Editing Voxel

{{short description|Element representing a value on a grid in three dimensional space}}
[[File:voxels.svg|thumb|A set of voxels in a stack, with a single voxel shaded]]
[[File:Voxelgitter.png|thumb|Illustration of a voxel grid containing color values]]
{{VG Graphics}}

A '''voxel''' is a three-dimensional counterpart to a [[pixel]]. It represents a value on a [[regular grid]] in a [[three-dimensional space]]. Voxels are frequently used in the [[Data visualization|visualization]] and analysis of [[medical imaging|medical]] and scientific data (e.g. [[geographic information system]]s (GIS)).<ref>Chmielewski, Sz., Tompalski, P. (2017). "Estimating outdoor advertising media visibility with voxel-based approach". ''Applied Geography'', 87:1–13 {{doi|10.1016/j.apgeog.2017.07.007}}. Preprint download:  {{cite web |url=https://www.researchgate.net/publication/318744436 |title=Estimating outdoor advertising media visibility with voxel-based approach (PDF Download Available) |access-date=2017-10-02 |url-status=live |archive-url=https://web.archive.org/web/20171002220053/https://www.researchgate.net/publication/318744436_Estimating_outdoor_advertising_media_visibility_with_voxel-based_approach |archive-date=2017-10-02 }}</ref> They are also commonly used in video games, both as a technological feature, as in ''[[Outcast (video game)|Outcast]]'', and a graphical style, which was popularised by ''[[Minecraft]]''.<ref>{{cite web |last1=Sprinks |first1=Harry Ted |title=10 Games To Play If You Love Voxel Graphics |url=https://gamerant.com/games-play-love-voxel-graphics/ |website=Game Rant |access-date=27 November 2024 |language=en |date=16 August 2023}}</ref>

As with pixels in a 2D [[bitmap]], voxels themselves do not typically have their position (i.e. [[coordinate]]s) explicitly encoded with their values. Instead, [[Rendering (computer graphics)|rendering]] systems infer the position of a voxel based upon its position relative to other voxels (i.e., its position in the [[data structure]] that makes up a single [[Volumetric display|volumetric image]]). Some volumetric displays use voxels to describe their [[Display resolution|resolution]]. For example, a cubic volumetric display might be able to show 512×512×512 (or about 134 million) voxels.

In contrast to pixels and voxels, [[polygon (computer graphics)|polygons]] are often explicitly represented by the coordinates of their [[Vertex (geometry)|vertices]] (as [[Point (geometry)|points]]). A direct consequence of this difference is that polygons can efficiently represent simple 3D structures with much empty or homogeneously filled space, while voxels excel at representing regularly sampled spaces that are non-homogeneously filled.

One of the definitions is: 
<blockquote>
Voxel is an image of a three-dimensional space region limited by given sizes, which has its own ''nodal point'' coordinates in an accepted coordinate system, its own ''form'', its own ''state parameter'' that indicates its belonging to some modeled object, and has ''properties'' of modeled region.
</blockquote>

This definition has the following advantage. If fixed voxel form is used within the whole model it is much easier to operate with voxel ''nodal points'' (i.e. three coordinates of this point). Yet, there is the simple form of record: indexes of the elements in the model set (i.e. integer coordinates). Model set elements in this case are ''state parameters,'' indicating voxel belonging to the modeled object or its separate parts, including their surfaces.<ref name="Shchurova">{{cite journal|last=Shchurova|first=Catherine I.|title=A methodology to design a 3D graphic editor for micro-modeling of fiber-reinforced composite parts|journal=Advances in Engineering Software|date=2015|volume=90|pages=76–82|publisher=Advances in Engineering Software Volume 90, December 2015, Pages 76-82|doi=10.1016/j.advengsoft.2015.07.001}}
</ref>

== Etymology ==
The word ''voxel'' originated by analogy to "[[pixel#Etymology|pixel]]", with ''vo'' representing "[[volume]]" (instead of pixel's "picture") and ''el'' representing "element";<ref name="JF">{{cite book
  | last = Foley | first = James D.
  |author2= Andries van Dam |author3= John F. Hughes |author4= Steven K. Feiner
  | title = Computer Graphics: Principles and Practice
  | publisher= [[Addison-Wesley]]|year= 1990| isbn= 978-0-201-12110-0
  | series= The Systems Programming Series
  | chapter= Spatial-partitioning representations; Surface detail
  | quote= These cells are often called ''voxels'' (volume    elements), in analogy to pixels. 
| title-link = Computer Graphics: Principles and Practice
  }}
</ref> a similar formation with ''el''&nbsp;for "element" is the word "[[Texel (graphics)|texel]]".<ref name=JF />
The term ''hypervoxel'' is a generalization of voxel for [[higher-dimensional space]]s.

