\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.8.1 - 2D and 3D Linear Geometry Kernel
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
List of all members
CGAL::Direction_3< Kernel > Class Template Reference
3D Kernel Objects

#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.

See Also
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< Kernel > operator- () const
 The direction opposite to d.
 
Vector_3< Kernel > vector () const
 returns a vector that has the same direction as d.
 
Direction_3< Kernel > transform (const Aff_transformation_3< Kernel > &t) const
 returns the direction obtained by applying t on d.
 

Member Function Documentation

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
\( 0 \leq i \leq2\).