Editing Texture mapping

{{Short description|Method of defining surface detail on a computer-generated graphic or 3D model}}
[[File:Hand-painted house 3D model stages.png|thumb|upright=1.3|Mapping a two-dimensional texture onto a 3D model]]
[[File:Texturedm1a2.png|thumb|1: 3D model without textures<br/>2: Same model with textures]]

'''Texture mapping'''<ref>{{cite web|url=http://web.cse.ohio-state.edu/~whmin/courses/cse5542-2013-spring/15-texture.pdf|title=Texture Mapping|last=Wang|first=Huamin|work=department of Computer Science and Engineering|publisher=[[Ohio State University]]|access-date=2016-01-15|archive-date=2016-03-04|archive-url=https://web.archive.org/web/20160304074441/http://web.cse.ohio-state.edu/~whmin/courses/cse5542-2013-spring/15-texture.pdf|url-status=dead}}</ref><ref>{{Cite web|url=http://www.inf.pucrs.br/flash/tcg/aulas/texture/texmap.pdf|title=Texture Mapping|website=www.inf.pucrs.br|access-date=September 15, 2019}}</ref><ref>{{cite web|url=http://www.cs.uregina.ca/Links/class-info/405/WWW/Lab5/#References|title=CS 405 Texture Mapping|website=www.cs.uregina.ca|access-date=22 March 2018}}</ref> is a term used in [[computer graphics]] to describe how 2D images are projected onto 3D models. The most common variant is the [[UV mapping|UV unwrap]], which can be described as an inverse paper cutout, where the surfaces of a 3D model is cut apart so that it can be unfolded into a 2D coordinate space (UV Space).

== Semantic ==
Texture mapping can both refer to the task of unwrapping a 3D model, the abstract that a 3D model has textures applied to it and the related algorithm of the [[3D software]].

Texture map refers to a [[Raster graphics]] also called image, texture. If the texture stores a specific property it's also referred to as color map, roughness map, etc. 

The coordinate space which converts from the 3D space of a 3D model into a 2D space so that it can sample from the Texture map is called: UV Space, UV Coordinates, Texture Space.

== Algorithm ==
A simplified explanation of how an algorithm could work to [[Rendering (computer graphics)|render]] an image:

# For each pixel we trace the coordinates of the screen into the 3D scene.
# If we hit a 3D model, or more precisely the polygon of a 3D model we read the 2D UV coordinates.
# We use the UV Coordinates to read the color from the texture and apply it to the pixel.

==History==
The original technique was pioneered by [[Edwin Catmull]] in 1974 as part of his doctoral thesis.<ref name="Catmull thesis">{{cite thesis|author-link=Edwin Catmull|last=Catmull|first=E.|year=1974|url=http://www.pixartouchbook.com/storage/catmull_thesis.pdf|title=A subdivision algorithm for computer display of curved surfaces|degree=PhD|publisher=University of Utah}}</ref>

Texture mapping originally referred to '''diffuse mapping''', a method that simply mapped [[pixel]]s from a texture to a [[Polygon mesh|3D surface]] ("wrapping" the image around the object). In recent decades, the advent of multi-pass rendering, [[multitexturing]], [[mipmap]]s, and more complex mappings such as [[height mapping]], [[bump mapping]], [[normal mapping]], [[displacement mapping]], [[reflection mapping]], [[specular mapping]], [[ambient occlusion|occlusion mapping]], and many other variations on the technique (controlled by a [[materials system]]) have made it possible to simulate near-[[Photorealistic rendering|photorealism]] in [[Real-time data|real time]] by vastly reducing the number of [[polygon]]s and lighting calculations needed to construct a realistic and functional 3D scene.

[[File:Bumpandopacity.png|thumb|280px|right|Examples of [[multitexturing]]:<br/>1:&nbsp;Untextured sphere, 2:&nbsp;Texture and bump maps, 3:&nbsp;Texture map only, 4:&nbsp;Opacity and texture maps]]

