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class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#2D_vector_graphics"> <div class="vector-toc-text"> 2.1 2D vector graphics </div> </a> <ul id="toc-2D_vector_graphics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-3D_geometry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#3D_geometry"> <div class="vector-toc-text"> 2.2 3D geometry </div> </a> <ul id="toc-3D_geometry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Volumetric_data" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Volumetric_data"> <div class="vector-toc-text"> 2.3 Volumetric data </div> </a> <ul id="toc-Volumetric_data-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Photogrammetry_and_scanning" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Photogrammetry_and_scanning"> <div class="vector-toc-text"> 2.4 Photogrammetry and scanning </div> </a> <ul id="toc-Photogrammetry_and_scanning-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Neural_approximations_and_light_fields" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Neural_approximations_and_light_fields"> <div class="vector-toc-text"> 2.5 Neural approximations and light fields </div> </a> <ul id="toc-Neural_approximations_and_light_fields-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Outputs" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Outputs"> <div class="vector-toc-text"> 3 Outputs </div> </a> <ul id="toc-Outputs-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Techniques" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Techniques"> <div class="vector-toc-text"> 4 Techniques </div> </a> <button aria-controls="toc-Techniques-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Techniques subsection </button> <ul id="toc-Techniques-sublist" class="vector-toc-list"> <li id="toc-Rasterization" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rasterization"> <div class="vector-toc-text"> 4.1 Rasterization </div> </a> <ul id="toc-Rasterization-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ray_casting" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ray_casting"> <div class="vector-toc-text"> 4.2 Ray casting </div> </a> <ul id="toc-Ray_casting-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ray_tracing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ray_tracing"> <div class="vector-toc-text"> 4.3 Ray tracing </div> </a> <ul id="toc-Ray_tracing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Radiosity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Radiosity"> <div class="vector-toc-text"> 4.4 Radiosity </div> </a> <ul id="toc-Radiosity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Path_tracing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Path_tracing"> <div class="vector-toc-text"> 4.5 Path tracing </div> </a> <ul id="toc-Path_tracing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Neural_rendering" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Neural_rendering"> <div class="vector-toc-text"> 4.6 Neural rendering </div> </a> <ul id="toc-Neural_rendering-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Scientific_and_mathematical_basis" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Scientific_and_mathematical_basis"> <div class="vector-toc-text"> 5 Scientific and mathematical basis </div> </a> <button aria-controls="toc-Scientific_and_mathematical_basis-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Scientific and mathematical basis subsection </button> <ul id="toc-Scientific_and_mathematical_basis-sublist" class="vector-toc-list"> <li id="toc-The_rendering_equation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#The_rendering_equation"> <div class="vector-toc-text"> 5.1 The rendering equation </div> </a> <ul id="toc-The_rendering_equation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_bidirectional_reflectance_distribution_function" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#The_bidirectional_reflectance_distribution_function"> <div class="vector-toc-text"> 5.2 The bidirectional reflectance distribution function </div> </a> <ul id="toc-The_bidirectional_reflectance_distribution_function-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geometric_optics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Geometric_optics"> <div class="vector-toc-text"> 5.3 Geometric optics </div> </a> <ul id="toc-Geometric_optics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Visual_perception" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Visual_perception"> <div class="vector-toc-text"> 5.4 Visual perception </div> </a> <ul id="toc-Visual_perception-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sampling_and_filtering" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sampling_and_filtering"> <div class="vector-toc-text"> 5.5 Sampling and filtering </div> </a> <ul id="toc-Sampling_and_filtering-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Hardware" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Hardware"> <div class="vector-toc-text"> 6 Hardware </div> </a> <button aria-controls="toc-Hardware-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Hardware subsection </button> <ul id="toc-Hardware-sublist" class="vector-toc-list"> <li id="toc-History" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> 6.1 History </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-GPUs" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#GPUs"> <div class="vector-toc-text"> 6.2 GPUs </div> </a> <ul id="toc-GPUs-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Chronology_of_algorithms_and_techniques" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Chronology_of_algorithms_and_techniques"> <div class="vector-toc-text"> 7 Chronology of algorithms and techniques </div> </a> <ul id="toc-Chronology_of_algorithms_and_techniques-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> 8 See also </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> 9 References </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> 10 Further reading </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> 11 External links </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > Toggle the table