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CGAL::Line_3<Kernel>

Definition

An object l of the data type Line_3<Kernel> is a directed straight line in the three-dimensional Euclidean space 3.

Creation

Line_3<Kernel> l ( Point_3<Kernel> p, Point_3<Kernel> q);
introduces a line l passing through the points p and q. Line l is directed from p to q.


Line_3<Kernel> l ( Point_3<Kernel> p, Direction_3<Kernel> d);
introduces a line l passing through point p with direction d.


Line_3<Kernel> l ( Point_3<Kernel> p, Vector_3<Kernel> v);
introduces a line l passing through point p and oriented by v.


Line_3<Kernel> l ( Segment_3<Kernel> s);
returns the line supporting the segment s, oriented from source to target.


Line_3<Kernel> l ( Ray_3<Kernel> r);
returns the line supporting the ray r, with the same orientation.

Operations

bool l.operator== ( h) const Test for equality: two lines are equal, iff they have a non empty intersection and the same direction.

bool l.operator!= ( h) const Test for inequality.

Point_3<Kernel> l.projection ( Point_3<Kernel> p) const
returns the orthogonal projection of p on l.

Point_3<Kernel> l.point ( int i) const returns an arbitrary point on l. It holds point(i) = point(j), iff i=j.

Predicates

bool l.is_degenerate () const returns true iff line l is degenerated to a point.

bool l.has_on ( Point_3<Kernel> p) const
returns true iff p lies on l.

Miscellaneous

Plane_3<Kernel> l.perpendicular_plane ( Point_3<Kernel> p) const
returns the plane perpendicular to l passing through p.

Line_3<Kernel> l.opposite () const returns the line with opposite direction.

Vector_3<Kernel> l.to_vector () const returns a vector having the same direction as l.

Direction_3<Kernel> l.direction () const returns the direction of l.

Line_3<Kernel> l.transform ( Aff_transformation_3<Kernel> t) const
returns the line obtained by applying t on a point on l and the direction of l.

See Also

Kernel::Line_3

Next: Plane_3<Kernel>
Navigation: Up   Table of Contents   Package Overview   Bibliography   Index   Title   Acknowledging CGAL
CGAL Open Source Project. Release 3.9. 26 September 2011.