Editing 2.5D (section)

==Computer graphics==

===Axonometric and oblique projection===
{{See also|Isometric computer graphics}}
[[File:Lincity-ng.png|225px|thumb|''[[Lincity]]'' tiles 2D [[axonometric]] graphical elements to form a pseudo-3D game environment.]]

In [[axonometric projection]] and [[oblique projection]], two forms of [[parallel projection]], the viewpoint is rotated slightly to reveal other facets of the environment than what are visible in a [[top-down perspective]] or side view, thereby producing a three-dimensional effect. An object is "considered to be in an inclined position resulting in foreshortening of all three axes",<ref name="WPCleanerAuto1">{{cite web|url=http://www.merriam-webster.com/dictionary/axonometric%20projection|title=Axonometric Projection|publisher=[[Merriam-Webster]]|website=merriam-webster.com|access-date=19 March 2018|archive-date=19 September 2011|archive-url=https://web.archive.org/web/20110919224952/http://www.merriam-webster.com/dictionary/axonometric%20projection|url-status=dead}}</ref> and the image is a "representation on a single plane (as a drawing surface) of a three-dimensional object placed at an angle to the plane of projection."<ref name="WPCleanerAuto1" /> Lines perpendicular to the plane become points, lines parallel to the plane have true length, and lines inclined to the plane are foreshortened.

They are popular camera perspectives among [[2D computer graphics|2D]] video games, most commonly those released for [[History of video game consoles (fourth generation)|16-bit]] or earlier and [[Handheld video game|handheld consoles]], as well as in later [[strategy video game|strategy]] and [[role-playing video game]]s. The advantage of these perspectives is that they combine the visibility and mobility of a [[Top-down perspective|top-down game]] with the character recognizability of a [[Side-scrolling video game|side-scrolling game]]. Thus the player can be presented an overview of the game world in the ability to see it from above, more or less, and with additional details in artwork made possible by using an angle: Instead of showing a humanoid in top-down perspective, as a head and shoulders seen from above, the entire body can be drawn when using a slanted angle; turning a character around would reveal how it looks from the sides, the front and the back, while the top-down perspective will display the same head and shoulders regardless.

{{multiple image
| align     = left
| width     = 125
| image1    = Sprite anatomy 2d.svg
| image2    = Sprite anatomy 3d.svg
| footer    = Anatomy of an axonometric sprite. 2D [[Sprite (computer graphics)|sprite]] coordinates are on the left. 3D model coordinates are on the right.
}}
There are three main divisions of axonometric projection: ''isometric'' (equal measure), ''dimetric'' (symmetrical and unsymmetrical), and ''trimetric'' (single-view or only two sides). The most common of these drawing types in [[engineering drawing]] is isometric projection. This projection is tilted so that all three axes create equal angles at intervals of 120 degrees. The result is that all three axes are equally foreshortened. In video games, a form of dimetric projection with a 2:1 pixel ratio is more common due to the problems of anti-aliasing and square pixels found on most computer monitors.

In [[oblique projection]] typically all three axes are shown without foreshortening. All lines parallel to the axes are drawn to scale, and diagonals and curved lines are distorted. One tell-tale sign of oblique projection is that the face pointed toward the camera retains its right angles with respect to the image plane.{{clarify|date=January 2011}}

Two examples of oblique projection are ''[[Ultima VII: The Black Gate]]'' and ''[[Paperboy (video game)|Paperboy]]''. Examples of axonometric projection include ''[[SimCity 2000]]'', and the role-playing games ''[[Diablo (video game)|Diablo]]'' and ''[[Baldur's Gate (video game)|Baldur's Gate]]''.

===Billboarding===
In three-dimensional scenes, the term billboarding is applied to a technique in which objects are sometimes represented by two-dimensional images applied to a single polygon which is typically kept perpendicular to the line of sight. The name refers to the fact that objects are seen as if drawn on a [[billboard]]. This technique was commonly used in early 1990s video games when consoles did not have the hardware power to render fully 3D objects. This is also known as a backdrop. This can be used to good effect for a significant performance boost when the geometry is sufficiently distant that it can be seamlessly replaced with a 2D [[Sprite (computer graphics)|sprite]]. In games, this technique is most frequently applied to objects such as particles (smoke, sparks, rain) and low-detail vegetation. It has since become mainstream, and is found in many games such as ''[[Rome: Total War]]'', where it is exploited to simultaneously display thousands of individual soldiers on a battlefield. Early examples include early first-person shooters like ''[[Marathon Trilogy]]'', ''[[Wolfenstein 3D]]'', ''[[Doom (1993 video game)|Doom]]'', ''[[Hexen: Beyond Heretic|Hexen]]'' and ''[[Duke Nukem 3D]]'' as well as racing games like ''[[Carmageddon]]'' and ''[[Super Mario Kart]]'' and platformers like ''[[Super Mario 64]]''.