==Texture maps==
{{Redirect|Texture maps|the album by Steve Roach|Texture Maps: The Lost Pieces Vol. 3}}
A '''{{visible anchor|texture map}}'''<ref>{{Cite web|url=http://www.microsoft.com/msj/0199/direct3d/direct3d.aspx|title=DirectX 6.0 Goes Ballistic With Multiple New Features And Much Faster Code|last=Fosner|first=Ron|date=January 1999|website=Microsoft.com|url-status=dead|archive-url=https://web.archive.org/web/20161031110040/http://www.microsoft.com/msj/0199/direct3d/direct3d.aspx|archive-date=October 31, 2016|access-date=September 15, 2019}}</ref><ref>{{cite web|url=http://homepages.gac.edu/~hvidsten/courses/MC394/projects/project5/texture_map_guide.html|title=The OpenGL Texture Mapping Guide|author=Hvidsten|first=Mike|date=Spring 2004|website=homepages.gac.edu|access-date=22 March 2018|archive-date=23 May 2019|archive-url=https://web.archive.org/web/20190523063623/http://homepages.gac.edu/~hvidsten/courses/MC394/projects/project5/texture_map_guide.html|url-status=dead}}</ref> is an image applied (mapped) to the surface of a shape or [[polygon]].<ref>Jon Radoff, Anatomy of an MMORPG, {{cite web|url=http://radoff.com/blog/2008/08/22/anatomy-of-an-mmorpg/|title=Anatomy of an MMORPG|date=August 22, 2008|website=radoff.com|url-status=live|archive-url=https://web.archive.org/web/20091213053756/http://radoff.com/blog/2008/08/22/anatomy-of-an-mmorpg/|archive-date=2009-12-13|access-date=2009-12-13}}</ref> This may be a [[bitmap image]] or a [[procedural texture]]. They may be stored in common [[image file formats]], referenced by [[3d model formats|3D model formats]] or [[materials system|material definitions]], and assembled into [[resource bundles]].

They may have one to three dimensions, although two dimensions are most common for visible surfaces. For use with modern hardware, texture map data may be stored in [[Morton order|swizzled]] or tiled orderings to improve [[cache coherency]]. [[Rendering APIs]] typically manage texture map resources (which may be located in [[device memory]]) as buffers or surfaces, and may allow '[[render to texture]]' for additional effects such as post processing or [[environment mapping]].

They usually contain [[RGB]] color data (either stored as [[direct color]], [[Texture compression|compressed formats]], or [[indexed color]]), and sometimes an additional channel for [[alpha blending]] ([[RGBA]]) especially for [[Billboard (computer graphics)|billboards]] and ''decal'' overlay textures. It is possible to use the [[alpha channel]] (which may be convenient to store in formats parsed by hardware) for other uses such as [[specularity]].

Multiple texture maps (or [[Image channels|channels]]) may be combined for control over [[specularity]], [[Normal (geometry)|normals]], [[displacement mapping|displacement]], or [[subsurface scattering]] e.g. for skin rendering.

Multiple texture images may be combined in [[texture atlases]] or [[array textures]] to reduce state changes for modern hardware. (They may be considered a modern evolution of [[Tile map|tile map graphics]]). Modern hardware often supports [[cube map]] textures with multiple faces for environment mapping.

===Creation===
Texture maps may be acquired by [[3D scanning|scanning]]/[[digital photography]], designed in [[image manipulation software]] such as [[GIMP]], [[Photoshop]], or painted onto 3D surfaces directly in a [[3D paint tool]] such as [[Mudbox]] or [[ZBrush]].

===Texture application===
This process is akin to applying patterned paper to a plain white box. Every vertex in a polygon is assigned a [[texture coordinate]] (which in the 2D case is also known as [[UV coordinate]]s).<ref>{{cite web |last1=Roberts |first1=Susan |title=How to use textures |url=https://freeassetsunity.com/how-to-use-textures/ |url-status=usurped |archive-url=https://web.archive.org/web/20210924034033/https://freeassetsunity.com/how-to-use-textures/ |archive-date=24 September 2021 |access-date=20 March 2021}}</ref> This may be done through explicit assignment of [[vertex attributes]], manually edited in a 3D modelling package through [[UV unwrapping tools]]. It is also possible to associate a procedural transformation from 3D space to texture space with the [[Material (computer graphics)|material]]. This might be accomplished via [[planar projection]] or, alternatively, [[Cylindrical coordinates|cylindrical]] or [[Spherical coordinates|spherical]] mapping. More complex mappings may consider the distance along a surface to minimize distortion. These coordinates are interpolated across the faces of polygons to sample the texture map during rendering. Textures may be '''repeated''' or '''mirrored''' to extend a finite rectangular bitmap over a larger area, or they may have a one-to-one unique "[[injective]]" mapping from every piece of a surface (which is important for [[render mapping]] and [[light mapping]], also known as [[Baking (computer graphics)|baking]]).

