CGAL::Direction_2< Kernel > Class Template Reference

#include <CGAL/Direction_2.h>

Definition

template<typename Kernel>
class CGAL::Direction_2< Kernel >

An object d of the class Direction_2 is a vector in the two-dimensional 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().

Is Model Of:

Kernel::Direction_2

Creation
	Direction_2 (const Vector_2< Kernel > &v)
	introduces the direction d of vector v. More...
	Direction_2 (const Line_2< Kernel > &l)
	introduces the direction d of line l. More...
	Direction_2 (const Ray_2< Kernel > &r)
	introduces the direction d of ray r. More...
	Direction_2 (const Segment_2< Kernel > &s)
	introduces the direction d of segment s. More...
	Direction_2 (const Kernel::RT &x, const Kernel::RT &y)
	introduces a direction d passing through the origin and the point with Cartesian coordinates \( (x, y)\). More...

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

Miscellaneous
Vector_2< Kernel >	vector () const
	returns a vector that has the same direction as d. More...
Direction_2< Kernel >	transform (const Aff_transformation_2< Kernel > &t) const
	returns the direction obtained by applying t on d. More...

Constructor & Destructor Documentation

Direction_2() [1/5]

template<typename Kernel >

CGAL::Direction_2< Kernel >::Direction_2

(

const Vector_2< Kernel > &

v

)

introduces the direction d of vector v.

Direction_2() [2/5]

template<typename Kernel >

CGAL::Direction_2< Kernel >::Direction_2

(

const Line_2< Kernel > &

l

)

introduces the direction d of line l.

Direction_2() [3/5]

template<typename Kernel >

CGAL::Direction_2< Kernel >::Direction_2

(

const Ray_2< Kernel > &

r

)

introduces the direction d of ray r.

Direction_2() [4/5]

template<typename Kernel >

CGAL::Direction_2< Kernel >::Direction_2

(

const Segment_2< Kernel > &

s

)

introduces the direction d of segment s.

Direction_2() [5/5]

template<typename Kernel >

CGAL::Direction_2< Kernel >::Direction_2	(	const Kernel::RT &	x,
		const Kernel::RT &	y
	)

introduces a direction d passing through the origin and the point with Cartesian coordinates \( (x, y)\).

Member Function Documentation

counterclockwise_in_between()

template<typename Kernel >

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.

delta()

template<typename Kernel >

Kernel::RT CGAL::Direction_2< Kernel >::delta

(

int

i

)

const

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

Precondition

\( 0 \leq i \leq1\).

dx()

template<typename Kernel >

Kernel::RT CGAL::Direction_2< Kernel >::dx

(

)

const

returns delta(0).

dy()

template<typename Kernel >

Kernel::RT CGAL::Direction_2< Kernel >::dy

(

)

const

returns delta(1).

operator!=()

template<typename Kernel >

bool CGAL::Direction_2< Kernel >::operator!=

(

const Direction_2< Kernel > &

e

)

const

operator-()

template<typename Kernel >

Direction_2<Kernel> CGAL::Direction_2< Kernel >::operator-

(

)

const

The direction opposite to d.

operator<()

template<typename Kernel >

bool CGAL::Direction_2< Kernel >::operator<

(

const Direction_2< Kernel > &

e

)

const

operator<=()

template<typename Kernel >

bool CGAL::Direction_2< Kernel >::operator<=

(

const Direction_2< Kernel > &

e

)

const

operator==()

template<typename Kernel >

bool CGAL::Direction_2< Kernel >::operator==

(

const Direction_2< Kernel > &

e

)

const

operator>()

template<typename Kernel >

bool CGAL::Direction_2< Kernel >::operator>

(

const Direction_2< Kernel > &

e

)

const

operator>=()

template<typename Kernel >

bool CGAL::Direction_2< Kernel >::operator>=

(

const Direction_2< Kernel > &

e

)

const

transform()

template<typename Kernel >

Direction_2<Kernel> CGAL::Direction_2< Kernel >::transform

(

const Aff_transformation_2< Kernel > &

t

)

const

returns the direction obtained by applying t on d.

vector()

template<typename Kernel >

Vector_2<Kernel> CGAL::Direction_2< Kernel >::vector

(

)

const

returns a vector that has the same direction as d.