===Skyboxes and skydomes===
{{See also|Skybox (video games)}}
Skyboxes and skydomes are methods used to easily create a background to make a game [[level (video gaming)|level]] look bigger than it really is. If the level is enclosed in a cube, the sky, distant mountains, distant buildings, and other unreachable objects are rendered onto the cube's faces using a technique called [[cube mapping]], thus creating the illusion of distant three-dimensional surroundings.  A ''skydome'' employs the same concept but uses a [[sphere]] or [[Sphere|hemisphere]] instead of a cube.

As a viewer moves through a 3D scene, it is common for the skybox or skydome to remain stationary with respect to the viewer. This technique gives the skybox the illusion of being very far away since other objects in the scene appear to move, while the skybox does not. This imitates real life, where distant objects such as clouds, stars and even mountains appear to be stationary when the viewpoint is displaced by relatively small distances. Effectively, everything in a skybox will always appear to be infinitely distant from the viewer.  This consequence of skyboxes dictates that designers should be careful not to carelessly include images of discrete objects in the textures of a skybox since the viewer may be able to perceive the inconsistencies of those objects' sizes as the scene is traversed.

===Scaling along the Z axis===
In some games, sprites are scaled larger or smaller depending on its distance to the player, producing the illusion of motion along the Z (forward) axis. [[Sega]]'s 1986 video game ''[[Out Run]]'', which runs on the [[Sega OutRun]] [[arcade system board]], is a good example of this technique.

In ''Out Run'', the player drives a Ferrari into depth of the game window. The palms on the left and right side of the street are the same [[bitmap]], but have been scaled to different sizes, creating the illusion that some are closer than others. The angles of movement are "left and right" and "into the depth" (while still capable of doing so technically, this game did not allow making a U-turn or going into reverse, therefore moving "out of the depth", as this did not make sense to the high-speed game play and tense time limit). Notice the view is comparable to that which a driver would have in [[reality]] when driving a car. The position and size of any billboard is generated by a (complete 3D) perspective transformation as are the vertices of the poly-line representing the center of the street. Often the center of the street is stored as a spline and sampled in a way that on straight streets every sampling point corresponds to one scan-line on the screen. Hills and curves lead to multiple points on one line and one has to be chosen. Or one line is without any point and has to be interpolated lineary from the adjacent lines. Very memory intensive billboards are used in ''Out Run'' to draw corn-fields and water waves which are wider than the screen even at the largest viewing distance and also in [[Test Drive (1987 video game)|''Test Drive'']] to draw trees and cliffs.

''[[Drakkhen]]'' was notable for being among the first [[role-playing video game]]s to feature a three-dimensional playing field. However, it did not employ a conventional 3D game engine, instead emulating one using character-scaling algorithms. The player's party travels overland on a flat terrain made up of vectors, on which 2D objects are zoomed. ''Drakkhen'' features an animated day-night cycle, and the ability to wander freely about the game world, both rarities for a game of its era. This type of engine was later used in the game ''[[Eternam]]''.

Some mobile games that were released on the Java ME platform, such as the mobile version of [[Asphalt Urban GT|Asphalt: Urban GT]] and [[Driver: L.A. Undercover]], used this method for rendering the scenery. While the technique is similar to some of Sega's arcade games, such as [[Thunder Blade]] and [[Cool Riders]] and the 32-bit version of [[Road Rash (video game)#CD-based versions|Road Rash]], it uses polygons instead of sprite scaling for buildings and certain objects though it looks flat shaded. Later mobile games (mainly from Gameloft), such as [[Asphalt 4: Elite Racing]] and the mobile version of [[Iron Man 2 (video game)|Iron Man 2]], uses a mix of sprite scaling and texture mapping for some buildings and objects.

===Parallax scrolling===
{{Main|Parallax scrolling}}
[[File:Parallax_scroll.gif|thumb|225px|right|An example of [[parallax scrolling]]|alt=Three different image layers scrolling at different speeds]]
[[Parallax]]ing refers to when a collection of [[2D computer graphics|2D]] [[sprite (computer graphics)|sprite]]s or layers of sprites are made to move independently of each other and/or the background to create a sense of added depth.<ref name="Pile">{{cite book |last=Pile Jr |first=John |author-link=John Pile Jr |date=May 2013 |title=2D Graphics Programming for Games |url=http://www.crcpress.com/product/isbn/9781466501898 |location=New York, NY |publisher=CRC Press |isbn=978-1466501898 }}</ref>{{rp|103}} This depth cue is created by relative motion of layers. The technique grew out of the [[multiplane camera]] technique used in [[traditional animation]] since the 1940s.<ref name=art>{{cite web|title=The Art of Parallax Scrolling |url=http://mos.futurenet.com/pdf/net/NET165_tut_flash.pdf |first=Wyatt |last=Paul |date=August 2007 |access-date=2009-07-06 |url-status=dead |archive-url=https://web.archive.org/web/20091007223458/http://mos.futurenet.com/pdf/net/NET165_tut_flash.pdf |archive-date=2009-10-07 }}</ref> This type of graphical effect was first used in the 1982 [[arcade game]] ''[[Moon Patrol]]''.<ref>{{cite web|title=Chronology of the History of Video Games: Golden Age |url=http://www.thocp.net/software/games/golden_age.htm |first=Ted |last=Stahl |date=2006-07-26 |access-date=2009-11-21 |archive-url=https://web.archive.org/web/20091127183910/http://www.thocp.net/software/games/golden_age.htm |archive-date=27 November 2009 |url-status=live }}</ref>
Examples include the skies in ''[[Rise of the Triad]]'', the arcade version of ''[[Rygar]]'', ''[[Sonic the Hedgehog (1991 video game)|Sonic the Hedgehog]]'', ''[[Street Fighter II]]'', ''[[Shadow of the Beast (1989 video game)|Shadow of the Beast]]'' and ''[[Castlevania: Rondo of Blood#Castlevania: The Dracula X Chronicles|Dracula X Chronicles]]'', as well as ''[[Super Mario World]]''.

