# Voxel

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).

## 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.

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.

## 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.

### Computer gaming

• Many NovaLogic games have used voxel-based rendering technology, including the Delta Force series and the Comanche series.
• Westwood Studios' and 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.
• The multi-player role playing game Hexplore uses a voxel engine allowing the player to rotate the isometric rendered playfield.

A portmanteau (IPA: /pɔərtˈmÃ¦ntoʊ/) is a word or morpheme that fuses two or more words or word parts to give a combined or loaded meaning.
regular grid is a tessellation of the Euclidean plane by congruent rectangles or a space-filling tessellation of rectilinear parallelepipeds. Grids of this type appear on graph paper and may be used in finite element analysis.
3D computer graphics (in contrast to 2D computer graphics) are graphics that utilize a three-dimensional representation of geometric data that is stored in the computer for the purposes of performing calculations and rendering 2D images.
pixel (short for picture element, using the common abbreviation "pix" for "pictures") is a single point in a graphic image. Each such information element is not really a dot, nor a square, but an abstract sample.
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 refers to the 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
Science (from the Latin scientia, 'knowledge'), in the broadest sense, refers to any systematic knowledge or practice.[1] Examples of the broader use included political science and computer science, which are not incorrectly named, but rather named according to
3D display is any display device capable of conveying three-dimensional images to the viewer.

There are many types of 3D displays: stereoscopic 3D displays show a different image to each eye; autostereoscopic 3D displays do this without the need for any special glasses or
coordinate system is a system for assigning an n-tuple of numbers or scalars to each point in an n-dimensional space. "Scalars" in many cases means real numbers, but, depending on context, can mean complex numbers or elements of some other commutative ring.
Computed tomography (CT), originally known as computed axial tomography (CAT or CT scan) and body section roentgenography, is a medical imaging method employing tomography where digital geometry processing is used to generate a three-dimensional image of the
The Hounsfield scale is a quantitative scale for describing radiodensity.

## Definition

The radiodensity of distilled water at standard pressure and temperature (STP) is defined as zero Hounsfield units (HU). The radiodensity of air at STP is defined as -1000 HU.
Magnetic resonance imaging (MRI), formerly referred to as magnetic resonance tomography (MRT) and, in scientific circles and as originally marketed by companies such as General Electric, nuclear magnetic resonance imaging (NMRI) or NMR zeugmatography imaging
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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. In some contexts, a scalar value may be understood to be numeric. A scalar data type is the type of a scalar variable.
Ultrasound is a cyclic sound pressure with a frequency greater than the upper limit of human hearing, this limit being approximately 20 kilohertz (20,000 hertz).

## Ability to hear ultrasound

In physics, density is mass m per unit volume V—how heavy something is compared to its size. A small, heavy object, such as a rock or a lump of lead, is denser than a lighter object of the same size or a larger object of the same weight, such as pieces of
In fluid dynamics and hydrometry, the volumetric flow rate, also volume flow rate and rate of fluid flow, is the volume of fluid which passes through a given surface per unit time (for example cubic meters per second [m3 s-1
Rendering is the process of generating an image from a model, by means of computer programs. The model is a description of three dimensional objects in a strictly defined language or data structure. It would contain geometry, viewpoint, texture, lighting, and shading information.
surface normal, or simply normal, to a flat surface is a vector which is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P.
Color or colour[1] (see spelling differences) is the visual perceptual property corresponding in humans to the categories called red, yellow, blue, black, etc.
heightmap or heightfield is a raster image used to store values, such as surface elevation data, for display in 3D computer graphics. A heightmap can be used in bump mapping to calculate where this 3D data would create shadow in a material, in displacement mapping to
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.
Volume rendering is a technique used to display a 2D projection of a 3D discretely sampled data set.

A typical 3D data set is a group of 2D slice images acquired by a CT or MRI scanner. Usually these are acquired in a regular pattern (e.g.
POLYGONE is an Electronic Warfare Tactics Range located on the border between France and Germany. It is one of only two in Europe, the other being RAF Spadeadam.

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Marching cubes is a computer graphics algorithm, published in the 1987 SIGGRAPH proceedings by Lorensen and Cline,[1] for extracting a polygonal mesh of an isosurface from a 3D scalar field (sometimes called voxels).
NovaLogic Inc.

Corporation
Founded 1985

Key people Manos, John Garcia
Industry Computer and video game industry
Products Delta Force games and the Comanche Series of games
Owner John Garcia
Delta Force is a tactical first-person shooter computer game by developer and publisher NovaLogic. It was released for the PC on November 1, 1998. Delta Force was designed to be a military simulation loosely based on the Delta Force special operations force.
Comanche is a series of computer games published by NovaLogic. The goal of each of these games is to fly military missions in a Comanche helicopter. It was the first commercial flight simulation based on voxel technology via the company's proprietary Voxel Space engine
Westwood Studios

Video game developer (defunct)
Founded 1985

Industry Video games
Products Command & Conquer
Website Westwood Studios
Westwood Studios
Westwood Studios

Video game developer (defunct)
Founded 1985