# Voxels

A lot of stacked voxels.
Only one is highlighted.

Voxel (composed of the English volume vox and el from elements ) describes a grid point ("image" point, data element) in a three-dimensional grid in computer graphics . This corresponds to a pixel in a 2D image, a raster graphic . As with pixels, with voxels the position is usually not stored explicitly, but implicitly derived from the position of other voxels. In contrast, with points or polygonsthe positions of the corner coordinates are saved. A direct consequence of this difference is that polygons can be used to efficiently represent a 3D structure with much empty or homogeneously filled space. Voxels, on the other hand, are good at representing an equidistantly sampled space that is not filled homogeneously.

## description

Voxel means two things:

Pictorial illustration of a voxel grid. Each voxel contains a color value, shown here by the different gray coloring of the spheres.

### Spatial data set

In the case of a spatial data set that is available in a discretized form in Cartesian coordinates , voxel designates the discrete value at an XYZ coordinate of the data set. This definition is the three-dimensional equivalent of a pixel , so a voxel has no particular shape. This is also referred to as isotropic voxels or “volume pixels”. The data contained in the voxel grids are often color values ​​that are determined using the means of the volume graphic for visualization . This form of data representation is mainly used in medical imaging , where the discrete values ​​can be understood as density ( bone , fatty tissue ) and visualized accordingly.

There are specialized algorithms for representing these voxels. The Marching Cubes algorithm allows the conversion of voxel data into polygons. However, this requires a threshold value because the polygons are usually not transparent. Another method is the direct rendering of the voxel data. This can be done with raycasting by throwing a ray through the voxel grid and calculating the color values. It is canceled if opacity is reached.

### Ray tracing

In other cases, a voxel refers to a cuboid cell within a regularly divided cuboid or unlimited space. Most often this meaning is used in certain techniques to speed up ray tracing . However, since it does not adapt to local conditions, this method is not very efficient. It is better to use an acceleration structure like the kd tree .

## use

Voxels are commonly used in medicine or to represent landscapes in computer games and simulations. Voxel Terrain is used instead of a height map because it can represent overhangs, caves, arches and other 3D features of a landscape. These concave features cannot be represented with an elevation field because it only stores the topmost level of the landscape and everything below is assumed to be filled.

## Computer games

Voxel-based computer games include:

## Individual evidence

1. Voxels instead of pixels: Current methods of 3D representation. In: computerwoche.de. Computerwoche, May 31, 1991, accessed January 19, 2017 .
2. ^ Alan Watt (2002): 3D-Computergrafik, 3rd edition, Addison-Wesley
3. http://voxelstein3d.sourceforge.net/