== Rendering ==
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 iso-surface extraction, however other methods exist as well.

Both [[Ray tracing (graphics)|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.

=== Incremental error rasterisation ===

Another technique for voxels involves raster graphics where one simply raytraces every pixel of the display into the scene, tracking an [[incremental error algorithm|error term to determine when to step]]. A typical implementation will raytrace each pixel of the display starting at the bottom of the screen using what is known as a y-buffer. When a voxel is reached that has a higher y value on the display it is added to the y-buffer overriding the previous value and connected with the previous y-value on the screen interpolating the color values. There is a major downside to voxel rasterization when transformation is applied which causes severe [[aliasing]]. The advantage was the ability to rasterise using cheap integer calculations on a [[CPU]] without [[hardware acceleration]].<ref name=":0">{{cite web|url=http://www.tnlc.com/eep/voxels.html|title=Voxels|work=tnlc.com|url-status=live|archive-url=https://web.archive.org/web/20140417001519/http://www.tnlc.com/eep/voxels.html|archive-date=2014-04-17}}</ref>

''[[Outcast (video game)|Outcast]]'', and other 1990s video games employed this graphics technique for effects such as [[reflection (computer graphics)|reflection]] and [[bump-mapping]] and usually for [[terrain rendering]]. ''Outcast'''s [[rendering (computer graphics)|graphics engine]] was mainly a combination of a ray casting ([[heightmap]]) engine, used to render the landscape, and a [[texture mapping]] [[polygon mesh|polygon]] engine used to render objects. The "Engine Programming" section of the game's credits in the manual has several subsections related to graphics, among them: "Landscape Engine", "Polygon Engine", "Water & Shadows Engine" and "Special effects Engine".<ref>{{cite book|title=Outcast manual|year=1999|publisher=Infogrames|pages=34}}</ref> Although ''Outcast'' is often cited as a forerunner of voxel technology,<ref>{{Cite journal| title = 'Klötzchenwelten' [Worlds of little blocks] in c't Magazin issue 04/2009 | pages=183| last=Bertuch | first=Manfred | journal=C't: Magazin für Computertechnik| publisher = Heise Zeitschriften Verlag GmbH & Co. KG | year = 2009 | location = Hannover| issn = 0724-8679}}</ref> this is somewhat misleading. The game does not actually model three-dimensional volumes of voxels. Instead, it models the ground as a surface, which may be seen as being made up of voxels. The ground is decorated with objects that are modeled using texture-mapped polygons. When ''Outcast'' was developed, the term "voxel engine", when applied to computer games, commonly referred to a ray casting engine (for example the [[Voxel Space]] engine). On the engine technology page of the game's website, the landscape engine is also referred to as the "Voxels engine".<ref>{{cite web|url=http://www.outcast-thegame.com/tech/paradise.htm |title=OUTCAST – Technology: Paradise |date=7 May 2006 |work=archive.org |url-status=dead |archive-url=https://web.archive.org/web/20060507235618/http://www.outcast-thegame.com/tech/paradise.htm |archive-date=7 May 2006 }}</ref> The engine is purely [[software]]-based: it does not rely on hardware-acceleration via a 3D [[graphics card]].<ref name="Voxel terrain engine">"[http://www.codermind.com/articles/Voxel-terrain-engine-building-the-terrain.html Voxel terrain engine] {{webarchive|url=https://web.archive.org/web/20131113094653/http://www.codermind.com/articles/Voxel-terrain-engine-building-the-terrain.html |date=2013-11-13 }}", introduction. In a coder's mind, 2005.</ref>

[[John Carmack]] also experimented with voxels for the ''[[Quake III Arena]]'' engine.<ref>{{cite web|url=http://www.tomshardware.com/reviews/voxel-ray-casting,2423-2.html|title=A Little Bit Of History – Next-Gen 3D Rendering Technology: Voxel Ray Casting|date=21 October 2009|work=tomshardware.com}}</ref> One such problem cited by Carmack was the lack of graphics cards designed specifically for such rendering requiring them to be software rendered.

