Voxel

# Voxel

Discussion

Encyclopedia
A voxel is a volume element, representing a value on a regular grid
Regular grid
A regular grid is a tessellation of n-dimensional Euclidean space by congruent parallelotopes . Grids of this type appear on graph paper and may be used in finite element analysis as well as finite volume methods and finite difference methods...

in three dimensional
3D computer graphics
3D computer graphics are graphics that use a three-dimensional representation of geometric data that is stored in the computer for the purposes of performing calculations and rendering 2D images...

space. This is analogous to a pixel
Pixel
In digital imaging, a pixel, or pel, is a single point in a raster image, or the smallest addressable screen element in a display device; it is the smallest unit of picture that can be represented or controlled....

, which represents 2D
2D computer graphics
2D computer graphics is the computer-based generation of digital images—mostly from two-dimensional models and by techniques specific to them...

image data in a bitmap
Bitmap
In computer graphics, a bitmap or pixmap is a type of memory organization or image file format used to store digital images. The term bitmap comes from the computer programming terminology, meaning just a map of bits, a spatially mapped array of bits. Now, along with pixmap, it commonly refers to...

(which is sometimes referred to as a pixmap
Raster graphics
In computer graphics, a raster graphics image, or bitmap, is a data structure representing a generally rectangular grid of pixels, or points of color, viewable via a monitor, paper, or other display medium...

). 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
Point (geometry)
In geometry, topology and related branches of mathematics a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero-dimensional; i.e., they do not have volume, area, length, or any other higher-dimensional analogue. In branches of mathematics...

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
Medical imaging
Medical imaging is the technique and process used to create images of the human body for clinical purposes or medical science...

and scientific
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

data. Some volumetric display
Volumetric display
A volumetric display device is a graphical display device that forms a visual representation of an object in three physical dimensions, as opposed to the planar image of traditional screens that simulate depth through a number of different visual effects...

s use voxels to describe their resolution. For example, a display might be able to show 512×512×512 voxels.

## Voxel data

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 filter
Low-pass filter
A low-pass filter is an electronic filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter...

ing the data set. Visually acceptable approximations to this low pass filter can be attained by polynomial interpolation
Polynomial interpolation
In numerical analysis, polynomial interpolation is the interpolation of a given data set by a polynomial: given some points, find a polynomial which goes exactly through these points.- Applications :...

such as tri-linear or tri-cubic interpolation
Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points....

.

The value of a voxel may represent various properties. In CT
Computed tomography
X-ray computed tomography or Computer tomography , is a medical imaging method employing tomography created by computer processing...

scans, the values are Hounsfield units
Hounsfield scale
The Hounsfield scale, named after Sir Godfrey Newbold Hounsfield, is a quantitative scale for describing radiodensity.-Definition:The Hounsfield unit scale is a linear transformation of the original linear attenuation coefficient measurement into one in which the radiodensity of distilled water at...

, giving the opacity of material to X-rays. Different types of value are acquired from MRI
Magnetic resonance imaging
Magnetic resonance imaging , nuclear magnetic resonance imaging , or magnetic resonance tomography is a medical imaging technique used in radiology to visualize detailed internal structures...

or ultrasound
Medical ultrasonography
Diagnostic sonography is an ultrasound-based diagnostic imaging technique used for visualizing subcutaneous body structures including tendons, muscles, joints, vessels and internal organs for possible pathology or lesions...

.

Voxels can contain multiple scalar
Scalar (computing)
In computing, a scalar variable or field is one that can hold only one value at a time; as opposed to composite variables like array, list, hash, 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...

values - essentially vector data; in the case of ultrasound
Ultrasound
Ultrasound is cyclic sound pressure with a frequency greater than the upper limit of human hearing. Ultrasound is thus not separated from "normal" sound based on differences in physical properties, only the fact that humans cannot hear it. Although this limit varies from person to person, it is...

scans with B-mode and Doppler data, density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

, and volumetric flow rate
Volumetric flow rate
The volumetric flow rate in fluid dynamics and hydrometry, is the volume of fluid which passes through a given surface per unit time...

are captured as separate channels of data relating to the same voxel positions.

Other values may be useful for immediate 3D rendering
Rendering (computer graphics)
Rendering is the process of generating an image from a model , by means of computer programs. A scene file contains objects in a strictly defined language or data structure; it would contain geometry, viewpoint, texture, lighting, and shading information as a description of the virtual scene...

, such as a surface normal vector
Surface normal
A surface normal, or simply normal, to a flat surface is a vector that 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. The word "normal" is also used as an adjective: a line normal to a...

and color
Color
Color or colour is the visual perceptual property corresponding in humans to the categories called red, green, blue and others. Color derives from the spectrum of light interacting in the eye with the spectral sensitivities of the light receptors...

