Kernel::CompareYAtX_2 Concept Reference

Definition

Refines:

AdaptableFunctor (with three arguments)

See Also

CGAL::compare_y_at_x()

Operations
A model of this concept must provide:
Comparison_result	operator() (const Kernel::Point_2 &p, const Kernel::Line_2 &h)
	compares the \( y\)-coordinates of p and the vertical projection of p on h. More...
Comparison_result	operator() (const Kernel::Point_2 &p, const Kernel::Line_2 &h1, const Kernel::Line_2 &h2)
	This function compares the y-coordinates of the vertical projection of p on h1 and on h2. More...
Comparison_result	operator() (const Kernel::Line_2 &l1, const Kernel::Line_2 &l2, const Kernel::Line_2 &h)
	Let p be the intersection of lines l1 and l2. More...
Comparison_result	operator() (const Kernel::Line_2 &l1, const Kernel::Line_2 &l2, const Kernel::Line_2 &h1, const Kernel::Line_2 &h2)
	Let p be the intersection of lines l1 and l2. More...
Comparison_result	operator() (const Kernel::Point_2 &p, const Kernel::Segment_2 &s)
	compares the y-coordinates of p and the vertical projection of p on s. More...
Comparison_result	operator() (const Kernel::Point_2 &p, const Kernel::Segment_2 &s1, const Kernel::Segment_2 &s2)
	This function compares the \( y\)-coordinates of the vertical projection of p on s1 and on s2. More...

Member Function Documentation

Comparison_result Kernel::CompareYAtX_2::operator()	(	const Kernel::Point_2 &	p,
		const Kernel::Line_2 &	h
	)

compares the \( y\)-coordinates of p and the vertical projection of p on h.

See Figure fig-compare2 (e).

Precondition

h is not vertical.

Comparison_result Kernel::CompareYAtX_2::operator()	(	const Kernel::Point_2 &	p,
		const Kernel::Line_2 &	h1,
		const Kernel::Line_2 &	h2
	)

This function compares the y-coordinates of the vertical projection of p on h1 and on h2.

See Figure fig-compare2 (e).

Precondition

h1 and h2 are not vertical.

Comparison_result Kernel::CompareYAtX_2::operator()	(	const Kernel::Line_2 &	l1,
		const Kernel::Line_2 &	l2,
		const Kernel::Line_2 &	h
	)

Let p be the intersection of lines l1 and l2.

This function compares the \( y\)-coordinates of p and the vertical projection of p on h. See (Figure fig-compare2 (f)).

Precondition

l1, l2 intersect and h is not vertical.

Comparison_result Kernel::CompareYAtX_2::operator()	(	const Kernel::Line_2 &	l1,
		const Kernel::Line_2 &	l2,
		const Kernel::Line_2 &	h1,
		const Kernel::Line_2 &	h2
	)

Let p be the intersection of lines l1 and l2.

This function compares the y-coordinates of the vertical projection of p on h1 and on h2. See (Figure fig-compare2 (g)).

Precondition

l1 and l2 intersect; h1 and h2 are not vertical.

Comparison_result Kernel::CompareYAtX_2::operator()	(	const Kernel::Point_2 &	p,
		const Kernel::Segment_2 &	s
	)

compares the y-coordinates of p and the vertical projection of p on s.

If s is vertical, then return CGAL::EQUAL when p lies on s, CGAL::SMALLER when p lies under s, and CGAL::LARGER otherwise.

Precondition

p is within the x range of s.

Comparison_result Kernel::CompareYAtX_2::operator()	(	const Kernel::Point_2 &	p,
		const Kernel::Segment_2 &	s1,
		const Kernel::Segment_2 &	s2
	)

This function compares the \( y\)-coordinates of the vertical projection of p on s1 and on s2.

If s1 or s2 is vertical, then return CGAL::EQUAL if they intersect, otherwise return CGAL::SMALLER if s1 lies below s2, and return CGAL::LARGER otherwise.

Precondition

p is within the x range of s1 and s2.