\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.12.1 - 2D Circular Geometry Kernel
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AlgebraicKernelForCircles Concept Reference
2D Circular Geometry Kernel Reference » Algebraic Concepts

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
See also
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.