CGAL 4.12.1 - 2D Arrangements
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.