.

## Uses

Common uses of voxels include volumetric imaging in medicine and representation of terrain in games and simulations. Voxel terrain is used instead of a heightmap
Heightmap
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...

because of its ability to represent overhangs, caves, arches, and other 3D terrain features. These concave features cannot be represented in a heightmap due to only the top 'layer' of data being represented, leaving everything below it filled (the volume that would otherwise be the inside of the caves, or the underside of arches or overhangs).

### Visualization

A volume containing voxels can be visualized either by direct volume rendering
Volume rendering
In scientific visualization and computer graphics, volume rendering is a set of techniques 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 aCT, MRI, or MicroCT scanner....

or by the extraction of polygon
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...

iso-surfaces which follow the contours of given threshold values. The marching cubes
Marching cubes
Marching cubes is a computer graphics algorithm, published in the 1987 SIGGRAPH proceedings by Lorensen and Cline, for extracting a polygonal mesh of an isosurface from a three-dimensional scalar field...

algorithm is often used for iso-surface extraction, however other methods exist as well.

### Computer gaming

• C4 Engine
C4 Engine
The C4 Engine is a computer game engine developed by Terathon Software that is used to create 3D games and other types of interactive virtual simulations for Windows , Mac OS X , and PlayStation 3...

is a game engine that uses voxels for in game terrain and has a voxel editor for its built in level editor. C4 Engine uses a LOD system with its voxel terrain that was developed by the game engine's creator. All games using the current or newer versions of the engine have the ability to use voxels.
• Upcoming Miner Wars 2081
Miner Wars 2081
Miner Wars 2081 is a first-person action-survival space simulation game set in the year 2081. This first instalment of the Miner Wars franchise is currently being developed by Keen Software House a...

uses their own Voxel Rage engine to let the user deform the terrain of asteroids allowing tunnels to be formed.
• Many NovaLogic
NovaLogic
NovaLogic is a software developer and publisher established in 1985 and based in Calabasas, California. The company was founded by current CEO John A. Garcia....

games have used voxel-based rendering technology, including the Delta Force, Armored Fist and Comanche series
Comanche series
Comanche is a series of simulation games published by NovaLogic. The goal of each of these games is to fly military missions in a RAH-66 Comanche attack helicopter, which was in development and prototyping at the time of release....

.
• Westwood Studios
Westwood Studios
Westwood Studios was a computer and video game developer, based in Las Vegas, Nevada. It was founded by Brett Sperry and Louis Castle in as Westwood Associates, and renamed to Westwood Studios when it merged with Virgin Interactive in...

' Command & Conquer: Tiberian Sun
Command & Conquer: Tiberian Sun
Command & Conquer: Tiberian Sun is a real-time strategy video game developed by Westwood Studios and released in . The main storyline follows the second major war between the Global Defense Initiative of the United Nations, and the global terrorist organization known as the Brotherhood of Nod who...

and Command & Conquer: Red Alert 2
Command & Conquer: Red Alert 2
Command & Conquer: Red Alert 2 is a 2.5D real-time strategy computer game by Westwood Studios, which was released for Microsoft Windows on October 23, 2000 as the follow-up to Command & Conquer: Red Alert. Set in the early 1970s, Red Alert 2 supposedly picks up at the conclusion of the Allied...

use voxels to render most vehicles.
• Westwood Studios
Westwood Studios
Westwood Studios was a computer and video game developer, based in Las Vegas, Nevada. It was founded by Brett Sperry and Louis Castle in as Westwood Associates, and renamed to Westwood Studios when it merged with Virgin Interactive in...

' Blade Runner video game used voxels to render characters and artifacts.
• Outcast, a game made by Belgian
Belgium
Belgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...

developer
Video game developer
A video game developer is a software developer that creates video games. A developer may specialize in a certain video game console, such as Nintendo's Wii, Microsoft's Xbox 360, Sony's PlayStation 3, or may develop for a variety of systems, including personal computers.Most developers also...

