CGAL::Line_d<Kernel>

Definition

An instance of data type Line_d is an oriented line in $$d-dimensional Euclidean space.

Types

Line_d<Kernel>::R
	the representation type.
Line_d<Kernel>::RT
	the ring type.
Line_d<Kernel>::FT
	the field type.
Line_d<Kernel>::LA
	the linear algebra layer.

Creation

Line_d<Kernel> l;
	introduces a variable l of type Line_d<Kernel>.
Line_d<Kernel> l ( Point_d<Kernel> p, Point_d<Kernel> q);
	introduces a line through p and q and oriented from p to q. Precondition: $$p and $$q are distinct and have the same dimension.
Line_d<Kernel> l ( Point_d<Kernel> p, Direction_d<Kernel> dir);
	introduces a line through p with direction dir. Precondition: p.dimension()==dir.dimension(), dir is not degenerate.
Line_d<Kernel> l ( Segment_d<Kernel> s);
	introduces a variable l of type Line_d<Kernel> and initializes it to the line through s.source() and s.target() with direction from s.source() to s.target(). Precondition: $$s is not degenerate.
Line_d<Kernel> l ( Ray_d<Kernel> r);
	introduces a variable l of type Line_d<Kernel> and initializes it to the line through r.point(1) and r.point(2).

Operations

int	l.dimension ()	returns the dimension of the ambient space.
Point_d<Kernel>	l.point ( int i)	returns an arbitrary point on l. It holds that point(i) == point(j), iff i==j. Furthermore, l is directed from point(i) to point(j), for all i < j.
Line_d<Kernel>	l.opposite ()	returns the line (point(2),point(1)) of opposite direction.
Direction_d<Kernel>
	l.direction ()	returns the direction of l.
Line_d<Kernel>	l.transform ( Aff_transformation_d<Kernel> t)
		returns $$t(l). Precondition: l.dimension()==t.dimension().
Line_d<Kernel>	l + Vector_d<Kernel> v
		returns l+v, i.e., l translated by vector $$v. Precondition: l.dimension()==v.dimension().
Point_d<Kernel>	l.projection ( Point_d<Kernel> p)
		returns the point of intersection of l with the hyperplane that is orthogonal to l and that contains p. Precondition: l.dimension()==p.dimension().
bool	l.has_on ( Point_d<Kernel> p)
		returns true if $$p lies on l and false otherwise. Precondition: l.dimension()==p.dimension().

Non-Member Functions

bool	weak_equality ( l1, l2)
		Test for equality as unoriented lines. Precondition: l1.dimension()==l2.dimension().
bool	parallel ( l1, l2)
		returns true if l1 and l2 are parallel as unoriented lines and false otherwise. Precondition: l1.dimension()==l2.dimension().

Implementation

Lines are implemented by a pair of points as an item type. All operations like creation, initialization, tests, direction calculation, input and output on a line $$l take time $$O(l.dimension()). dimension(), coordinate and point access, and identity test take constant time. The operations for intersection calculation also take time $$O(l.dimension()). The space requirement is $$O(l.dimension()).