====Texture space====
Texture mapping maps the model surface (or [[screen space]] during rasterization) into '''texture space'''; in this space, the texture map is visible in its undistorted form. [[UV unwrapping]] tools typically provide a view in texture space for manual editing of texture coordinates. Some rendering techniques such as [[subsurface scattering]] may be performed approximately by texture-space operations.

===Multitexturing===
Multitexturing is the use of more than one texture at a time on a polygon.<ref>Blythe, David. ''[https://web.archive.org/web/20200228185024/https://pdfs.semanticscholar.org/fc76/bb3649978a1939d9bd9d9d3769f47ebfc6c1.pdf Advanced Graphics Programming Techniques Using OpenGL].'' Siggraph 1999. ([[PDF]]) (see: [https://web.archive.org/web/20120108033621/http://www.opengl.org/resources/code/samples/sig99/advanced99/notes/node60.html Multitexture])</ref> For instance, a [[Lightmap|light map]] texture may be used to light a surface as an alternative to recalculating that lighting every time the surface is rendered. '''Microtextures''' or '''detail textures''' are used to add higher frequency details, and '''dirt maps''' may add weathering and variation; this can greatly reduce the apparent periodicity of repeating textures. Modern graphics may use more than 10 layers, which are combined using [[shaders]], for greater fidelity. Another multitexture technique is [[bump mapping]], which allows a texture to directly control the facing direction of a surface for the purposes of its lighting calculations; it can give a very good appearance of a complex surface (such as tree bark or rough concrete) that takes on lighting detail in addition to the usual detailed coloring. Bump mapping has become popular in recent video games, as graphics hardware has become powerful enough to accommodate it in real-time.<ref>[https://web.archive.org/web/20150914190914/http://web4.cs.ucl.ac.uk/staff/j.kautz/publications/rtbumpmapHWWS01.pdf Real-Time Bump Map Synthesis], Jan Kautz<sup>1</sup>, Wolfgang Heidrichy<sup>2</sup> and Hans-Peter Seidel<sup>1</sup>, (<sup>1</sup>Max-Planck-Institut für Informatik, <sup>2</sup>University of British Columbia)</ref>

===Texture filtering===
The way that samples (e.g. when viewed as [[pixel]]s on the screen) are calculated from the [[texel (graphics)|texel]]s (texture pixels) is governed by [[texture filtering]]. The cheapest method is to use the [[Nearest-neighbor interpolation|nearest-neighbour interpolation]], but [[bilinear interpolation]] or [[trilinear interpolation]] between [[mipmap]]s are two commonly used alternatives which reduce [[aliasing]] or [[jaggies]]. In the event of a texture coordinate being outside the texture, it is either [[Clamping (graphics)|clamped]] or [[Wrapping (graphics)|wrapped]]. [[Anisotropic filtering]] better eliminates directional artefacts when viewing textures from oblique viewing angles.

===Texture streaming===
Texture streaming is a means of using [[data stream]]s for textures, where each texture is available in two or more different resolutions, as to determine which texture should be loaded into memory and used based on draw distance from the viewer and how much memory is available for textures. Texture streaming allows a rendering engine to use low resolution textures for objects far away from the viewer's camera, and resolve those into more detailed textures, read from a data source, as the point of view nears the objects.

===Baking===
As an optimization, it is possible to render detail from a complex, high-resolution model or expensive process (such as [[global illumination]]) into a surface texture (possibly on a low-resolution model). ''Baking'' is also known as '''render mapping'''. This technique is most commonly used for [[lightmapping|light maps]], but may also be used to generate [[normal maps]] and [[displacement maps]].  Some computer games (e.g. [[Messiah (video game)|Messiah]]) have used this technique. The original [[Quake (video game)|Quake]] software engine used on-the-fly baking to combine light maps and colour maps ("[[surface caching]]").

Baking can be used as a form of [[Level of detail (computer graphics)|level of detail]] generation, where a complex scene with many different elements and materials may be approximated by a ''single'' element with a ''single'' texture, which is then algorithmically reduced for lower rendering cost and fewer [[drawcalls]]. It is also used to take high-detail models from [[3D sculpting software]] and [[point cloud scanning]] and approximate them with [[meshes]] more suitable for realtime rendering.

==Rasterisation algorithms==
Various techniques have evolved in software and hardware implementations. Each offers different trade-offs in precision, versatility and performance.

