 
introduces the direction d of vector $$v.
 
 
introduces the direction d of line $$l.
 
 
introduces the direction d of ray $$r.
 
 
introduces the direction d of segment $$s.
 
 
introduces a direction d passing through the origin
and the point with Cartesian coordinates $$(x, y).



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

 returns delta(0). 

 returns delta(1). 
There is a total order on directions. We compare the angles between the positive $$xaxis and the directions in counterclockwise order.

 

 







 


Furthermore, we have

 
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.  
 
 The direction opposite to d. 

 returns a vector that has the same direction as d. 
 
 
returns the direction obtained by applying $$t on d. 