Line_2<Kernel>

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CGAL::Line_2<Kernel>

Definition

An object l of the data type Line_2<Kernel> is a directed straight line in the two-dimensional Euclidean plane

². It is defined by the set of points with Cartesian coordinates

(x,y) that satisfy the equation l : ax + by + c = 0

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

Kernel::RT

l.b ()

returns the second coefficient of

Kernel::RT

l.c ()

returns the third coefficient of

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

Let us first define two Cartesian two-dimensional points in the Euclidean plane

². Their dimension and the fact that they are Cartesian is expressed by the suffix _2 and the representation type Cartesian.


  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);

CGAL::Line_2<Kernel>

Definition

Creation

Operations

Predicates

Miscellaneous

Example

See Also