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. A portmanteau (IPA pronunciation: RP, US) is a word or morpheme that fuses two or more words or word parts to give a combined or loaded meaning. ... Example of regular grid. ... 3D computer graphics are different from 2D computer graphics in that a three-dimensional representation of geometric data is stored in the computer for the purposes of performing calculations and rendering 2D images. ... This example shows an image with a portion greatly enlarged, in which the individual pixels are rendered as little squares and can easily be seen. ... 2D computer graphics is the computer-based generation of digital images—mostly from two-dimensional models (such as 2D geometric models, text, and digital images) and by techniques specific to them. ... Medical imaging designates the ensemble of techniques and processes used to create images of the human body (or parts thereof) for clinical purposes (medical procedures seeking to reveal, diagnose or examine disease) or medical science (including the study of normal anatomy and function). ... Part of a scientific laboratory at the University of Cologne. ... A 3D display prototype by Philips A 3D display is any display device capable of conveying three-dimensional images to the viewer. ...

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). See Cartesian coordinate system or Coordinates (elementary mathematics) for a more elementary introduction to this topic. ...

Voxel data

a data set of voxels for a macromolecule

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. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... A data set (or dataset) is a collection of data, usually presented in tabular form. ... A macromolecule is a large molecule with a large molecular mass bonded covalently, but generally the use of the term is restricted to polymers and molecules which structurally include polymers. ...

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. It has been suggested that Synchrotron X-ray tomographic microscopy, X-ray tomography be merged into this article or section. ... The Hounsfield scale is a quantitative scale for describing radiodensity. ... “MRI” redirects here. ... Medical ultrasonography (sonography) is an ultrasound-based diagnostic imaging technique used to visualize muscles and internal organs, their size, structures and possible pathologies or lesions. ...

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. In computing, a scalar is a variable or field that can hold only one value at a time; as opposed to composite variables like array, list, record, etc. ... Ultrasound is a form of cyclic sound pressure with a frequency greater than the upper limit of human hearing, this limit being approximately 20 kilohertz (20,000 hertz). ... Medical ultrasonography (sonography) is an ultrasound-based diagnostic imaging technique used to visualize muscles and internal organs, their size, structures and possible pathologies or lesions. ... In physics, density is mass m per unit volume V. For the common case of a homogeneous substance, it is expressed as: where, in SI units: ρ (rho) is the density of the substance, measured in kg·m-3 m is the mass of the substance, measured in kg V is... In fluid dynamics, the volumetric flow rate, also volume flow rate and rate of fluid flow, is the volume of fluid which passes through a given volume per unit time (for example gallons per minute or squeaks per parsec). ...

Other values may be useful for immediate 3D rendering, such as a surface normal vector and color. This article does not cite any references or sources. ... A surface normal, or just normal to a flat surface is a three-dimensional vector which is perpendicular to that surface. ... Color is an important part of the visual arts. ...

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 heightmap created with Terragen The same heightmap converted to a 3D mesh and rendered with Anim8or In computer graphics, a heightmap or heightfield is a raster image used to store values, such as surface elevation data, for display in 3D computer graphics. ... Run-length encoding (RLE) is a very simple form of data compression in which runs of data (that is, sequences in which the same data value occurs in many consecutive data elements) are stored as a single data value and count, rather than as the original run. ...

Uses

Visualization

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. A volume rendered cadaver head using view-aligned texture mapping and diffuse reflection Volume rendering is a technique used to display a 2D projection of a 3D discretely sampled data set. ... Look up polygon in Wiktionary, the free dictionary. ... Head and cerebral structures (hidden) extracted from 150 MRI slices using marching-cubes (about 150. ...

Computer gaming

• 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 most 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 Amok 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. Perimeter relies on voxels for its unique terrain molding.
• 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 games Shadow Warrior and Blood use voxels instead of sprites as an option for many of the items pickups and scenery.
• Crysis uses voxels for its terrain system.
• Duke Nukem 3D has an optional voxel model pack created by fans, 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.

NovaLogic was a computer game software developer and publisher established in 1985 and based in Calabasas, California. ... Delta Force is a first-person shooter computer game by developer and publisher NovaLogic. ... The Comanche series is a series of computer games published by NovaLogic. ... Westwood Studios (1985-2003) was a computer and video game developer, founded in 1985 as Westwood Associates by Brett Sperry and Louis Castle and based in Las Vegas, Nevada. ... Westwood Studios (1985-2003) was a computer and video game developer, founded in 1985 as Westwood Associates by Brett Sperry and Louis Castle and based in Las Vegas, Nevada. ... Blade Runner is a Westwood Studios PC game loosely based on the 1982 movie of the same name. ... Outcast is an action-adventure computer game by Belgian developer Appeal, released in 1999 by publisher Infogrames. ... A video game developer is a software developer (a business or an individual) that creates video games. ... Amok (sometimes spelled AMOK, , A+M+O+K, or A•M•O•K) is an action game for the Sega Saturn in which you guide a robot called Slambird through nine different scenarios to complete several objectives. ... It has been suggested that Arcade Racer Joystick be merged into this article or section. ... “SMAC” redirects here. ... Master of Orion (MOO) is an intergalatic turn-based computer strategy game that was released in 1993. ... Shadow Warrior is a first-person shooter computer game featuring Lo Wang, a master ninja assassin or Shadow Warrior, developed by 3D Realms and released on May 13, 1997 by GT Interactive. ... Blood is a PC game developed by Monolith Productions and distributed by GT Interactive. ... In computer graphics, a sprite (also known by other names; see Synonyms below) is a two-dimensional image or animation that is integrated into a larger scene. ... For the particle accelerator, see CRYSIS. Crysis is an upcoming science fiction first-person shooter computer game that is currently in development by German developer Crytek. ... Duke Nukem 3D is a first-person shooter computer game developed by 3D Realms and published by Apogee Software. ... Worms Armageddon Cover Art Worms is a series of turn-based computer games with the common theme of players each controlling a small platoon of worms across a two-dimensional (and, in more recent games, three-dimensional), deformable landscape. ... Look up polygon in Wiktionary, the free dictionary. ...

See also

• Volume rendering
• resel

A volume rendered cadaver head using view-aligned texture mapping and diffuse reflection Volume rendering is a technique used to display a 2D projection of a 3D discretely sampled data set. ... A resel is a resolution element - a concept used in image analysis. ...

External links

• VisualCube, a small volumetric display (true 3d display) out of 6x6x6 voxels, each represented by a 2-color LED
• Volex, a volumetric display using LED
• Voxel3D, voxel based modeling software
• Voxel Section Editor III, voxel based modeling software for Command & Conquer games
• 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
• SensAble Technologies Inc - have developed a haptically (force-feedback) enabled voxel sculpting tool called FreeForm; used in Medical engineering & Product Design