===Affine texture mapping===
[[File:Perspective correct texture mapping.svg|thumb|400px|Because affine texture mapping does not take into account the depth information about a polygon's vertices, where the polygon is not perpendicular to the viewer, it produces a noticeable defect, especially when rasterized as triangles.]]

'''Affine texture mapping''' linearly interpolates texture coordinates across a surface, and so is the fastest form of texture mapping. Some software and hardware (such as the original [[PlayStation (console)|PlayStation]]) [[3D projection|project]] vertices in 3D space onto the screen during rendering and [[Linear interpolation|linearly interpolate]] the texture coordinates ''in screen space'' between them. This may be done by incrementing [[Fixed point arithmetic|fixed point]] [[UV coordinates]], or by an [[incremental error algorithm]] akin to [[Bresenham's line algorithm]].

In contrast to perpendicular polygons, this leads to noticeable distortion with perspective transformations (see figure: the checker box texture appears bent), especially as primitives near the [[3d camera coordinate system|camera]]. Such distortion may be reduced with the subdivision of the polygon into smaller ones.

For the case of rectangular objects, using quad primitives can look less incorrect than the same rectangle split into triangles, but because interpolating 4 points adds complexity to the rasterization, most early implementations preferred triangles only. Some hardware, such as the [[#Forward texture mapping|forward texture mapping]] used by the Nvidia [[NV1]], was able to offer efficient quad primitives. With perspective correction (see below) triangles become equivalent and this advantage disappears.

[[File:Affine texture mapping tri vs quad.svg|thumb|400px|For rectangular objects, especially when perpendicular to the view, linearly interpolating across a quad can give a superior affine result versus the same rectangle split into two affine triangles.]]

For rectangular objects that are at right angles to the viewer, like floors and walls, the perspective only needs to be corrected in one direction across the screen, rather than both. The correct perspective mapping can be calculated at the left and right edges of the floor, and then an affine linear interpolation across that horizontal span will look correct, because every pixel along that line is the same distance from the viewer.

===Perspective correctness===
'''Perspective correct''' texturing accounts for the vertices' positions in 3D space, rather than simply interpolating coordinates in 2D screen space.<ref name="NGen15">{{cite magazine|date=March 1996|title=The Next Generation 1996 Lexicon A to Z: Perspective Correction|url=https://archive.org/details/nextgen-issue-015/page/n39/mode/2up|magazine=[[Next Generation (magazine)|Next Generation]]|publisher=[[Imagine Media]]|issue=15|page=38}}</ref> This achieves the correct visual effect but it is more expensive to calculate.<ref name="NGen15"/>

To perform perspective correction of the texture coordinates <math>u</math> and <math>v</math>, with <math>z</math> being the depth component from the viewer's point of view, we can take advantage of the fact that the values <math>\frac{1}{z}</math>, <math>\frac{u}{z}</math>, and <math>\frac{v}{z}</math> are linear in screen space across the surface being textured. In contrast, the original <math>z</math>, <math>u</math> and <math>v</math>, before the division, are not linear across the surface in screen space. We can therefore linearly interpolate these reciprocals across the surface, computing corrected values at each pixel, to result in a perspective correct texture mapping.

To do this, we first calculate the reciprocals at each vertex of our geometry (3 points for a triangle). For vertex <math>n</math> we have <math>\frac{u_n}{z_n}, \frac{v_n}{z_n}, \frac{1}{z_n}</math>. Then, we linearly interpolate these reciprocals between the <math>n</math> vertices (e.g., using [[Barycentric coordinate system|barycentric coordinates]]), resulting in interpolated values across the surface. At a given point, this yields the interpolated <math>u_i, v_i</math>, and <math>zReciprocal_i = \frac{1}{z_i}</math>. Note that this <math>u_i, v_i</math> cannot be yet used as our texture coordinates as our division by <math>z</math> altered their coordinate system.

