CGAL::Line_2<Kernel>

Definition

²

The line splits $$ ² in a positive and a negative side. A point $$p with Cartesian coordinates $$(px, py) is on the positive side of l, iff a px + b py + c > 0, it is on the negative side of l, iff a px + b py + c < 0. The positive side is to the left of l.

Creation

Line_2<Kernel> l ( Kernel::RT a, Kernel::RT b, Kernel::RT c);
	introduces a line l with the line equation in Cartesian coordinates $$ax +by +c = 0.
Line_2<Kernel> l ( Point_2<Kernel> p, Point_2<Kernel> q);
	introduces a line l passing through the points $$p and $$q. Line l is directed from $$p to $$q.
Line_2<Kernel> l ( Point_2<Kernel> p, Direction_2<Kernel> d);
	introduces a line l passing through point $$p with direction $$d.
Line_2<Kernel> l ( Point_2<Kernel> p, Vector_2<Kernel> v);
	introduces a line l passing through point $$p and oriented by $$v.
Line_2<Kernel> l ( Segment_2<Kernel> s);
	introduces a line l supporting the segment $$s, oriented from source to target.
Line_2<Kernel> l ( Ray_2<Kernel> r);
	introduces a line l supporting the ray $$r, with same orientation.

Operations

bool	l.operator== ( h)
		Test for equality: two lines are equal, iff they have a non empty intersection and the same direction.
bool	l.operator!= ( h)
		Test for inequality.
Kernel::RT	l.a ()	returns the first coefficient of $$l.
Kernel::RT	l.b ()	returns the second coefficient of $$l.
Kernel::RT	l.c ()	returns the third coefficient of $$l.
Point_2<Kernel>	l.point ( int i)	returns an arbitrary point on l. It holds point(i) == point(j), iff i==j. Furthermore, l is directed from point(i) to point(j), for all i $$< j.
Point_2<Kernel>	l.projection ( Point_2<Kernel> p)
		returns the orthogonal projection of $$p onto l.
Kernel::FT	l.x_at_y ( Kernel::FT y)
		returns the $$x-coordinate of the point at l with given $$y-coordinate. Precondition: l is not horizontal.
Kernel::FT	l.y_at_x ( Kernel::FT x)
		returns the $$y-coordinate of the point at l with given $$x-coordinate. Precondition: l is not vertical.

Predicates

bool	l.is_degenerate ()	line l is degenerate, if the coefficients a and b of the line equation are zero.
bool	l.is_horizontal ()
bool	l.is_vertical ()
Oriented_side	l.oriented_side ( Point_2<Kernel> p)
		returns ON_ORIENTED_BOUNDARY, ON_NEGATIVE_SIDE, or the constant ON_POSITIVE_SIDE, depending on the position of $$p relative to the oriented line l.

For convenience we provide the following boolean functions:

bool	l.has_on ( Point_2<Kernel> p)
bool	l.has_on_positive_side ( Point_2<Kernel> p)
bool	l.has_on_negative_side ( Point_2<Kernel> p)

Miscellaneous

Vector_2<Kernel>	l.to_vector ()	returns a vector having the direction of l.
Direction_2<Kernel>
	l.direction ()	returns the direction of l.
Line_2<Kernel>	l.opposite ()	returns the line with opposite direction.
Line_2<Kernel>	l.perpendicular ( Point_2<Kernel> p)
		returns the line perpendicular to l and passing through $$p, where the direction is the direction of l rotated counterclockwise by 90 degrees.
Line_2<Kernel>	l.transform ( Aff_transformation_2<Kernel> t)
		returns the line obtained by applying $$t on a point on l and the direction of l.

Example

²

  Point_2< Cartesian<double> >  p(1.0,1.0), q(4.0,7.0);

To define a line $$l we write:

  Line_2< Cartesian<double> > l(p,q);

See Also