CGAL::Arr_circle_segment_traits_2< Kernel >::Curve_2 Class Reference

#include <CGAL/Arr_circle_segment_traits_2.h>

Definition

The Curve_2 class nested within the traits class can represent arbitrary circular arcs, full circles and line segments and support their construction in various ways.

The copy and default constructor as well as the assignment operator are provided. In addition, an operator<< for the curves is defined for standard output streams.

Creation
	Curve_2 (const typename Kernel::Segment_2 &seg)
	constructs an curve corresponding to the line segment seg.
	Curve_2 (const typename Kernel::Point_2 &source, const typename Kernel::Point_2 &target)
	constructs an curve corresponding to the line segment directed from source to target, both having rational coordinates.
	Curve_2 (const typename Kernel::Line_2 &line, const Point_2 &source, const Point_2 &target)
	constructs an curve corresponding to the line segment supported by the given line, directed from source to target. More...
	Curve_2 (const typename Kernel::Circle_2 &circ)
	constructs an curve corresponding to the given circle. More...
	Curve_2 (const typename Kernel::Point_2 &c, const typename Kernel::FT &r, Orientation orient=COUNTERCLOCKWISE)
	constructs an curve corresponding to a circle centered at the rational point c whose radius r is rational.
	Curve_2 (const typename Kernel::Circle_2 &circ, const Point_2 &source, const Point_2 &target)
	constructs a circular arc supported by circ, which has a center point with rational coordinates and whose squared radius is rational, with the given endpoints. More...
	Curve_2 (const typename Kernel::Point_2 &c, const typename Kernel::FT &r, Orientation orient, const Point_2 &source, const Point_2 &target)
	constructs a circular arc supported by a circle centered at the rational point c whose radius r is rational, directed from source to target with the given orientation. More...
	Curve_2 (const typename Kernel::Point_2 &source, const typename Kernel::Point_2 &mid, const typename Kernel::Point_2 &target)
	constructs an circular arc whose endpoints are source and target that passes through mid. More...

Access Functions
bool	is_full () const
	indicates whether the curve represents a full circle.
const Point_2 &	source () const
	returns the source point. More...
const Point_2 &	target () const
	returns the target point. More...
Orientation	orientation () const
	returns the orientation of the curve (COLLINEAR in case of line segments).
bool	is_linear () const
	determines whether cv is a line segment.
bool	is_circular () const
	determines whether cv is a circular arc.
Kernel::Line_2	supporting_line () const
	returns the supporting line of cv. More...
Kernel::Circle_2	supporting_circle () const
	returns the supporting circle of cv. More...

Constructor & Destructor Documentation

Curve_2() [1/5]

template<typename Kernel >

CGAL::Arr_circle_segment_traits_2< Kernel >::Curve_2::Curve_2	(	const typename Kernel::Line_2 &	line,
		const Point_2 &	source,
		const Point_2 &	target
	)

constructs an curve corresponding to the line segment supported by the given line, directed from source to target.

Note that the two endpoints may have one-root coordinates.

Precondition

Both endpoints must lie on the given supporting line.

Curve_2() [2/5]

template<typename Kernel >

CGAL::Arr_circle_segment_traits_2< Kernel >::Curve_2::Curve_2

(

const typename Kernel::Circle_2 &

circ

)

constructs an curve corresponding to the given circle.

circ has a center point with rational coordinates and its squared radius is rational.

Curve_2() [3/5]

template<typename Kernel >

CGAL::Arr_circle_segment_traits_2< Kernel >::Curve_2::Curve_2	(	const typename Kernel::Circle_2 &	circ,
		const Point_2 &	source,
		const Point_2 &	target
	)

constructs a circular arc supported by circ, which has a center point with rational coordinates and whose squared radius is rational, with the given endpoints.

The orientation of the arc is the same as the orientation of circ.

Precondition

Both endpoints must lie on the given supporting circle.

Curve_2() [4/5]

template<typename Kernel >

CGAL::Arr_circle_segment_traits_2< Kernel >::Curve_2::Curve_2	(	const typename Kernel::Point_2 &	c,
		const typename Kernel::FT &	r,
		Orientation	orient,
		const Point_2 &	source,
		const Point_2 &	target
	)

constructs a circular arc supported by a circle centered at the rational point c whose radius r is rational, directed from source to target with the given orientation.

Precondition

Both endpoints must lie on the supporting circle.

Curve_2() [5/5]

template<typename Kernel >

CGAL::Arr_circle_segment_traits_2< Kernel >::Curve_2::Curve_2	(	const typename Kernel::Point_2 &	source,
		const typename Kernel::Point_2 &	mid,
		const typename Kernel::Point_2 &	target
	)

constructs an circular arc whose endpoints are source and target that passes through mid.

All three points have rational coordinates.

Precondition

The three points must not be collinear.

Member Function Documentation

source()

template<typename Kernel >

const Point_2& CGAL::Arr_circle_segment_traits_2< Kernel >::Curve_2::source

(

)

const

returns the source point.

Precondition

cv is not a full circle.

supporting_circle()

template<typename Kernel >

Kernel::Circle_2 CGAL::Arr_circle_segment_traits_2< Kernel >::Curve_2::supporting_circle

(

)

const

returns the supporting circle of cv.

Precondition

cv is a circular arc.

supporting_line()

template<typename Kernel >

Kernel::Line_2 CGAL::Arr_circle_segment_traits_2< Kernel >::Curve_2::supporting_line

(

)

const

returns the supporting line of cv.

Precondition

cv is a line segment.

target()

template<typename Kernel >

const Point_2& CGAL::Arr_circle_segment_traits_2< Kernel >::Curve_2::target

(

)

const

returns the target point.

Precondition

cv is not a full circle.