To correct back to the <math>u, v</math> space we first calculate the corrected <math>z</math> by again taking the reciprocal <math>z_{correct} = \frac{1}{zReciprocal_i} = \frac{1}{\frac{1}{z_i}}</math>. Then we use this to correct our <math>u_i, v_i</math>: <math>u_{correct} = u_i \cdot z_i</math> and <math> v_{correct} = v_i \cdot z_i</math>.<ref>{{Cite web|url=http://www.lysator.liu.se/~mikaelk/doc/perspectivetexture/|title=Perspective Texturemapping|last=Kalms|first=Mikael|date=1997|website=www.lysator.liu.se|access-date=2020-03-27}}</ref>

This correction makes it so that in parts of the polygon that are closer to the viewer the difference from pixel to pixel between texture coordinates is smaller (stretching the texture wider) and in parts that are farther away this difference is larger (compressing the texture).
:Affine texture mapping directly interpolates a texture coordinate <math>u^{}_{\alpha}</math> between two endpoints <math>u^{}_0</math> and <math>u^{}_1</math>:
::<math>u^{}_{\alpha}= (1 - \alpha ) u_0 + \alpha u_1</math>  where  <math>0 \le \alpha \le 1</math>
:Perspective correct mapping interpolates after dividing by depth <math>z^{}_{}</math>, then uses its interpolated reciprocal to recover the correct coordinate:
::<math>u^{}_{\alpha}= \frac{ (1 - \alpha ) \frac{ u_0 }{ z_0 } + \alpha \frac{ u_1 }{ z_1 } }{ (1 - \alpha ) \frac{ 1 }{ z_0 } + \alpha \frac{ 1 }{ z_1 } }</math>

3D graphics hardware typically supports perspective correct texturing.

Various techniques have evolved for rendering texture mapped geometry into images with different quality/precision trade-offs, which can be applied to both software and hardware.

Classic software texture mappers generally did only simple mapping with at most one lighting effect (typically applied through a [[lookup table]]), and the perspective correctness was about 16 times more expensive.

===Restricted camera rotation===
[[File:Freedoom 2018.png|300px|thumb|right|[[Doom engine]] did not permit ramped floors or slanted walls. This requires perspective correction only once per each horizontal or vertical span, rather than per-pixel.]]

The ''[[Doom engine]]'' restricted the world to vertical walls and horizontal floors/ceilings, with a camera that could only rotate about the vertical axis. This meant the walls would be a constant depth coordinate along a vertical line and the floors/ceilings would have a constant depth along a horizontal line. After performing one perspective correction calculation for the depth, the rest of the line could use fast affine mapping. Some later renderers of this era simulated a small amount of camera [[Pitch (orientation)|pitch]] with [[Shear (transformation)|shearing]] which allowed the appearance of greater freedom whilst using the same rendering technique.

Some engines were able to render texture mapped [[heightmaps]] (e.g. [[Nova Logic]]'s [[Voxel Space]], and the engine for [[Outcast (video game)|Outcast]]) via [[Bresenham's line algorithm|Bresenham]]-like incremental algorithms, producing the appearance of a texture mapped landscape without the use of traditional geometric primitives.<ref>"[https://web.archive.org/web/20131113094653/http://www.codermind.com/articles/Voxel-terrain-engine-building-the-terrain.html Voxel terrain engine]", introduction. In a coder's mind, 2005 (archived 2013).</ref>

===Subdivision for perspective correction===
Every triangle can be further subdivided into groups of about 16 pixels in order to achieve two goals. First, keeping the arithmetic mill busy at all times. Second, producing faster arithmetic results.{{vague|date=March 2020}}

====World space subdivision====
For perspective texture mapping without hardware support, a triangle is broken down into smaller triangles for rendering and affine mapping is used on them. The reason this technique works is that the distortion of affine mapping becomes much less noticeable on smaller polygons. The [[Sony PlayStation]] made extensive use of this because it only supported affine mapping in hardware but had a relatively high triangle throughput compared to its peers.

====Screen space subdivision====
[[File:Texturemapping subdivision.svg|thumb|200 px|Screen space sub division techniques. Top left: Quake-like, top right: bilinear, bottom left: const-z]]

Software renderers generally preferred screen subdivision because it has less overhead. Additionally, they try to do linear interpolation along a line of pixels to simplify the set-up (compared to 2d affine interpolation) and thus again the overhead (also affine texture-mapping does not fit into the low number of registers of the [[x86]] CPU; the [[68000]] or any [[RISC]] is much more suited).

