CGAL 5.3  2D and 3D Linear Geometry Kernel

#include <CGAL/Direction_2.h>
An object d
of the class Direction_2
is a vector in the twodimensional vector space \( \mathbb{R}^2\) 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()
.
Creation  
Direction_2 (const Vector_2< Kernel > &v)  
introduces the direction d of vector v .  
Direction_2 (const Line_2< Kernel > &l)  
introduces the direction d of line l .  
Direction_2 (const Ray_2< Kernel > &r)  
introduces the direction d of ray r .  
Direction_2 (const Segment_2< Kernel > &s)  
introduces the direction d of segment s .  
Direction_2 (const Kernel::RT &x, const Kernel::RT &y)  
introduces a direction d passing through the origin and the point with Cartesian coordinates \( (x, y)\).  
Operations  
There is a total order on directions. We compare the angles between the positive \( x\)axis and the directions in counterclockwise order.  
Kernel::RT  delta (int i) const 
returns values, such that d == Direction_2<Kernel>(delta(0),delta(1)) . More...  
Kernel::RT  dx () const 
returns delta(0) .  
Kernel::RT  dy () const 
returns delta(1) .  
bool  operator== (const Direction_2< Kernel > &e) const 
bool  operator!= (const Direction_2< Kernel > &e) const 
bool  operator< (const Direction_2< Kernel > &e) const 
bool  operator> (const Direction_2< Kernel > &e) const 
bool  operator<= (const Direction_2< Kernel > &e) const 
bool  operator>= (const Direction_2< Kernel > &e) const 
bool  counterclockwise_in_between (const Direction_2< Kernel > &d1, const Direction_2< Kernel > &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. More...  
Direction_2< Kernel >  operator () const 
The direction opposite to d .  
Miscellaneous  
Vector_2< Kernel >  vector () const 
returns a vector that has the same direction as d .  
Direction_2< Kernel >  transform (const Aff_transformation_2< Kernel > &t) const 
returns the direction obtained by applying t on d .  
bool CGAL::Direction_2< Kernel >::counterclockwise_in_between  (  const Direction_2< Kernel > &  d1, 
const Direction_2< Kernel > &  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
.
Kernel::RT CGAL::Direction_2< Kernel >::delta  (  int  i  )  const 
returns values, such that d
== Direction_2<Kernel>(delta(0),delta(1))
.