''[[Comanche (video game series)|Comanche]]'' was also the first commercial [[flight simulation]] based on voxel technology. [[NovaLogic]] used the proprietary [[Voxel Space]] engine developed for the company by Kyle Freeman<ref>{{cite web|url=http://patents.justia.com/inventor/kyle-g-freeman|title=Kyle G. Freeman Inventions, Patents and Patent Applications – Justia Patents Search|work=justia.com|url-status=live|archive-url=https://web.archive.org/web/20140201194745/http://patents.justia.com/inventor/kyle-g-freeman|archive-date=2014-02-01}}</ref> (written entirely in [[Assembly language]]) to create open landscapes.<ref>{{cite web|url=http://www.flightsim.com/vbfs/content.php?2994-NovaLogic-Awarded-Patent-For-Voxel-Space-Graphics-Engine|title=FlightSim.Com – NovaLogic Awarded Patent For Voxel Space Graphics Engine|work=flightsim.com|url-status=live|archive-url=https://web.archive.org/web/20150924013816/http://www.flightsim.com/vbfs/content.php?2994-NovaLogic-Awarded-Patent-For-Voxel-Space-Graphics-Engine|archive-date=2015-09-24}}</ref> This rendering technique allowed for much more detailed and realistic terrain compared to simulations based on [[vector graphics]] at that time.<ref name="Voxel terrain engine" />

=== Gallery ===
<gallery widths="200px" heights="200px">
3D rendering of a micro CT scan of a piece of dried leaf..ogv|3D rendering of a [[X-ray microtomography|μCT]] scan of a leaf piece, resolution circa 40&nbsp;μm/voxel when viewed at the full size
Ribo-Voxels.png|A (smoothed) rendering of a [[data set]] of voxels for a [[macromolecule]]
</gallery>

== Data ==
A voxel represents a single sample, or data point, on a regularly spaced, three-dimensional grid. This data point can consist of a single piece of data, such as an opacity, or multiple pieces of data, such as a color in addition to opacity. A voxel represents only a single point on this grid, not a volume; the space between each voxel is not represented in a voxel-based dataset. Depending on the type of data and the intended use for the dataset, this missing information may be reconstructed and/or approximated, e.g. via interpolation.

[[File:Abdominal CT with scan range and field of view, with box and text.jpg|thumb|In [[computed tomography]] ([[abdominal CT]] pictured), voxels are generated by multiplying the [[field of view]] (FOV) by the ''scan range''.]]
The value of a voxel may represent various properties. In [[computed tomography|CT]] scans, the values are [[Hounsfield scale|Hounsfield units]], giving the opacity of material to X-rays.<ref name="squires">Novelline, Robert. ''Squire's Fundamentals of Radiology''. Harvard University Press. 5th edition. 1997. {{ISBN|0-674-83339-2}}.</ref>{{rp|29}} Different types of value are acquired from [[magnetic resonance imaging|MRI]] or [[medical ultrasonography|ultrasound]].

Voxels can contain multiple [[scalar (computing)|scalar]] values, essentially vector (tensor) data; in the case of [[ultrasound]] scans with B-mode and [[Medical ultrasonography#Doppler ultrasonography|Doppler]] data, [[density]], and [[volumetric flow rate]] are captured as separate channels of data relating to the same voxel positions.

While voxels provide the benefit of precision and depth of reality, they are typically large data sets and are unwieldy to manage given the bandwidth of common computers. However, through efficient compression and manipulation of large data files, interactive visualization can be enabled on consumer market computers.

Other values may be useful for immediate 3D [[rendering (computer graphics)|rendering]], such as a surface [[surface normal|normal vector]] and [[color]].

Technologies to extend voxels into 4 and 5 dimensions of data are under investigation.<ref>{{Cite web|last=Society|first=The Optical|title=High-speed laser writing method could pack 500 terabytes of data into CD-sized glass disc|url=https://phys.org/news/2021-10-high-speed-laser-method-terabytes-cd-sized.html|access-date=2021-10-31|website=phys.org|language=en}}</ref>

== Uses ==
Uses of voxels include volumetric imaging in medicine and representation of terrain in games and simulations. Voxel terrain is used instead of a [[heightmap]] 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).

