2D Intersection of Curves Reference

Baruch Zukerman, Ron Wein, and Efi Fogel

This package provides three free functions implemented based on the sweep-line paradigm: given a collection of input curves, compute all intersection points, compute the set of subcurves that are pairwise interior-disjoint induced by them, and check whether there is at least one pair of curves among them that intersect in their interior.

Introduced in: CGAL 2.4
Depends on: 2D Arrangements
BibTeX: cgal:wfz-ic2-15a
License: GPL

This chapter describes three functions implemented using the sweep-line algorithm: given a collection \( {\mathcal C}\) of planar curves, compute all intersection points among them, obtain the set of maximal pairwise interior-disjoint 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 output-sensitive manner.

Classified Reference Pages

Functions

• CGAL::compute_intersection_points
• CGAL::compute_subcurves
• CGAL::do_curves_intersect

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...

Function Documentation

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.

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 value-type of InputIterator is a curve type and the value-type of OutputIterator is a point type. The output points are reported in an increasing \(xy\)-lexicographical order.

#include <CGAL/Sweep_line_2_algorithms.h>

Examples:

Arrangement_on_surface_2/sweep_line.cpp.

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.

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 value-type of InputIterator is Traits::Curve_2, and the value-type of OutputIterator is Traits::Point_2. The output points are reported in an increasing \( xy\)-lexicographical order.

#include <CGAL/Sweep_line_2_algorithms.h>

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.

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 value-type of InputIterator is a curve type, and the value-type of OutputIterator is an \(x\)-monotone curve type.

#include <CGAL/Sweep_line_2_algorithms.h>

Examples:

Arrangement_on_surface_2/sweep_line.cpp.

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.

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 value-type of InputIterator is Traits::Curve_2, and the value-type of OutputIterator is Traits::X_monotone_curve_2.

#include <CGAL/Sweep_line_2_algorithms.h>

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.

The function returns true if such a pair is found, and false if all curves are pairwise disjoint in their interior. The value-type of InputIterator is a curve type.

#include <CGAL/Sweep_line_2_algorithms.h>

Examples:

Arrangement_on_surface_2/sweep_line.cpp.

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.

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 value-type of InputIterator is Traits::Curve_2.

#include <CGAL/Sweep_line_2_algorithms.h>