Appeal, sports outdoor landscapes that are rendered by a voxel engine.
• The videogame Amok for the Sega Saturn
Sega Saturn
The is a 32-bit fifth-generation video game console that was first released by Sega on November 22, 1994 in Japan, May 11, 1995 in North America, and July 8, 1995 in Europe...

makes use of voxels in its scenarios.
• The computer game Vangers
Vangers
Vangers is a 1998 video game that combines elements of the racing and role-playing genres, developed by K-D Lab, a Russian company...

uses voxels for its two-level terrain system.
• The computer game Thunder Brigade was based entirely on a voxel renderer, according to BlueMoon Interactive making videocards redundant and offering increasing detail instead of decreasing detail with proximity.
• Master of Orion III
Master of Orion III
Master of Orion III is a 4X turn-based strategy game and the third in the Master of Orion series. MoO3 was developed by Quicksilver Software and published by Infogrames on February 25, 2003.-Backstory:...

uses voxel graphics to render space battles and solar systems. Battles displaying 1000 ships at a time were rendered slowly on computers without hardware graphic acceleration.
• Sid Meier's Alpha Centauri
Sid Meier's Alpha Centauri
Sid Meier's Alpha Centauri is the critically acclaimed science fiction 4X turn-based strategy video game sequel to the Civilization series. Sid Meier, designer of Civilization, and Brian Reynolds, designer of Civilization II, developed Alpha Centauri after they left MicroProse to join the newly...

uses voxel models to render units.
• Build engine
Build engine
The Build engine is a first-person shooter engine created by Ken Silverman for 3D Realms. Like the Doom engine, the Build engine represents its world on a two-dimensional grid using closed 2D shapes called sectors, and uses simple flat objects called sprites to populate the world geometry with...

Shadow Warrior, often known by its initials SW, is a first-person shooter computer game developed by 3D Realms and released on May 13, 1997 by GT Interactive. Shadow Warrior was developed using Ken Silverman's Build engine and improved on 3D Realms' previous Build engine game, Duke Nukem 3D...

and Blood use voxels instead of sprites
Sprite (computer graphics)
In computer graphics, a sprite is a two-dimensional image or animation that is integrated into a larger scene...

as an option for many of the items pickups and scenery. Duke Nukem 3D
Duke Nukem 3D
Duke Nukem 3D is a first-person shooter computer game developed by 3D Realms and published by GT Interactive Software. The full version was released for the PC . It is a sequel to the platform games Duke Nukem and Duke Nukem II published by Apogee...

has an optional voxel model pack created by fans, which contains the high resolution pack models converted to voxels.
• Crysis
Crysis
Crysis is a science fiction first-person shooter video game developed by Crytek , published by Electronic Arts for Microsoft Windows, and released in November 2007. It is the first game of a trilogy. A separate game entitled Crysis Warhead was released on September 12, 2008, and follows similar...

uses a combination of heightmaps and voxels for its terrain system.
• Worms 4: Mayhem
Worms 4: Mayhem
Worms 4: Mayhem is a 3D artillery game in the Worms series developed by Team17. It is much like its 3D predecessor Worms 3D, except that players can customize their worm's appearance as well as create their own unique weapons in an added feature called "The Weapon Factory." The game also contains...

uses a "poxel" (polygon
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...

and voxel) engine to simulate land deformation similar to the older 2D Worms games.
• The computer game Minecraft
Minecraft
Minecraft is a sandbox-building independent video game written in Java originally by Swedish creator Markus "Notch" Persson and now by his company, Mojang, formed from the proceeds of the game. It was released as an alpha on May 17, 2009, with a beta version on December 20, 2010...

uses large-scale voxels to simulate randomly generated terrain, although, the voxels are referred to as "blocks" due to their size.
• The multi-player role playing game Hexplore
Hexplore
Hexplore is a 1998 role playing computer game from Infogrames and Doki Denki Studio.- Premise :Set in 1000 AD, the player explores the world as MacBride, the adventurer. Early in the game you are joined by three party members, an archer, a warrior and a sorcerer...

uses a voxel engine allowing the player to rotate the isometric rendered playfield.
• Voxelstein 3D also uses voxels for fully destructible environments.
• The computer game Voxatron, produced by Lexaloffle, is composed and generated fully using voxels.
Ace of Spades is a free-to-play sandbox building and FPS game developed by Ben Aksoy for the PC. The game notably uses Ken Silverman's Voxlap engine.-Summary:...

uses Ken Silverman
Ken Silverman
Ken Silverman is a game programmer, best known for writing the Build engine used in Duke Nukem 3D, Shadow Warrior, Blood, and more than a dozen other games in the mid- to late-1990s...

's Voxlap engine.
• The game Blockade Runner uses a Voxel engine.

## Voxel editors

While scientific volume visualization doesn't require modifying the actual voxel data, voxel editors can be used to create art (especially 3D pixel art
Pixel art
Pixel art is a form of digital art, created through the use of raster graphics software, where images are edited on the pixel level. Graphics in most old computer and video games, graphing calculator games, and many mobile phone games are mostly pixel art.- History :The term pixel art was first...