=== Computer games ===
* ''[[3D Dot Game Heroes]]'' uses voxels to present retro-looking graphics.
* ''[[7 Days to Die]]'' is a voxel-based open world survival horror game developed by The Fun Pimps Entertainment.
* ''[[Ace of Spades (video game)|Ace of Spades]]'' used [[Ken Silverman]]'s Voxlap engine before being rewritten in a bespoke [[OpenGL]] engine.
* ''[[Amok (video game)|Amok]]'' uses voxels for its environments.<ref>{{cite magazine |title=Review Crew: Amok|magazine=[[Electronic Gaming Monthly]] |issue=93|publisher=[[Ziff Davis]]|date=April 1997|page=53}}</ref>
* ''[[Armored Fist 3]]'' is a computer game made by [[NovaLogic]] that used voxel-based rendering technology.
* ''[[Blade Runner (1997 video game)#Development|Blade Runner]]'' is a video game that used voxels to render characters and artifacts.
* ''[[Castle Story]]'', a castle building Real Time Strategy game in development, has terrain consisting of smoothed voxels.
* ''[[Cloudpunk]]'', a cyberpunk adventure game, is almost entirely voxel-based.
* ''[[Comanche (video game series)|Comanche]]'', a series of computer games made by [[NovaLogic]] that used the [[Voxel Space]] voxel rasterization for terrain rendering.<ref>{{cite web |url=http://projectorgames.net/blog/?p=168 |title=A brief history of Voxel games. &#124; DjArcas's Blog |access-date=2013-12-18 |url-status=live |archive-url=https://web.archive.org/web/20131218235557/http://projectorgames.net/blog/?p=168 |archive-date=2013-12-18 }}</ref>
* ''[[Command & Conquer: Tiberian Sun]]'', ''[[Command & Conquer: Red Alert 2]]'' and ''[[Command & Conquer: Yuri's Revenge]]'' are computer games made by [[Westwood Studios]] that used voxels to render most vehicles.
* ''[[Crysis]]'', as well as ''[[Cryengine 2]]'' and ''[[Cryengine 3]]'', use a combination of [[heightmaps]] and voxels for their terrain systems.
* ''[[Cube World]]'', an [[action role-playing game]], features procedurally generated voxel landscapes.
* ''[[Delta Force (video game)|Delta Force]]'' is a computer game made by [[NovaLogic]] that used the in-house [[Voxel Space]] rendering engine.
* ''[[Dual Universe]]'' is a single-shard universe MMORPG game that uses voxels to build spaceships, civilizations, and space stations.
* ''[[Enshrouded]]'' is a voxel-based survival RPG by Keen Games released in 2024.
* ''[[EverQuest Next]]'' and ''EverQuest Next: Landmark'', cancelled MMORPGs by [[Sony Online Entertainment]], made extensive use of voxels for world creation as well as player generated content
* ''[[Hexplore]]'', a multi-player role playing game, uses a voxel engine allowing the player to rotate the isometric rendered playfield.
* ''[[Hytale]]'' is an upcoming RPG Sandbox voxel-based game which is developed by [[Hypixel Studios]] and funded by [[Riot Games]].
* ''[[Master of Orion III]]'' 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.
* ''[[Medieval Engineers]]'' is the second voxel-based engineering game by [[Keen Software House]] inspired from medieval technology.
* ''[[Minecraft]]'' is a [[Sandbox game|sandbox]] video game that uses voxels to store terrain [[Voxel#Voxel data|data]],<ref>{{cite web |title=Chunk format: Block format |url=http://minecraft.wiki/w/Chunk_format#Block_format |work=Minecraft Wiki |access-date=24 September 2023 |language=en}}</ref> but does not use [[Voxel#Rendering|voxel rendering techniques]]. Instead it uses [[Polygonal modeling|polygon rendering]] to display each voxel as a cubic "block".<ref>{{cite web |title=Tutorials/Units of measure: Distance |url=https://minecraft.wiki/w/Tutorials/Units_of_measure#Distance |access-date=24 September 2023 |work=Minecraft Wiki |language=en}}</ref>
* ''[[Moonglow Bay]]'' is a fishing role-playing video game, released in 2021 and developed by Bunnyhug, using voxel art style.
* ''[[Miner Wars 2081]]'' is a 6DOF open world game made by [[Keen Software House]] that uses its own VRage voxel rendering engine to let the user deform the terrain of asteroids allowing tunnels to be formed.
* ''Nivalis'' is an upcoming cyberpunk slice-of-life, set in voxel-based world, previously featured in ''Cloudpunk''.
* ''[[No Man's Sky]]'' is a space exploration game consisting of procedurally generated star systems containing explorable planets, moons and asteroids made up of voxels. The voxel engine allows for both terrain destruction and creation.
* ''[[Outcast (video game)|Outcast]]'', is a third-person action computer game made by former Belgian [[video game developer]] Appeal,<ref>{{cite web|url=http://www.mobygames.com/company/appeal-sa|title=Appeal S.A. - MobyGames|work=mobygames.com|url-status=live|archive-url=https://web.archive.org/web/20141219131019/http://www.mobygames.com/company/appeal-sa|archive-date=2014-12-19}}</ref> with landscapes rendered by a voxel engine.
* ''[[Phase Zero]]'' is a 2002 unreleased [[Action game|action]]-[[Shooter game|shooter]] [[video game]] for [[Atari Jaguar]], with landscapes rendered by the engine [[Voxel Space]].
