 CGAL 4.14.1 - 2D and 3D Linear Geometry Kernel
CGAL::Direction_3< Kernel > Class Template Reference

#include <CGAL/Direction_3.h>

Definition

An object of the class Direction_3 is a vector in the three-dimensional vector space $$\mathbb{R}^3$$ where we forget about their 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 lines that have the same orientation or the direction normal to parallel planes that have the same orientation. For example, you can ask for the direction orthogonal to an oriented plane, or the direction of an oriented line.

Is Model Of:
Kernel::Direction_3

Creation

Direction_3 (const Vector_3< Kernel > &v)
introduces a direction d initialized with the direction of vector v.

Direction_3 (const Line_3< Kernel > &l)
introduces the direction d of line l.

Direction_3 (const Ray_3< Kernel > &r)
introduces the direction d of ray r.

Direction_3 (const Segment_3< Kernel > &s)
introduces the direction d of segment s.

Direction_3 (const Kernel::RT &x, const Kernel::RT &y, const Kernel::RT &z)
introduces a direction d initialized with the direction from the origin to the point with Cartesian coordinates $$(x, y, z)$$.

Operations

Kernel::RT delta (int i) const
returns values, such that d== Direction_3<Kernel>(delta(0),delta(1),delta(2)). More...

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

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

Kernel::RT dz () const
returns delta(2).

bool operator== (const Direction_3< Kernel > &e) const
Test for equality.

bool operator!= (const Direction_3< Kernel > &e) const
Test for inequality.

Direction_3< Kerneloperator- () const
The direction opposite to d.

Vector_3< Kernelvector () const
returns a vector that has the same direction as d.

Direction_3< Kerneltransform (const Aff_transformation_3< Kernel > &t) const
returns the direction obtained by applying t on d.

◆ delta()

template<typename Kernel >
 Kernel::RT CGAL::Direction_3< Kernel >::delta ( int i ) const

returns values, such that d== Direction_3<Kernel>(delta(0),delta(1),delta(2)).

Precondition
$$0 \leq i \leq2$$.