\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 3D Periodic Triangulations

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Periodic_3Offset_3 Concept Reference
Concepts

## Definition

The concept `Periodic_3Offset_3` describes a three-dimensional integer vector with some specialized access functions and operations.

Has Models:
  CGAL::Periodic_3_offset_3

See Also
  `Periodic_3DelaunayTriangulationTraits_3`

## Creation
| Periodic_3Offset_3 ()
| Default constructor.
| Periodic_3Offset_3 (int x, int y, int z)
| Constructs the offset (x,y,z).

## Operations
Periodic_3Offset_3 | operator+ (const Periodic_3Offset_3 &other) const
| Return the vector sum of `o` and `other`.
Periodic_3Offset_3 | operator- (const Periodic_3Offset_3 &other) const
| Return the vector difference of `o` and `other`.
Periodic_3Offset_3 | operator- () const
| Return the negative vector of `o`.
void | operator+= (const Periodic_3Offset_3 &other) const
| Add `other` to `o` using vector addition.
void | operator-= (const Periodic_3Offset_3 &other) const
| Subtract `other` from `o` using vector subtraction.
bool | operator== (const Periodic_3Offset_3 &other) const
| Return `true` if `other` and `o` represent the same vector.
bool | operator!= (const Periodic_3Offset_3 &other) const
| Return `true` if `other` and `o` do not represent the same vector.
bool | operator< (const Periodic_3Offset_3 &other) const
| Compare `o` and `other` lexicographically.

## Access Functions
int | operator[] (int i)
| Return the \( i\)-th entry of `o`.
int | x () const
| Return the \( x\)-entry of `o`.
int | y () const
| Return the \( y\)-entry of `o`.
int | z ()
| Return the \( z\)-entry of `o`.
bool | is_null () const
| Returns `true` if `o` is equal to (0,0,0).
istream & | operator>> (istream &is, Periodic_3_offset_3 &off)
| Inputs an offset from `is`.
ostream & | operator<< (ostream &os, Periodic_3_offset_3 &off) const
| Outputs an offset from `os`.