A different approach was taken for ''[[Quake (video game)|Quake]]'', which would calculate perspective correct coordinates only once every 16 pixels of a scanline and linearly interpolate between them, effectively running at the speed of linear interpolation because the perspective correct calculation runs in parallel on the co-processor.<ref>Abrash, Michael. ''Michael Abrash's Graphics Programming Black Book Special Edition.'' The Coriolis Group, Scottsdale Arizona, 1997. {{ISBN|1-57610-174-6}} ([http://www.gamedev.net/reference/articles/article1698.asp PDF] {{Webarchive|url=https://web.archive.org/web/20070311022026/http://www.gamedev.net/reference/articles/article1698.asp |date=2007-03-11 }}) (Chapter 70, pg. 1282)</ref> The polygons are rendered independently, hence it may be possible to switch between spans and columns or diagonal directions depending on the orientation of the [[polygon normal]] to achieve a more constant z but the effort seems not to be worth it.

====Other techniques====
Another technique was approximating the perspective with a faster calculation, such as a polynomial. Still another technique uses 1/z value of the last two drawn pixels to linearly extrapolate the next value. The division is then done starting from those values so that only a small remainder has to be divided<ref>{{cite patent
 | inventor-last = Spackman
 | inventor-first = John Neil
 | issue-date = 1998-04-14
 | title = Apparatus and method for performing perspectively correct interpolation in computer graphics
 | patent-number = 5739818
 | country-code = US
}}</ref> but the amount of bookkeeping makes this method too slow on most systems.

Finally, [[Build engine|the Build engine]] extended the constant distance trick used for Doom by finding the line of constant distance for arbitrary polygons and rendering along it.

===Hardware implementations===
Texture mapping hardware was originally developed for simulation (e.g. as implemented in the [[Evans and Sutherland]] ESIG and Singer-Link Digital Image Generators DIG), and professional [[Workstation#Graphics workstations|graphics workstations]] such as [[Silicon Graphics]], broadcast [[digital video effect]]s machines such as the [[Ampex ADO]] and later appeared in [[Arcade cabinet]]s, consumer [[video game console]]s, and PC [[video card]]s in the mid-1990s. In [[flight simulation]], texture mapping provided important motion and altitude cues necessary for pilot training not available on untextured surfaces. It was also in flight simulation applications, that texture mapping was implemented for real-time processing with prefiltered texture patterns stored in memory for real-time access by the video processor.<ref>{{cite journal |last1=Yan |first1=Johnson |title=Advances in Computer-Generated Imagery for Flight Simulation |journal=IEEE |date=August 1985 |volume=5 |issue=8 |pages=37–51 |doi=10.1109/MCG.1985.276213 |url=https://ieeexplore.ieee.org/document/4056245|url-access=subscription }}</ref>

Modern [[graphics processing unit]]s (GPUs) provide specialised [[fixed function unit]]s called ''texture samplers'', or [[texture mapping unit|''texture mapping units'']], to perform texture mapping, usually with [[trilinear filtering]] or better multi-tap [[anisotropic filtering]] and hardware for decoding specific formats such as [[S3 Texture Compression|DXTn]]. As of 2016, texture mapping hardware is ubiquitous as most [[System on a chip|SOC]]s contain a suitable GPU.

Some hardware combines texture mapping with [[hidden-surface determination]] in [[Tiled rendering|tile based deferred rendering]] or [[scanline rendering]]; such systems only fetch the visible [[Texel (graphics)|texels]] at the expense of using greater workspace for transformed vertices. Most systems have settled on the [[Z-buffering]] approach, which can still reduce the texture mapping workload with front-to-back [[Sorting algorithm|sorting]].

Among earlier graphics hardware, there were two competing paradigms of how to deliver a texture to the screen:
* '''Forward texture mapping''' iterates through each texel on the texture, and decides where to place it on the screen.
* '''Inverse texture mapping''' instead iterates through pixels on the screen, and decides what texel to use for each.

Inverse texture mapping is the method which has become standard in modern hardware.

====Inverse texture mapping====
With this method, a pixel on the screen is mapped to a point on the texture. Each vertex of a [[rendering primitive]] is projected to a point on the screen, and each of these points is [[UV mapping|mapped to a u,v texel coordinate]] on the texture. A rasterizer will interpolate between these points to fill in each pixel covered by the primitive.

The primary advantage is that each pixel covered by a primitive will be traversed exactly once. Once a primitive's vertices are transformed, the amount of remaining work scales directly with how many pixels it covers on the screen.

The main disadvantage versus forward texture mapping is that the [[memory access pattern]] in the [[texture space]] will not be linear if the texture is at an angle to the screen. This disadvantage is often addressed by [[texture cache|texture caching]] techniques, such as the [[swizzled texture]] memory arrangement.