* ''[[Planet Coaster]]'' is a 2016 [[construction and management simulation]] developed and published by [[Frontier Developments]] which uses a voxel-based terrain editor.<ref>{{cite news|last1=Zak|first1=Robert|title="There's never been a better time": Planet Coaster rides to meet the demand for deep simulation games|url=http://www.pcgamesn.com/planet-coaster/there-s-never-been-a-better-time-planet-coaster-rides-to-meet-the-demand-for-deep-simulation-games|access-date=11 July 2016|date=4 April 2016|url-status=live|archive-url=https://web.archive.org/web/20160704161730/http://www.pcgamesn.com/planet-coaster/there-s-never-been-a-better-time-planet-coaster-rides-to-meet-the-demand-for-deep-simulation-games|archive-date=4 July 2016}}</ref>
* ''[[Resogun]]'' is a 2013 voxel-based side-scrolling shoot 'em up video game developed by Finnish developer [[Housemarque]].
* ''[[Roblox]]'' uses voxels for terrain, as well as for primitive [[global illumination]] and shadows.
* ''[[Robocraft]]'', a vehicular combat game in which players build combat machines out of voxels and premade components
* ''[[Shadow Warrior]]'' and ''[[Blood (video game)|Blood]]'' use [[Build engine]] for first-person shooter game voxel rendering, instead of [[Sprite (computer graphics)|sprites]], as an option for many of the items pickups and scenery. ''[[Duke Nukem 3D]]'' has a fan-created pack in a similar style.
* ''[[Shattered Steel]]'' featured deforming landscapes using voxel technology.
* ''[[Sid Meier's Alpha Centauri]]'' uses voxel models to render units.
* ''[[SkySaga: Infinite Isles]]'' is a voxel-based sandbox MMORPG, being developed by Radiant Worlds and published by [[Smilegate]].
* ''[[Space Engineers]]'' is a voxel-based sandbox game set in space, developed and published by [[Keen Software House]].
* ''[[Starbase (video game)|Starbase]]'', a voxel-based [[massively multiplayer online role-playing game]] set in space, being developed and published by [[Frozenbyte]].
* ''[[StarMade]]'', a voxel-based sandbox game set in space, developed and published by Robin "Schema" Promesberger.
* ''[[Teardown (video game)|Teardown]]'', a voxel-based game featuring fully destructible environments, developed and published by the studio Tuxedo Labs
* ''[[The Sandbox (2012 video game)|The Sandbox]]''
* ''[[Trove (video game)|Trove]]'' is a voxel-based MMORPG with building elements, developed and published by [[Trion Worlds]].<ref>{{cite web|url=http://trovegame.com|title=Trove – A Voxel MMO Adventure from Trion Worlds|work=trovegame.com|url-status=live|archive-url=https://web.archive.org/web/20140722160000/http://www.trovegame.com/|archive-date=2014-07-22}}</ref>
* ''[[Vangers]]'' is a computer game uses voxels for its two-level terrain system.<ref>{{cite web |url=http://www.kdlab.com/vangers/eng/features.html |title=VANGERS |work=kdlab.com |access-date=2009-12-20 |url-status=dead |archive-url=https://web.archive.org/web/20100114235648/http://www.kdlab.com/vangers/eng/features.html |archive-date=2010-01-14 }}</ref>
* ''[[Veloren]]'', is an action-adventure role-playing game set in a vast fantasy world.<ref>{{cite web |url=https://veloren.net/ |title=Veloren |work=Veloren.net |access-date=2024-06-12 |archive-date=2024-06-12 |url-status=live |archive-url=https://web.archive.org/web/20240612222650/https://veloren.net/ }}</ref>
* ''[[Vox (game)|Vox]]'', released in 2012, is a voxel based exploration/RPG game focused on player generated content.
* ''[[Voxatron]]'', a computer game produced by Lexaloffle, is composed and generated fully using voxels.<ref>{{cite web|url=https://arstechnica.com/gaming/news/2011/01/we-3-voxels-why-voxatron-is-an-exciting-indie-shooter.ars|title=We <3 voxels: why Voxatron is an exciting indie shooter|author=Ars Technica|date=14 January 2011 |url-status=live|archive-url=https://web.archive.org/web/20111013010452/http://arstechnica.com/gaming/news/2011/01/we-3-voxels-why-voxatron-is-an-exciting-indie-shooter.ars|archive-date=2011-10-13}}</ref><ref>{{cite web |url=http://lexaloffle.com/bbs/?tid=201 |title=Lexaloffle BBS :: Voxatron |work=lexaloffle.com |access-date=2011-01-12 |url-status=live |archive-url=https://web.archive.org/web/20110108191219/http://www.lexaloffle.com/bbs/?tid=201 |archive-date=2011-01-08 }}</ref>
* ''[[Werewolf vs. Comanche]]'' is a computer game made by [[NovaLogic]] that used voxel-based rendering technology. It was originally bundled and shipped with the ''Comanche 2'' game although they were two separate games.
* ''[[Worms 4: Mayhem]]'' uses a voxel-based engine to simulate land deformation similar to the older 2D ''Worms'' games.
* ''[[Luanti]]'' (previously ''[[Minetest]]'') is a moddable sandbox video game that uses voxels to store terrain data, but does not use voxel rendering techniques. Instead, it uses polygon rendering to display each voxel as a cubic "block"

