# Introduction

This is a basic introduction to what voxels *are*, what they are *not* and their general use cases.

## What is a voxel in theory?

To quote Wikipedia:

In 3D computer graphics, a voxel represents a value on a regular grid in three-dimensional space.

— Wikipedia on Voxels

Since most people don't have a good understanding/foundation of math (in this case: linear algebra), let's explain this piece by piece.

A voxel represents a value...

An individual voxel can be absolutely *anything*. Yes, **anything**.

There could even be *another* grid of voxels 'inside' each voxel!

...on a regular grid...

Taking the definition from Wikipedia...

A regular grid is a tessellation of n-dimensional Euclidean space by congruent parallelotopes (e.g. bricks). [...]

...and breaking it down:

Tessellation

The grid is formed by*dividing space*into**cells**.n-dimensional

The grid has*at least*one dimension.

But since we are in 3D space, at least three.Euclidian space

The*axes*are at*90° degree angles*to each other,*everywhere*.Congruent

*Every*cell in the grid has*exactly*the**same shape**.Parallelotopes

- The cells are shaped like boxes.
- Each opposing side has the same area/shape.
- Their edges in a given axis are parallel.

Now you *might* think that the *cells* of the grid are the voxels, but that is not the case! The voxels are theoretically *on the corners* where the cells meet, they are neither *inside* the cells nor *are* they the cells; a voxel is a *point sample*, not a little cube.

In practice you will usually notice this when either *rounding* or *off-by-one* errors occur.

...in three-dimensional space.

- There must be
*at least*three-dimensions, so as to form a**volume**. - Adding more spatial dimensions turns the voxels hyper-volumetric,

making them**hypervoxels**(there is no shorthand or acronym for this). - Adding a time-dimension turns them into temporal voxels,

making them**toxels**.

That is the definition of a voxel; and if that all sounded complicated... well that's because it is! Mathematics are like that sometimes.

Let us continue with voxels in practice...

## What is a voxel in practice?

As noted in the theory section, a voxel can be * anything*...

- Numerical things, like density, color and direction.
- Labelled things such as states, types, names, etc. etc.
- Structured things: text, an item, or some other object.

...and this is *without* taking the encoding, be it in-memory or on-disk, into account.
The only limit is your imagination... and the size of your memory/disk!

**TODO:** This section needs more content.

## What is *not* a voxel?

If values are generated in a *two*-dimensional grid and *expanded* into a *third* dimension on-demand,
such as *during rendering*, you are * not* using voxels.

That's just a plain old heightmap *pretending* to be voxels!

**Important:**

This does **not** mean that *columns* of values arranged in a grid, like run-length encoded data might be, are not voxels!
The way that voxels are *stored* does not matter as long as the grid is indexable.

## What are voxels used for?

*Many* things, but three of them stick out:

Since you are visiting this wiki, you might already know what you intend to use voxels for; if not, please take some time to think about it, otherwise just read on ahead! :)

For making **art** made of voxels,
we highly recommend checking out MagicaVoxel,
which is currently considered to be *the* best voxel-editor you can get; it's completely free!

Perhaps share your creation?