\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Circular Geometry Kernel

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2D Circular Geometry Kernel Reference

##

Pedro Machado Manhães de Castro, Sylvain Pion, and Monique Teillaud
This package is an extension of the linear CGAL kernel. It offers functionalities on circles, circular arcs and line segments in the plane.

Introduced in: CGAL 3.2
BibTeX: cgal:cpt-cgk2-16a
License: GPL
Windows Demo: Arrangement of Circular Arcs
Common Demo Dlls: dlls

## Classified Reference Pages

## Geometric Concepts

- `CircularKernel`

### Functors

- `CircularKernel::ConstructLine_2`
- `CircularKernel::ConstructCircle_2`
- `CircularKernel::ConstructCircularArcPoint_2`
- `CircularKernel::ConstructLineArc_2`
- `CircularKernel::ConstructCircularArc_2`
- `CircularKernel::ComputeCircularX_2`
- `CircularKernel::ComputeCircularY_2`
- `CircularKernel::ConstructCircularMinVertex_2`
- `CircularKernel::ConstructCircularMaxVertex_2`
- `CircularKernel::ConstructCircularSourceVertex_2`
- `CircularKernel::ConstructCircularTargetVertex_2`
- `CircularKernel::ConstructBbox_2`
- `CircularKernel::CompareX_2`
- `CircularKernel::CompareY_2`
- `CircularKernel::CompareXY_2`
- `CircularKernel::Equal_2`
- `CircularKernel::CompareYatX_2`
- `CircularKernel::CompareYtoRight_2`
- `CircularKernel::HasOn_2`
- `CircularKernel::DoOverlap_2`
- `CircularKernel::DoIntersect_2`
- `CircularKernel::BoundedSide_2`
- `CircularKernel::HasOnBoundedSide_2`
- `CircularKernel::HasOnUnboundedSide_2`
- `CircularKernel::InXRange_2`
- `CircularKernel::IsVertical_2`
- `CircularKernel::IsXMonotone_2`
- `CircularKernel::IsYMonotone_2`
- `CircularKernel::MakeXMonotone_2`
- `CircularKernel::MakeXYMonotone_2`
- `CircularKernel::Intersect_2`
- `CircularKernel::Split_2`
- `CircularKernel::GetEquation`

## Geometric Kernels and Classes

### Kernels

- `CGAL::Circular_kernel_2<Kernel,AlgebraicKernelForCircles>`
- `CGAL::Exact_circular_kernel_2`

### Points

- `CGAL::Circular_arc_point_2<CircularKernel>`

### Arcs

- `CGAL::Circular_arc_2<CircularKernel>`
- `CGAL::Line_arc_2<CircularKernel>`

## Geometric Global Functions

- `CGAL::compare_x()`
- `CGAL::compare_y()`
- `CGAL::compare_xy()`
- `CGAL::compare_y_at_x()`
- `CGAL::compare_y_to_right()`
- `CGAL::has_in_x_range()`
- `CGAL::has_on()`
- `CGAL::do_intersect()`
- `CGAL::intersection()`
- `CGAL::x_extremal_point()`
- `CGAL::y_extremal_point()`
- `CGAL::x_extremal_points()`
- `CGAL::y_extremal_points()`
- `CGAL::make_x_monotone()`
- `CGAL::make_xy_monotone()`

## Algebraic Concepts

- `AlgebraicKernelForCircles`

### Functors

- `AlgebraicKernelForCircles::ConstructPolynomial_1_2`
- `AlgebraicKernelForCircles::ConstructPolynomialForCircles_2_2`
- `AlgebraicKernelForCircles::CompareX`
- `AlgebraicKernelForCircles::CompareY`
- `AlgebraicKernelForCircles::CompareXY`
- `AlgebraicKernelForCircles::SignAt`
- `AlgebraicKernelForCircles::XCriticalPoints`
- `AlgebraicKernelForCircles::YCriticalPoints`
- `AlgebraicKernelForCircles::Solve`

## Algebraic Kernel and Classes

### Kernel

- `CGAL::Algebraic_kernel_for_circles_2_2<RT>`

### Polynomials

- `CGAL::Polynomial_1_2<RT>`
- `CGAL::Polynomial_for_circles_2_2<FT>`

### Roots of Polynomials

- `CGAL::Sqrt_extension<NT,ROOT>`
- `CGAL::Root_for_circles_2_2<FT>`
- `CGAL::Root_of_traits<RT>`

## Modules
| Algebraic Concepts
| Algebraic Kernel and Classes
| Geometric Concepts
| Geometric Global Functions
| Geometric Kernel and Classes