CGAL::Arr_algebraic_segment_traits_2< Coefficient >::Construct_x_monotone_segment_2 Class Reference

#include <CGAL/Arr_algebraic_segment_traits_2.h>

Object Creation Functors
template<typename OutputIterator >
OutputIterator	operator() (Curve_2 cv, Point_2 end_min, Point_2 end_max, OutputIterator oi)
	inserts a sequence of X_monotone_curve_2 objects (terminal segments) into an output container given through an output iterator.
template<typename OutputIterator >
OutputIterator	operator() (Curve_2 cv, Point_2 p, Site_of_point site_of_p, OutputIterator out)
	inserts a sequence of X_monotone_curve_2 objects into an output container given through an output iterator.
template<typename OutputIterator >
OutputIterator	operator() (Point_2 p, Point_2 q, OutputIterator out)
	inserts a sequence of X_monotone_curve_2 objects into an output container given through an output iterator.

Member Function Documentation

operator()() [1/3]

template<typename Coefficient >

template<typename OutputIterator >

OutputIterator CGAL::Arr_algebraic_segment_traits_2< Coefficient >::Construct_x_monotone_segment_2::operator()	(	Curve_2	cv,
		Point_2	end_min,
		Point_2	end_max,
		OutputIterator	oi
	)

inserts a sequence of X_monotone_curve_2 objects (terminal segments) into an output container given through an output iterator.

These terminal segments compose an \(x\)-monotone (or vertical) segment of a given curve that starts in end_min, and ends in end_max.

Parameters

cv	The input curve.
end_min	The starting point.
end_max	The ending point.
oi	The output iterator that points at the output container.

Returns

The past-the-end iterator of the output container.

Precondition

end_min must have a unique \(x\)-monotone segment to its right, or end_max must have a unique \(x\)-monotone segment to its left. Furthermore, end_min and end_max must be connected by an \(x\)-monotone segment of cv)

operator()() [2/3]

template<typename Coefficient >

template<typename OutputIterator >

OutputIterator CGAL::Arr_algebraic_segment_traits_2< Coefficient >::Construct_x_monotone_segment_2::operator()	(	Curve_2	cv,
		Point_2	p,
		Site_of_point	site_of_p,
		OutputIterator	out
	)

inserts a sequence of X_monotone_curve_2 objects into an output container given through an output iterator.

These segments form an \(x\)-monotone (or vertical) segment of the curve cv.

If site_of_p==POINT_IN_INTERIOR, the maximal segment is returned that contains p in its interior.

returned that contains p as its left endpoint.

returned that contains p as its left endpoint.

Precondition

(If site_of_p==POINT_IN_INTERIOR, p must be an interior point of an \(x\)-monotone or a vertical segment. must either have a unique \(x\)-monotone segment to the right, or a vertical segment from p upwards. must either have a unique \(x\)-monotone segment to the left, or a vertical segment from p downwards.)

operator()() [3/3]

template<typename Coefficient >

template<typename OutputIterator >

OutputIterator CGAL::Arr_algebraic_segment_traits_2< Coefficient >::Construct_x_monotone_segment_2::operator()	(	Point_2	p,
		Point_2	q,
		OutputIterator	out
	)

inserts a sequence of X_monotone_curve_2 objects into an output container given through an output iterator.

These segments form a straight-line segment connecting the points p and q. If p and q share the same \(x\)-coordinate, the constructed vertical segment consists of only one X_monotone_curve_2 object and can be computed efficiently. In the non-vertical case, the construction is only possible if p and q have both rational x- and y-coordinates.

Precondition

(p must not be equal to q.)