) and models for voxel based games.
Some editors are focused on a single approach to voxel editing while others mix various approaches. Some common approaches are:
• Slice based – The volume is sliced in one or more axes and the user can edit each image individually using 2D raster editor
Raster graphics editor
A raster graphics editor is a computer program that allows users to paint and edit pictures interactively on the computer screen and save them in one of many popular “bitmap” or “raster” formats such as JPEG, PNG, GIF and TIFF....

tools. These generally store color information in voxels.
• Sculpture – Similar to the vector counterpart
Digital sculpting
Digital sculpting, also known as Sculpt Modeling or 3D Sculpting, is the use of software that offers tools to push, pull, smooth, grab, pinch or otherwise manipulate a digital object as if it were made of a real-life substance such as clay....

but with no topology constraints. These usually store density information in voxels and lack color information.
• Building blocks – The user can add and remove blocks just like a construction set
Construction set
A construction set is a set of standardized pieces that allow for the construction of a variety of different models. The pieces avoid the lead time of manufacturing custom pieces, and of requiring special training or design time to construct complex systems...

toy.
• Minecraft
Minecraft
Minecraft is a sandbox-building independent video game written in Java originally by Swedish creator Markus "Notch" Persson and now by his company, Mojang, formed from the proceeds of the game. It was released as an alpha on May 17, 2009, with a beta version on December 20, 2010...

is a game built around a voxel art editor, where the player builds voxel art in a monster infested voxel world.

### Voxel editors for games

Many game developers use in-house editors that are not released to the public, but a few games have publicly available editors, some of them created by players.
• Slice based fan-made Voxel Section Editor III for Command & Conquer: Tiberian Sun
Command & Conquer: Tiberian Sun
Command & Conquer: Tiberian Sun is a real-time strategy video game developed by Westwood Studios and released in . The main storyline follows the second major war between the Global Defense Initiative of the United Nations, and the global terrorist organization known as the Brotherhood of Nod who...

and Command & Conquer: Red Alert 2
Command & Conquer: Red Alert 2
Command & Conquer: Red Alert 2 is a 2.5D real-time strategy computer game by Westwood Studios, which was released for Microsoft Windows on October 23, 2000 as the follow-up to Command & Conquer: Red Alert. Set in the early 1970s, Red Alert 2 supposedly picks up at the conclusion of the Allied...

.
• SLAB6 and VoxEd are sculpture based voxel editors used by Voxlap engine games, including Voxelstein 3D and Ace of Spades
Ace of Spades is a free-to-play sandbox building and FPS game developed by Ben Aksoy for the PC. The game notably uses Ken Silverman's Voxlap engine.-Summary:...

.
• The official Sandbox 2 editor for CryEngine 2 games (including Crysis
Crysis
Crysis is a science fiction first-person shooter video game developed by Crytek , published by Electronic Arts for Microsoft Windows, and released in November 2007. It is the first game of a trilogy. A separate game entitled Crysis Warhead was released on September 12, 2008, and follows similar...

) has support for sculpting voxel based terrain.

### General purpose voxel editors

There are a few voxel editors available that are not tied to specific games or engines. They can be used as alternatives or complements to traditional 3D vector modeling.

## Extensions

A generalization of a voxel is the doxel, or dynamic voxel. This is used in the case of a 4D
3-D film
A 3-D film or S3D film is a motion picture that enhances the illusion of depth perception...

dataset, for example, an image sequence that represents 3D space together with another dimension such as time. In this way, an image could contain 100×100×100×100 doxels, which could be seen as a series of 100 frames
Film frame
In filmmaking, video production, animation, and related fields, a film frame or video frame is one of the many still images which compose the complete moving picture...

of a 100×100×100 volume image (the equivalent for a 3D image would be showing a 2D cross section of the image in each frame). Although storage and manipulation of such data requires large amounts of memory, it allows the representation and analysis of spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

systems.

• Pixel
Pixel
In digital imaging, a pixel, or pel, is a single point in a raster image, or the smallest addressable screen element in a display device; it is the smallest unit of picture that can be represented or controlled....

– picture element
• Resel
Resel
A resel is a resolution element - a concept used in image analysis. It describes the actual spatial image resolution in an image .The number of resels in the image will be lower or equal to the number of pixel/voxels in the image....

– resolution element
• Sparse voxel octree
Sparse voxel octree
A sparse voxel octree is a 3D computer graphics rendering technique using a raycasting or sometimes a ray tracing approach into an octree data representation....

• Texel
Texel (graphics)
A texel, or texture element is the fundamental unit of texture space, used in computer graphics. Textures are represented by arrays of texels, just as pictures are represented by arrays of pixels....

– texture element
• Volume rendering
Volume rendering
In scientific visualization and computer graphics, volume rendering is a set of techniques 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 aCT, MRI, or MicroCT scanner....