecified_type Compare_y
A model of the concept AlgebraicKernelForCircles::CompareY.

typedef unspecified_type Compare_xy
A model of the concept AlgebraicKernelForCircles::CompareXY.

typedef unspecified_type Sign_at
A model of the concept AlgebraicKernelForCircles::SignAt.

typedef unspecified_type X_critical_points
A model of the concept AlgebraicKernelForCircles::XCriticalPoints.

typedef unspecified_type Y_critical_points
A model of the concept AlgebraicKernelForCircles::YCriticalPoints.

typedef unspecified_type Solve
A model of the concept AlgebraicKernelForCircles::Solve.