CGAL::Arr_Bezier_curve_traits_2< RatKernel, AlgKernel, NtTraits >::X_monotone_curve_2 Class Reference

#include <CGAL/Arr_Bezier_curve_traits_2.h>

Definition

template<typename RatKernel, typename AlgKernel, typename NtTraits>
class CGAL::Arr_Bezier_curve_traits_2< RatKernel, AlgKernel, NtTraits >::X_monotone_curve_2

The X_monotone_curve_2 class nested within the Bézier traits is used to represent \(x\)-monotone subcurves of Bézier curves.

The subcurve is defined by a supporting Bézier curve \(B(t)\) and a range of definition in the parameter space \([t_1, t_2] \subseteq [0,1]\), where \(B(t_1)\) is the subcurve source and \(B(t_2)\) is its target. Note that as the point endpoints may only be approximated, the parameter range defining the subcurve may only be approximately known.

It is not possible to construct \(x\)-monotone subcurves directly. Instead, use the Make_x_monotone_2 functor supplied by the traits class to subdivide a Curve_2 object into \(x\)-monotone subcurves.

Access Functions
Curve_2	supporting_curve () const
	returns the supporting Bézier curve of b.
Point_2	source () const
	returns the source point of b.
Point_2	target () const
	returns the target point of b.
Point_2	left () const
	returns the left ( \(xy\)-lexicographically smaller) endpoint of b.
Point_2	right () const
	returns the right ( \(xy\)-lexicographically smaller) endpoint of b.
std::pair< double, double >	parameter_range () const
	return the approximate parameter range defining the subcurve b.