CGAL 5.5.2  2D Intersection of Curves

This chapter describes three functions implemented using the sweepline algorithm: given a collection \( {\mathcal C}\) of planar curves, compute all intersection points among them, obtain the set of maximal pairwise interiordisjoint subcurves of the curves in \( {\mathcal C}\), or check whether there is at least one pair of curves in \( {\mathcal C}\) that intersect in their interior.
The first two operations are performed in an outputsensitive manner.
Functions  
template<class InputIterator , class OutputIterator >  
OutputIterator  CGAL::compute_intersection_points (InputIterator curves_begin, InputIterator curves_end, OutputIterator points, bool report_endpoints=false) 
Given a range of curves, compute all intersection points between two (or more) input curves. More...  
template<class InputIterator , class OutputIterator , class Traits >  
OutputIterator  CGAL::compute_intersection_points (InputIterator curves_begin, InputIterator curves_end, OutputIterator points, bool report_endpoints=false, Traits traits) 
Given a range of curves, compute all intersection points between two (or more) input curves. More...  
template<class InputIterator , class OutputIterator >  
OutputIterator  CGAL::compute_subcurves (InputIterator curves_begin, InputIterator curves_end, OutputIterator subcurves, bool multiple_overlaps=false) 
Given a range of curves, compute all \( x\)monotone subcurves that are pairwise disjoint in their interior, as induced by the input curves. More...  
template<class InputIterator , class OutputIterator , class Traits >  
OutputIterator  CGAL::compute_subcurves (InputIterator curves_begin, InputIterator curves_end, OutputIterator subcurves, bool multiple_overlaps=false, Traits traits=Default_traits()) 
Given a range of curves, compute all \( x\)monotone subcurves that are pairwise disjoint in their interior, as induced by the input curves. More...  
template<class InputIterator >  
bool  CGAL::do_curves_intersect (InputIterator curves_begin, InputIterator curves_end) 
Given a range of curves, check whether there is at least one pair of curves that intersect in their interior. More...  
template<class InputIterator , class Traits >  
bool  CGAL::do_curves_intersect (InputIterator curves_begin, InputIterator curves_end, Traits traits=Default_traits()) 
Given a range of curves, check whether there is at least one pair of curves that intersect in their interior. More...  
OutputIterator CGAL::compute_intersection_points  (  InputIterator  curves_begin, 
InputIterator  curves_end,  
OutputIterator  points,  
bool  report_endpoints = false 

) 
#include <CGAL/Surface_sweep_2_algorithms.h>
Given a range of curves, compute all intersection points between two (or more) input curves.
When the flag report_endpoints
is true
, this function reports all the curve endpoints as well. If a curve endpoint is also an intersection point, it is reported once (regardless of the value of the report_endpoints
flag). The valuetype of InputIterator
is a curve type and the valuetype of OutputIterator
is a point type. The output points are reported in an increasing \(xy\)lexicographical order.
OutputIterator CGAL::compute_intersection_points  (  InputIterator  curves_begin, 
InputIterator  curves_end,  
OutputIterator  points,  
bool  report_endpoints = false , 

Traits  traits  
) 
#include <CGAL/Surface_sweep_2_algorithms.h>
Given a range of curves, compute all intersection points between two (or more) input curves.
When the flag report_endpoints
is true
, this function reports all the curve endpoints as well. If a curve endpoint is also an intersection point, it is reported once (regardless of the value of the report_endpoints
flag). The Traits
type must be a model of the ArrangementTraits_2
concept, such that the valuetype of InputIterator
is Traits::Curve_2
, and the valuetype of OutputIterator
is Traits::Point_2
. The output points are reported in an increasing \( xy\)lexicographical order.
OutputIterator CGAL::compute_subcurves  (  InputIterator  curves_begin, 
InputIterator  curves_end,  
OutputIterator  subcurves,  
bool  multiple_overlaps = false 

) 
#include <CGAL/Surface_sweep_2_algorithms.h>
Given a range of curves, compute all \( x\)monotone subcurves that are pairwise disjoint in their interior, as induced by the input curves.
If the flag multiple_overlaps
is true
, then a subcurve that represents an overlap of \( k\) input curves is reported \( k\) times; otherwise, each subcurve is reported only once. The valuetype of InputIterator
is a curve type, and the valuetype of OutputIterator
is an \(x\)monotone curve type.
OutputIterator CGAL::compute_subcurves  (  InputIterator  curves_begin, 
InputIterator  curves_end,  
OutputIterator  subcurves,  
bool  multiple_overlaps = false , 

Traits  traits = Default_traits() 

) 
#include <CGAL/Surface_sweep_2_algorithms.h>
Given a range of curves, compute all \( x\)monotone subcurves that are pairwise disjoint in their interior, as induced by the input curves.
If the flag multiple_overlaps
is true
, then a subcurve that represents an overlap of \( k\) input curves is reported \( k\) times; otherwise, each subcurve is reported only once. The Traits
type must be a model of the ArrangementTraits_2
concept, such that the valuetype of InputIterator
is Traits::Curve_2
, and the valuetype of OutputIterator
is Traits::X_monotone_curve_2
.
bool CGAL::do_curves_intersect  (  InputIterator  curves_begin, 
InputIterator  curves_end  
) 
#include <CGAL/Surface_sweep_2_algorithms.h>
Given a range of curves, check whether there is at least one pair of curves that intersect in their interior.
The function returns true
if such a pair is found, and false
if all curves are pairwise disjoint in their interior. The valuetype of InputIterator
is a curve type.
bool CGAL::do_curves_intersect  (  InputIterator  curves_begin, 
InputIterator  curves_end,  
Traits  traits = Default_traits() 

) 
#include <CGAL/Surface_sweep_2_algorithms.h>
Given a range of curves, check whether there is at least one pair of curves that intersect in their interior.
The function returns true
if such a pair is found, and false
if all curves are pairwise disjoint in their interior. The Traits
type must be a model of the ArrangementTraits_2
concept, such that the valuetype of InputIterator
is Traits::Curve_2
.