Reflection mapping

<h2 id="types">Types</h2>
<h3>Sphere mapping</h3>
<a href="/facts/Sphere_mapping/465BBu9a">Sphere mapping</a> represents the <a href="/facts/Sphere/jywYLNM2">sphere</a> of incident illumination as though it were seen in the reflection of a reflective sphere through an <a href="/facts/Orthographic_projection_(geometry)/L3Cv9kYD">orthographic</a> camera. The texture image can be created by approximating this ideal setup, or using a <a href="/facts/Fisheye_lens/r7o5g3AT">fisheye lens</a> or via <a href="/facts/Pre-rendering/YtB5k4Jh">prerendering</a> a scene with a spherical mapping.
The spherical mapping suffers from limitations that detract from the realism of resulting renderings. Because spherical maps are stored as <a href="/facts/Azimuthal_projection/XYxklzIu">azimuthal projections</a> of the environments they represent, an abrupt point of singularity (a "<a href="/facts/Black_hole/1r2lmkcF">black hole</a>" effect) is visible in the reflection on the object where texel colors at or near the edge of the map are distorted due to inadequate resolution to represent the points accurately. The spherical mapping also wastes pixels that are in the square but not in the sphere.
The artifacts of the spherical mapping are so severe that it is effective only for viewpoints near that of the virtual orthographic camera.

<h3>Cube mapping</h3>

<a href="/facts/Cube_mapping/9X8IuHCS">Cube mapping</a> and other polyhedron mappings address the severe distortion of sphere maps. If cube maps are made and filtered correctly, they have no visible seams, and can be used independent of the viewpoint of the often-virtual camera acquiring the map. Cube and other polyhedron maps have since superseded sphere maps in most computer graphics applications, with the exception of acquiring <a href="/facts/Image-based_lighting/dlQ28BYA">image-based lighting</a>. Image-based lighting can be done with parallax-corrected cube maps.<a class="footnote-ref" id="fnref:4" href="#fn:4">4</a>
Generally, cube mapping uses the same <a href="/facts/Skybox_(video_games)/acFe28M5">skybox</a> that is used in outdoor renderings. Cube-mapped reflection is done by determining the <a href="/facts/Vector_(geometric)/bCLrdksy">vector</a> that the object is being viewed at. This camera ray is reflected about the <a href="/facts/Surface_normal/jhtLIhcu">surface normal</a> of where the camera vector intersects the object. This results in the reflected ray which is then passed to the <a href="/facts/Cube_map/9X8IuHCS">cube map</a> to get the <a href="/facts/Texel_(graphics)/woCwpxAU">texel</a> which provides the radiance value used in the lighting calculation. This creates the effect that the object is reflective.

<h3>HEALPix mapping</h3>
<a href="/facts/HEALPix/t9L8TXvn">HEALPix</a> environment mapping is similar to the other polyhedron mappings, but can be hierarchical, thus providing a unified framework for generating polyhedra that better approximate the sphere. This allows lower distortion at the cost of increased computation.<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a>

<h2 id="history">History</h2>
In 1974, <a href="/facts/Edwin_Catmull/4o0C8Nrl">Edwin Catmull</a> created an algorithm for "rendering images of bivariate surface patches"<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a><a class="footnote-ref" id="fnref:7" href="#fn:7">7</a> which worked directly with their mathematical definition. Further refinements were researched and documented by <a href="/facts/Bui_Tuong_Phong/s6S7TEPX">Bui-Tuong Phong</a> in 1975, and later <a href="/facts/James_Blinn/UxlnCaWD">James Blinn</a> and <a href="/facts/Martin_Newell_(computer_scientist)/QEIrHPxf">Martin Newell</a>, who developed environment mapping in 1976; these developments which refined Catmull's original algorithms led them to conclude that "these generalizations result in improved techniques for generating patterns and texture".<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a><a class="footnote-ref" id="fnref:9" href="#fn:9">9</a><a class="footnote-ref" id="fnref:10" href="#fn:10">10</a>
Gene Miller experimented with spherical environment mapping in 1982 at <a href="/facts/Mathematical_Applications_Group/94ljrS53">MAGI</a>.
Wolfgang Heidrich introduced Paraboloid Mapping in 1998.<a class="footnote-ref" id="fnref:11" href="#fn:11">11</a>
Emil Praun introduced Octahedron Mapping in 2003.<a class="footnote-ref" id="fnref:12" href="#fn:12">12</a>
Mauro Steigleder introduced Pyramid Mapping in 2005.<a class="footnote-ref" id="fnref:13" href="#fn:13">13</a>
Tien-Tsin Wong, et al. introduced the existing <a href="/facts/HEALPix/t9L8TXvn">HEALPix</a> mapping for rendering in 2006.<a class="footnote-ref" id="fnref:14" href="#fn:14">14</a>