== Editors ==
While scientific volume visualization does not require modifying the actual voxel data, voxel editors can be used to create art (especially 3D [[pixel art]]) 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 [[Raster graphics editor|2D raster editor]] tools. These generally store color information in voxels.
* Sculpture: Similar to the [[Digital sculpting|vector counterpart]] 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]] toy.
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 ''toxel'', or temporal voxel.<ref>{{cite book |last1=Hickson |first1=Steven |last2=Birchfield |first2=Stan |last3=Essa |first3=Irfan |last4=Christensen |first4=Henrik |title=2014 IEEE Conference on Computer Vision and Pattern Recognition |chapter=Efficient Hierarchical Graph-Based Segmentation of RGBD Videos |date=2014 |pages=344–351 |doi=10.1109/CVPR.2014.51|arxiv=1801.08981 |isbn=978-1-4799-5118-5 |s2cid=519623 }}</ref> This is used in the case of a [[Four-dimensional space|4D]] 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 toxels, which could be seen as a series of 100 [[Film frame|frames]] 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]] systems.

== See also ==
* [[Maxel]] – material element
* [[Hogel]] - holographic element
* [[Pixel]] – picture element
* [[Plane partition]]
* [[Resel]] – resolution element
* [[Sparse voxel octree]]
* [[Texel (graphics)|Texel]] – texture element
* [[Tixel]] - tactile element
* [[Tomography]]
* [[Volume mesh]]
* [[Volume rendering]]

== References ==
{{Reflist|30em}}

== External links ==
* {{moby game|id=-group/visual-technique-style-voxel-graphics|name=Games with voxel graphics}}
* [http://labs.cs.sunysb.edu/labs/projects/volume/Papers/Voxel/ Fundamentals of voxelization] [https://web.archive.org/web/20200509065342/http://labs.cs.sunysb.edu/labs/projects/volume/Papers/Voxel/ "Archived"]
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