Voxel

A voxel represents a value on a regular grid in three-dimensional space. As with pixels in a bitmap, voxels themselves do not typically have their position (their coordinates) explicitly encoded along with their values. Instead, the position of a voxel is inferred based upon its position relative to other voxels (i.e., its position in the data structure that makes up a single volumetric image). In contrast to pixels and voxels, points and polygons are often explicitly represented by the coordinates of their vertices. A direct consequence of this difference is that polygons are able to efficiently represent simple 3D structures with lots of empty or homogeneously filled space, while voxels are good at representing regularly sampled spaces that are non-homogeneously filled.

Voxels are frequently used in the visualization and analysis of medical and scientific data. Some volumetric displays use voxels to describe their resolution. For example, a display might be able to show 512×512×512 voxels.

The word voxel is based on a contraction of vox ("volume") and el (for "element"); similar formations with el  for "element" include the words pixel and texel.

A volume described as voxels can be visualized either by direct volume rendering or by the extraction of polygon iso-surfaces that follow the contours of given threshold values. The marching cubes algorithm is often used for isosurface extraction, however other methods exist as well.

Both ray-tracing and ray-casting, as well as rasterisation, can be applied to voxel data to obtain 2D raster graphics to depict on a monitor.

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