CGAL::Arr_Bezier_curve_traits_2< RatKernel, AlgKernel, NtTraits >::Curve_2 Class Reference

#include <CGAL/Arr_Bezier_curve_traits_2.h>

Definition

The Curve_2 class nested within the Bézier traits class is used to represent a Bézier curve of arbitrary degree, which is defined by a sequence of rational control points.

In addition to the methods listed below, the I/O operators operator<< and operator>> for standard output-streams are also supported. The copy constructor and assignment operator are supported as well.

Creation
	Curve_2 ()
	default constructor.
template<class InputIterator >
	Curve_2 (InputIterator pts_begin, InputIterator pts_end)
	constructs a Bézier curve as defined by the given range of control points. More...

Access Functions
size_t	number_of_control_points () const
	returns the number of control points that define B.
RatKernel::Point_2	control_point (size_t k) const
	returns the \( k\)th control point. More...
RatKernel::Point_2	operator() (const Rational &t) const
	returns the point \( B(t)\) on the curve that corresponds to the given rational parameter value.
AlgKernel::Point_2	operator() (const Algebraic &t) const
	returns the point \( B(t)\) on the curve that corresponds to the given algebraic parameter value.

Constructor & Destructor Documentation

Curve_2()

template<typename RatKernel , typename AlgKernel , typename NtTraits >

template<class InputIterator >

CGAL::Arr_Bezier_curve_traits_2< RatKernel, AlgKernel, NtTraits >::Curve_2::Curve_2	(	InputIterator	pts_begin,
		InputIterator	pts_end
	)

constructs a Bézier curve as defined by the given range of control points.

The value-type of InputIterator is RatKernel::Point_2.

Precondition

The input range must contain at least two control points.

Member Function Documentation

control_point()

template<typename RatKernel , typename AlgKernel , typename NtTraits >

RatKernel::Point_2 CGAL::Arr_Bezier_curve_traits_2< RatKernel, AlgKernel, NtTraits >::Curve_2::control_point

(

size_t

k

)

const

returns the \( k\)th control point.

Note that the first control point equals the curve source, while the last control point equals its target. The rest of the control points do not lie on the curve.

Precondition

\( k\) is smaller than the number of control points.