CGAL 6.1.2 - 2D Arrangements: CGAL::Arr_Bezier_curve_traits_2< RatKernel, AlgKernel, NtTraits >::X_monotone_curve_2 Class Reference

CGAL 6.1.2 - 2D Arrangements

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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`.