CircularKernel Concept Reference

Definition

Refines

Kernel

Has models

CGAL::Circular_kernel_2<Kernel,AlgebraicKernelForCircles>

CGAL::Exact_circular_kernel_2

See also

Kernel

Concepts
concept	BoundedSide_2
concept	CircularArc_2
	Concept for arcs of circles. More...
concept	CircularArcPoint_2
	Concept for points on circles, circular arcs or line arcs. More...
concept	CompareX_2
concept	CompareXY_2
concept	CompareY_2
concept	CompareYatX_2
	A function object concept to compare a point p and an arc a on the vertical line passing through p. More...
concept	CompareYtoRight_2
	A function object concept to compare vertically two arcs on the right side of a common point p: More...
concept	ComputeCircularX_2
concept	ComputeCircularY_2
concept	ConstructBbox_2
	A function object concept to construct a bounding box of geometric objects: More...
concept	ConstructCircle_2
concept	ConstructCircularArc_2
concept	ConstructCircularArcPoint_2
concept	ConstructCircularMaxVertex_2
concept	ConstructCircularMinVertex_2
concept	ConstructCircularSourceVertex_2
concept	ConstructCircularTargetVertex_2
concept	ConstructLine_2
concept	ConstructLineArc_2
concept	DoIntersect_2
	Testing whether two curves intersect. More...
concept	DoOverlap_2
	Testing whether the interiors of two curves overlap. More...
concept	Equal_2
	Testing equality between objects. More...
concept	GetEquation
concept	HasOn_2
	To test whether a point lies on a curve. More...
concept	HasOnBoundedSide_2
concept	HasOnUnboundedSide_2
concept	Intersect_2
concept	InXRange_2
	To test whether a point lies in the vertical range of a curve. More...
concept	IsVertical_2
concept	IsXMonotone_2
concept	IsYMonotone_2
concept	LineArc_2
	Concept for line segments supported by a line that is a model of Kernel::Line_2 and whose endpoints are models of the CircularKernel::CircularArcPoint_2 concept. More...
concept	MakeXMonotone_2
concept	MakeXYMonotone_2
concept	Split_2

Types
A model of CircularKernel is supposed to provide some basic types and to define the following geometric objects Moreover, a model of CircularKernel must provide predicates, constructions and other functionalities.
typedef unspecified_type	Linear_kernel
	Model of LinearKernel.
typedef unspecified_type	Algebraic_kernel
	Model of AlgebraicKernelForCircles.
typedef unspecified_type	RT
	Model of RingNumberType.
typedef unspecified_type	FT
	Model of FieldNumberType.
typedef unspecified_type	Root_of_2
	Model of RootOf_2.
typedef unspecified_type	Root_for_circles_2_2
	Model of AlgebraicKernelForCircles::RootForCircles_2_2.
typedef unspecified_type	Polynomial_1_2
	Model of AlgebraicKernelForCircles::Polynomial_1_2.
typedef unspecified_type	Polynomial_for_circles_2_2
	Model of AlgebraicKernelForCircles::PolynomialForCircles_2_2.
typedef unspecified_type	Point_2
	Model of Kernel::Point_2.
typedef unspecified_type	Line_2
	Model of Kernel::Line_2.
typedef unspecified_type	Circle_2
	Model of Kernel::Circle_2.
typedef unspecified_type	Line_arc_2
	Model of CircularKernel::LineArc_2.
typedef unspecified_type	Circular_arc_2
	Model of CircularKernel::CircularArc_2.
typedef unspecified_type	Circular_arc_point_2
	Model of CircularKernel::CircularArcPoint_2.

Predicates
typedef unspecified_type	Compare_x_2
	Model of CircularKernel::CompareX_2.
typedef unspecified_type	Compare_y_2
	Model of CircularKernel::CompareY_2.
typedef unspecified_type	Compare_xy_2
	Model of CircularKernel::CompareXY_2.
typedef unspecified_type	Equal_2
	Model of CircularKernel::Equal_2.
typedef unspecified_type	Compare_y_at_x_2
	Model of CircularKernel::CompareYatX_2.
typedef unspecified_type	Compare_y_to_right_2
	Model of CircularKernel::CompareYtoRight_2.
typedef unspecified_type	Has_on_2
	Model of CircularKernel::HasOn_2.
typedef unspecified_type	Do_overlap_2
	Model of CircularKernel::DoOverlap_2.
typedef unspecified_type	Do_intersect_2
	Model of CircularKernel::DoIntersect_2.
typedef unspecified_type	Bounded_side_2
	Model of CircularKernel::BoundedSide_2.
typedef unspecified_type	Has_on_bounded_side_2
	Model of CircularKernel::HasOnBoundedSide_2.
typedef unspecified_type	Has_on_unbounded_side_2
	Model of CircularKernel::HasOnUnboundedSide_2.
typedef unspecified_type	In_x_range_2
	Model of CircularKernel::InXRange_2.
typedef unspecified_type	Is_vertical_2
	Model of CircularKernel::IsVertical_2.
typedef unspecified_type	Is_x_monotone_2
	Model of CircularKernel::IsXMonotone_2.
typedef unspecified_type	Is_y_monotone_2
	Model of CircularKernel::IsYMonotone_2.

Constructions
typedef unspecified_type	Construct_line_2
	Model of CircularKernel::ConstructLine_2.
typedef unspecified_type	Construct_circle_2
	Model of CircularKernel::ConstructCircle_2.
typedef unspecified_type	Construct_bbox_2
	Model of CircularKernel::ConstructBbox_2.
typedef unspecified_type	Construct_circular_arc_point_2
	Model of CircularKernel::ConstructCircularArcPoint_2.
typedef unspecified_type	Construct_line_arc_2
	Model of CircularKernel::ConstructLineArc_2.
typedef unspecified_type	Construct_circular_arc_2
	Model of CircularKernel::ConstructCircularArc_2.
typedef unspecified_type	Compute_circular_x_2
	Model of CircularKernel::ComputeCircularX_2
typedef unspecified_type	Compute_circular_y_2
	Model of CircularKernel::ComputeCircularY_2
typedef unspecified_type	Construct_circular_min_vertex_2
	Model of CircularKernel::ConstructCircularMinVertex_2.
typedef unspecified_type	Construct_circular_max_vertex_2
	Model of CircularKernel::ConstructCircularMaxVertex_2.
typedef unspecified_type	Construct_circular_source_vertex_2
	Model of CircularKernel::ConstructCircularSourceVertex_2.
typedef unspecified_type	Construct_circular_target_vertex_2
	Model of CircularKernel::ConstructCircularTargetVertex_2.
typedef unspecified_type	Intersect_2
	Model of CircularKernel::Intersect_2.
typedef unspecified_type	Split_2
	Model of CircularKernel::Split_2.
typedef unspecified_type	Make_x_monotone_2
	Model of CircularKernel::MakeXMonotone_2.
typedef unspecified_type	Make_xy_monotone_2
	Model of CircularKernel::MakeXYMonotone_2.

Link with the algebraic kernel
typedef unspecified_type	Get_equation
	Model of CircularKernel::GetEquation.

Operations
As in the Kernel concept, for each of the function objects above, there must exist a member function that requires no arguments and returns an instance of that function object. The name of the member function is the uncapitalized name of the type returned with the suffix _object appended. For example, for the function object CircularKernel::Construct_circular_arc_2 the following member function must exist:
Construct_circular_arc_2	construct_circular_arc_2_object () const