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A voxel (a portmanteau of the words volumetric and pixel) is a volume element, representing a value on a regular grid in three dimensional space. This is analogous to a pixel, which represents 2D image data. Voxels are frequently used in the visualisation and analysis of medical and scientific data. Some true 3D displays use voxels to describe their resolution. For example, a display might be able to show 512×512×512 voxels.

As with pixels, voxels themselves typically do not contain their position in space (their coordinates) - but rather, it is inferred based on their position relative to other voxels (i.e. their position in the data structure that makes up a single volume image).

Contents 1 Voxel data 2 Uses 2.1 Visualization 2.2 Computer gaming 3 Trivia 4 See also 5 External links

A voxel represents the sub-volume box with constant scalar/vector value inside which is equal to scalar/vector value of the corresponding grid/pixel of the original discrete representation of the volumetric data. The boundaries of a voxel are exactly in the middle between neighboring grids. Voxel data sets have a limited resolution, as precise data is only available at the center of each cell. Under the assumption that the voxel data is sampling a suitably band-limited signal, accurate reconstructions of data points in between the sampled voxels can be attained by low-pass filtering the data set. Visually acceptable approximations to this low pass filter can be attained by polynomial interpolation such as tri-linear or tri-cubic interpolation.

The value of a voxel may represent various properties. In CT scans, the values are Hounsfield units, giving the opacity of material to X-rays. Different types of value are acquired from MRI or ultrasound.

Voxels can contain multiple scalar values what essentially is a vector data; in the case of ultrasound scans with B-mode and Doppler data, density, and volumetric flow rate are captured as separate channels of data relating to the same voxel positions.

Other values may be useful for immediate 3D rendering, such as a surface normal vector and color.

There are different kind of voxels, one is to see voxel as a way to represent volumetric object as 3D bitmaps instead of vectors (by opposition, polygonal objects are made of vectors). Another popular one is Voxel terrain which is generally used in games and simulations. Most commonly, this "voxel" terrain is actually stored and processed as a heightmap, the result of run-length encoding on a voxel grid.

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

• Many NovaLogic games have used voxel-based rendering technology, including the Delta Force series and the Comanche series.
• Westwood Studios' Command & Conquer: Tiberian Sun and Command & Conquer: Red Alert 2 use voxels to render certain vehicles.
• Westwood Studios' Blade Runner video game used voxels to render characters and artifacts.
• Outcast, a game made by Belgian developer Appeal (now bankrupt), sports outdoor landscapes that are rendered by a voxel engine.
• The videogame A+M+O+K for the Sega Saturn makes use of voxels in its scenarios.
• The turn-based strategy game Sid Meier's Alpha Centauri renders all units and terrain in 3D using voxels.
• The computer games Vangers and Perimeter both use a voxel renderer.
• Master of Orion 3 uses voxel graphics to render space battles and solar systems. Battles displaying 1000 ships at a time were rendered on computers without hardware graphic acceleration.
• The first person shooter game Shadow Warrior uses voxels instead of sprites as an option for many of the items pickups and scenery.
• Perimeter relies on voxels for its unique terrain molding.
• Crysis uses voxels for its terrain system
• Duke Nukem 3D has an optional voxel model pack, which contains the high resolution pack models converted to voxels
• Worms 4 Mayhem uses a "poxel" (polygon and voxel) engine to simulate land deformation similar to the older 2D Worms games

In the minimalist webcomic Pixel, in which pixels inside a computer are the main characters, one 'race' of supporting characters are the voxels, who have the "supernatural" power of moving in three dimensions.

• Volume rendering
• resel

• Volex, a volumetric display using LED
• Voxel3D, voxel based modeling software
• Voxlap Open source voxel engine written by Ken Silverman and Tom Dobrowolski
• HVox, another voxel-based terrain engine
• Iehovah, a volume based surface generation library for real-time visualization
• Pixell Game using two voxel heightmaps generated on launch to create the floor and ceiling of a 3d cave.
• Geek, a voxel terrain engine that uses perlin noise to create natural looking geometry
• Cavernosa, a terrain/cave sculpturing tool based on a hierarchical binary voxel grid
• A tutorial, that explains how to draw a voxel terrain with code in C++ such as Commanche/Outcast