An object of the class Direction_2<Kernel> is a vector in the two-dimensional vector space 2 where we forget about its length. They can be viewed as unit vectors, although there is no normalization internally, since this is error prone. Directions are used whenever the length of a vector does not matter. They also characterize a set of parallel oriented lines that have the same orientations. For example, you can ask for the direction orthogonal to an oriented plane, or the direction of an oriented line. Further, they can be used to indicate angles. The slope of a direction is dy()/dx().


Direction_2<Kernel> d ( Vector_2<Kernel> v);
introduces the direction d of vector v.

Direction_2<Kernel> d ( Line_2<Kernel> l);
introduces the direction d of line l.

Direction_2<Kernel> d ( Ray_2<Kernel> r);
introduces the direction d of ray r.

Direction_2<Kernel> d ( Segment_2<Kernel> s);
introduces the direction d of segment s.

Direction_2<Kernel> d ( Kernel::RT x, Kernel::RT y);
introduces a direction d passing through the origin and the point with Cartesian coordinates (x, y).


Kernel::RT ( int i) const returns values, such that d== Direction_2<Kernel>(delta(0),delta(1)).
Precondition: : 0 i 1.

Kernel::RT d.dx () const returns delta(0).

Kernel::RT d.dy () const returns delta(1).

There is a total order on directions. We compare the angles between the positive x-axis and the directions in counterclockwise order.

bool d.operator== ( e) const
bool d.operator!= ( e) const
bool d.operator< ( e) const
bool d.operator> ( e) const
bool d.operator<= ( e) const
bool d.operator>= ( e) const

Furthermore, we have

bool d.counterclockwise_in_between ( d1, d2) const
returns true, iff d is not equal to d1, and while rotating counterclockwise starting at d1, d is reached strictly before d2 is reached. Note that true is returned if d1 == d2, unless also d == d1.

Direction_2<Kernel> d.operator- () const The direction opposite to d.


Vector_2<Kernel> d.vector () const returns a vector that has the same direction as d.

Direction_2<Kernel> d.transform ( Aff_transformation_2<Kernel> t) const
returns the direction obtained by applying t on d.

See Also