The linear interpolation can be used directly for simple and efficient [[#Affine texture mapping|affine]] texture mapping, but can also be adapted for [[#Perspective correctness|perspective correctness]].

====Forward texture mapping====
Forward texture mapping maps each texel of the texture to a pixel on the screen. After transforming a rectangular primitive to a place on the screen, a forward texture mapping renderer iterates through each texel on the texture, splatting each one onto a pixel of the [[frame buffer]].

This was used by some hardware, such as the [[3DO Interactive Multiplayer|3DO]], the [[Sega Saturn]] and the [[NV1]].

The primary advantage is that the texture will be accessed in a simple linear order, allowing very efficient caching of the texture data. However, this benefit is also its disadvantage: as a primitive gets smaller on screen, it still has to iterate over every texel in the texture, causing many pixels to be overdrawn redundantly.

This method is also well suited for rendering quad primitives rather than reducing them to triangles, which provided an advantage when perspective correct texturing was not available in hardware. This is because the affine distortion of a quad looks less incorrect than the same quad split into two triangles (see [[#Affine texture mapping|affine texture mapping]] above). The NV1 hardware also allowed a quadratic interpolation mode to provide an even better approximation of perspective correctness.

The existing hardware implementations did not provide effective [[UV coordinates|UV coordinate mapping]], which became an important technique for 3D modelling and assisted in [[Clipping (computer graphics)|clipping]] the texture correctly when the primitive goes over the edge of the screen. These shortcomings could have been addressed with further development, but GPU design has since mostly moved toward inverse mapping.

{{clear}}

==Applications==
Beyond 3D rendering, the availability of texture mapping hardware has inspired its use for accelerating other tasks:

===Tomography===
It is possible to use texture mapping hardware to accelerate both the [[Tomographic reconstruction|reconstruction]] of [[voxel]] data sets<!--- or volume data set or 3D array or 3D texture? ---> from [[tomography|tomographic scan]]s, and to [[volume rendering|visualize the results]].<ref>{{cite web|title=texture mapping for tomography|url=https://patents.google.com/patent/US6002738}}</ref>

===User interfaces===
Many user interfaces use texture mapping to accelerate animated transitions of screen elements, e.g. [[Mission Control (macOS)|Exposé]] in [[Mac OS X]].

==See also==

* [[2.5D]]
* [[3D computer graphics]]
* [[Mipmap]]
* [[Materials system]]
* [[Parametrization (geometry)|Parametrization]]
* [[Texture synthesis]]
* [[Texture atlas]]
* [[Texture splatting]] – a technique for combining textures
* [[Shader (computer graphics)]]

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

==Software==

* [https://www.gcc.tu-darmstadt.de/home/proj/texrecon/index.en.jsp TexRecon] {{Webarchive|url=https://web.archive.org/web/20211127121726/https://www.gcc.tu-darmstadt.de/home/proj/texrecon/index.en.jsp |date=2021-11-27 }} &mdash; open-source software for texturing 3D models written in C++

==External links==
<!-- Please do not add links to free texture websites; this article is about texture mapping, not textures. Such a link is uninformative and will be deleted. -->
* [http://www.decew.net/OSS/References/chapter_2_texture_mapping.pdf Introduction into texture mapping using C and SDL] (PDF)
*[https://web.archive.org/web/20190103234143/http://www.riemers.net/eng/Tutorials/XNA/Csharp/Series4/Textured_terrain.php Programming a textured terrain] using XNA/DirectX, from www.riemers.net
* [http://www.gamers.org/dEngine/quake/papers/checker_texmap.html Perspective correct texturing]
* [https://web.archive.org/web/20071226193904/http://www.fawzma.com/time-texturing-texture-mapping-with-bezier-lines/ Time Texturing] Texture mapping with bezier lines
* [http://www.hpl.hp.com/research/ptm/ Polynomial Texture Mapping] {{Webarchive|url=https://web.archive.org/web/20190307055738/http://www.hpl.hp.com/research/ptm/ |date=2019-03-07 }} Interactive Relighting for Photos
* [http://www.um.es/geograf/sigmur/temariohtml/node43_ct.html 3 Métodos de interpolación a partir de puntos (in spanish)] Methods that can be used to interpolate a texture knowing the texture coords at the vertices of a polygon
* [https://cgifurniture.com/3d-texturing-tools-top-10/ 3D Texturing Tools]

{{Texture mapping techniques}}

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[[Category:Texture mapping| ]]
[[Category:Computer graphics]]