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Skybox_(video_games)/acFe28M5">Skybox (video games)</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="http://www.pauldebevec.com/ReflectionMapping/">The Story of Reflection mapping</a> by <a href="/facts/Paul_Debevec/KKnY4QeV">Paul Debevec</a></li>
<li><a href="http://www.nvidia.com/object/feature_cube.html">NVIDIA's paper</a> Cube Environment Mapping</li>
<li><a href="https://archive.today/20140702043618/http://sunandblackcat.com/tipFullView.php?l=eng&topicid=16">Approximation of reflective and transparent objects with environmental maps</a>[usurped]</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">"Higher Education | Pearson" (PDF). <a href="http://www.pearsonhighered.com/samplechapter/0321194969.pdf" target="_blank">http://www.pearsonhighered.com/samplechapter/0321194969.pdf</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">"Directory | Computer Science and Engineering" (PDF). web.cse.ohio-state.edu. Retrieved 2025-02-18. <a href="http://web.cse.ohio-state.edu/~whmin/courses/cse5542-2013-spring/17-env.pdf" target="_blank">http://web.cse.ohio-state.edu/~whmin/courses/cse5542-2013-spring/17-env.pdf</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">"Bump and Environment Mapping" (PDF). Archived from the original (PDF) on 2012-01-29. <a href="https://web.archive.org/web/20120129012326/http://www.ics.uci.edu/~majumder/VC/classes/BEmap.pdf" target="_blank">https://web.archive.org/web/20120129012326/http://www.ics.uci.edu/~majumder/VC/classes/BEmap.pdf</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">"Image-based Lighting approaches and parallax-corrected cubemap". 29 September 2012. <a href="http://seblagarde.wordpress.com/2012/09/29/image-based-lighting-approaches-and-parallax-corrected-cubemap/" target="_blank">http://seblagarde.wordpress.com/2012/09/29/image-based-lighting-approaches-and-parallax-corrected-cubemap/</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Tien-Tsin Wong, Liang Wan, Chi-Sing Leung, and Ping-Man Lam. Real-time Environment Mapping with Equal Solid-Angle Spherical Quad-Map Archived 2007-10-23 at the Wayback Machine, Shader X4: Lighting & Rendering, Charles River Media, 2006. <a href="http://appsrv.cse.cuhk.edu.hk/~lwan/paper/sphquadmap/sphquadmap.htm" target="_blank">http://appsrv.cse.cuhk.edu.hk/~lwan/paper/sphquadmap/sphquadmap.htm</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Blinn, James F.; Newell, Martin E. (October 1976). "Texture and reflection in computer generated images". Communications of the ACM. 19 (10): 542–547. doi:10.1145/360349.360353. ISSN 0001-0782. <a href="https://dl.acm.org/doi/10.1145/360349.360353" target="_blank">https://dl.acm.org/doi/10.1145/360349.360353</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">Catmull, E.A. Computer display of curved surfaces. Proc. Conf. on Comptr. Graphics, Pattern Recognition, and Data Structure, May 1975, pp. 11-17 (IEEE Cat. No. 75CH0981-1C). <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">Blinn, James F.; Newell, Martin E. (October 1976). "Texture and reflection in computer generated images". Communications of the ACM. 19 (10): 542–547. doi:10.1145/360349.360353. ISSN 0001-0782. <a href="https://dl.acm.org/doi/10.1145/360349.360353" target="_blank">https://dl.acm.org/doi/10.1145/360349.360353</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">"Computer Graphics". Archived from the original on 2021-02-24. Retrieved 2007-01-09. <a href="https://web.archive.org/web/20210224203858/http://www.comphist.org/computing_history/new_page_6.htm" target="_blank">https://web.archive.org/web/20210224203858/http://www.comphist.org/computing_history/new_page_6.htm</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">"Reflection Mapping History". <a href="http://www.debevec.org/ReflectionMapping/" target="_blank">http://www.debevec.org/ReflectionMapping/</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">Heidrich, W., and H.-P. Seidel. "View-Independent Environment Maps". Eurographics Workshop on Graphics Hardware 1998, pp. 39–45. <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">Emil Praun and Hugues Hoppe. "Spherical parametrization and remeshing". ACM Transactions on Graphics, 22(3):340–349, 2003. <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">Mauro Steigleder. "Pencil Light Transport". A thesis presented to the University of Waterloo, 2005. <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
<li id="fn:14">Tien-Tsin Wong, Liang Wan, Chi-Sing Leung, and Ping-Man Lam. Real-time Environment Mapping with Equal Solid-Angle Spherical Quad-Map Archived 2007-10-23 at the Wayback Machine, Shader X4: Lighting & Rendering, Charles River Media, 2006. <a href="http://appsrv.cse.cuhk.edu.hk/~lwan/paper/sphquadmap/sphquadmap.htm" target="_blank">http://appsrv.cse.cuhk.edu.hk/~lwan/paper/sphquadmap/sphquadmap.htm</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
</ol>

Reflection mapping open-in-new

Reflection mapping