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

#include <CGAL/Arr_Bezier_curve_traits_2.h>

Definition

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.