===Mode 7===
{{Main|Mode 7}}
[[Mode 7]], a display system effect that included rotation and scaling, allowed for a 3D effect while moving in any direction without any actual 3D models, and was used to simulate 3D graphics on the [[Super Nintendo Entertainment System|SNES]].

===Ray casting===
{{Main|Ray_casting#Ray_casting_in_early_computer_games|label 1=Raycasting in early computer games}}
[[File:Camera Rotation vs Shearing.gif|thumb|right|While tricks such as camera shearing (as seen on the right) are sometimes used to create an illusion of rotation, ray casting renderers cannot rotate said camera vertically<ref name="giantbomb_raycasting">{{cite web|url=https://www.giantbomb.com/ray-casting/3015-1517/|title=Ray Casting (Concept) - Giant Bomb|access-date=31 August 2021}}</ref> like true 3D renderers (left).]]
Ray casting is a [[First-person_(video_games)|first person]] pseudo-3D technique in which a ray for every vertical slice of the screen is sent from the position of the camera. These rays shoot out until they hit an object or wall, and that part of the wall is rendered in that vertical screen slice.<ref>{{cite web|url=http://lodev.org/cgtutor/raycasting.html|title=Raycasting|website=lodev.org|access-date=19 March 2018}}</ref> Due to the limited camera movement and internally 2D playing field, this is often considered 2.5D.<ref name="explanation_raycasting_2.5d">{{cite web|url=https://bytecode77.com/castenstein|access-date=31 August 2021|title=Castenstein - bytecode77}}</ref>

===Bump, normal and parallax mapping===
{{Main|Bump mapping|Normal mapping|Parallax mapping}}
'''Bump mapping''', '''normal mapping''' and '''parallax mapping''' are techniques applied to [[texture mapping|textures]] in [[3D rendering]] applications such as [[video game]]s to simulate bumps and wrinkles on the surface of an object without using more [[polygonal modeling|polygon]]s. To the end user, this means that textures such as stone walls will have more apparent depth and thus greater realism with less of an influence on the performance of the simulation.

'''Bump mapping''' is achieved by perturbing the [[surface normal]]s of an object and using a [[grayscale]] image and the perturbed normal during illumination calculations. The result is an apparently bumpy surface rather than a perfectly smooth surface although the surface of the underlying object is not actually changed. Bump mapping was introduced by Blinn in 1978.<ref name="Blinn">Blinn, James F. [http://dl.acm.org/citation.cfm?id=507101 "Simulation of Wrinkled Surfaces"], Computer Graphics, Vol. 12 (3), pp.&nbsp;286–292 SIGGRAPH-ACM (August 1978)</ref>

[[File:Bump-map-demo-full.png|thumb|right|300px|A sphere without [[bump mapping]] (left). The bump map to be applied to the sphere (middle). The sphere with the bump map applied (right).]]

In '''normal mapping''', the unit [[Vector (geometric)|vector]] from the shading point to the light source is [[dot product|dotted]] with the unit vector normal to that surface, and the dot product is the intensity of the light on that surface. Imagine a polygonal model of a sphere—you can only approximate the shape of the surface. By using a 3-channel bitmapped image textured across the model, more detailed normal vector information can be encoded. Each channel in the bitmap corresponds to a spatial dimension (''x'', ''y'' and ''z''). These spatial dimensions are relative to a constant coordinate system for object-space normal maps, or to a smoothly varying coordinate system (based on the derivatives of position with respect to texture coordinates) in the case of tangent-space normal maps. This adds much more detail to the surface of a model, especially in conjunction with advanced lighting techniques.

'''Parallax mapping''' (also called '''offset mapping''' or '''virtual displacement mapping''') is an enhancement of the bump mapping and normal mapping techniques implemented by displacing the texture coordinates at a point on the rendered polygon by a function of the view angle in tangent space (the angle relative to the surface normal) and the value of the [[height map]] at that point.  At steeper view-angles, the texture coordinates are displaced more, giving the illusion of depth due to [[parallax]] effects as the view changes.