of contents </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">Rendering (computer graphics)</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 39 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-39" aria-hidden="true" > 39 languages </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%B5%D9%8A%D9%8A%D8%B1_(%D8%B1%D8%B3%D9%88%D9%85%D9%8A%D8%A7%D8%AA_%D8%AD%D8%A7%D8%B3%D9%88%D8%A8%D9%8A%D8%A9)" title="تصيير (رسوميات حاسوبية) – Arabic" lang="ar" hreflang="ar" data-title="تصيير (رسوميات حاسوبية)" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Render" title="Render – Azerbaijani" lang="az" hreflang="az" data-title="Render" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target">Azərbaycanca</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%9A%E0%A6%BF%E0%A6%A4%E0%A7%8D%E0%A6%B0%E0%A6%BE%E0%A6%AF%E0%A6%BC%E0%A6%A8_(%E0%A6%AA%E0%A6%B0%E0%A6%BF%E0%A6%97%E0%A6%A3%E0%A6%95_%E0%A6%9A%E0%A6%BF%E0%A6%A4%E0%A7%8D%E0%A6%B0%E0%A6%B2%E0%A6%BF%E0%A6%96%E0%A6%A8)" title="চিত্রায়ন (পরিগণক চিত্রলিখন) – Bangla" lang="bn" hreflang="bn" data-title="চিত্রায়ন (পরিগণক চিত্রলিখন)" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A0%D0%B5%D0%BD%D0%B4%D1%8A%D1%80%D0%B8%D0%BD%D0%B3" title="Рендъринг – Bulgarian" lang="bg" hreflang="bg" data-title="Рендъринг" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Render_(ra%C4%8Dunarska_grafika)" title="Render (računarska grafika) – Bosnian" lang="bs" hreflang="bs" data-title="Render (računarska grafika)" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target">Bosanski</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Renderitzaci%C3%B3" title="Renderització – Catalan" lang="ca" hreflang="ca" data-title="Renderització" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Renderov%C3%A1n%C3%AD" title="Renderování – Czech" lang="cs" hreflang="cs" data-title="Renderování" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Rendere" title="Rendere – Danish" lang="da" hreflang="da" data-title="Rendere" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Bildsynthese" title="Bildsynthese – German" lang="de" hreflang="de" data-title="Bildsynthese" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%80%CF%8C%CE%B4%CE%BF%CF%83%CE%B7_(%CE%B3%CF%81%CE%B1%CF%86%CE%B9%CE%BA%CE%AC_%CF%85%CF%80%CE%BF%CE%BB%CE%BF%CE%B3%CE%B9%CF%83%CF%84%CE%AE)" title="Απόδοση (γραφικά υπολογιστή) – Greek" lang="el" hreflang="el" data-title="Απόδοση (γραφικά υπολογιστή)" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Renderizaci%C3%B3n" title="Renderización – Spanish" lang="es" hreflang="es" data-title="Renderización" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Renderizazio" title="Renderizazio – Basque" lang="eu" hreflang="eu" data-title="Renderizazio" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D9%86%D8%AF%D8%B1%DB%8C%D9%86%DA%AF_(%DA%AF%D8%B1%D8%A7%D9%81%DB%8C%DA%A9_%D8%B1%D8%A7%DB%8C%D8%A7%D9%86%D9%87%E2%80%8C%D8%A7%DB%8C)" title="رندرینگ (گرافیک رایانه‌ای) – Persian" lang="fa" hreflang="fa" data-title="رندرینگ (گرافیک رایانه‌ای)" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Rendu_photor%C3%A9aliste" title="Rendu photoréaliste – French" lang="fr" hreflang="fr" data-title="Rendu photoréaliste" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Renderizaci%C3%B3n" title="Renderización – Galician" lang="gl" hreflang="gl" data-title="Renderización" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A0%8C%EB%8D%94%EB%A7%81" title="렌더링 – Korean" lang="ko" hreflang="ko" data-title="렌더링" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8C%D5%A5%D5%B6%D5%A4%D5%A5%D6%80%D5%AB%D5%B6%D5%A3" title="Ռենդերինգ – Armenian" lang="hy" hreflang="hy" data-title="Ռենդերինգ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B0%E0%A5%87%E0%A4%82%E0%A4%A1%E0%A4%B0" title="रेंडर – Hindi" lang="hi" hreflang="hi" data-title="रेंडर" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Rekacitra" title="Rekacitra – Indonesian" lang="id" hreflang="id" data-title="Rekacitra" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Rendering" title="Rendering – Italian" lang="it" hreflang="it" data-title="Rendering" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Render%C4%93%C5%A1ana" title="Renderēšana – Latvian" lang="lv" hreflang="lv" data-title="Renderēšana" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Rendering" title="Rendering – Malay" lang="ms" hreflang="ms" data-title="Rendering" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Renderen" title="Renderen – Dutch" lang="nl" hreflang="nl" data-title="Renderen" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%AC%E3%83%B3%E3%83%80%E3%83%AA%E3%83%B3%E3%82%B0_(%E3%82%B3%E3%83%B3%E3%83%94%E3%83%A5%E3%83%BC%E3%82%BF)" title="レンダリング (コンピュータ) – Japanese" lang="ja" hreflang="ja" data-title="レンダリング (コンピュータ)" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Bildesyntese" title="Bildesyntese – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Bildesyntese" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Renderlash" title="Renderlash – Uzbek" lang="uz" hreflang="uz" data-title="Renderlash" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Renderowanie" title="Renderowanie – Polish" lang="pl" hreflang="pl" data-title="Renderowanie" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Renderiza%C3%A7%C3%A3o" title="Renderização – Portuguese" lang="pt" hreflang="pt" data-title="Renderização" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B5%D0%BD%D0%B4%D0%B5%D1%80%D0%B8%D0%BD%D0%B3" title="Рендеринг – Russian" lang="ru" hreflang="ru" data-title="Рендеринг" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Renderovanie" title="Renderovanie – Slovak" lang="sk" hreflang="sk" data-title="Renderovanie" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Upodabljanje" title="Upodabljanje – Slovenian" lang="sl" hreflang="sl" data-title="Upodabljanje" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Render%C3%B6inti" title="Renderöinti – Finnish" lang="fi" hreflang="fi" data-title="Renderöinti" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Rendering" title="Rendering – Swedish" lang="sv" hreflang="sv" data-title="Rendering" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B9%80%E0%B8%A3%E0%B9%87%E0%B8%99%E0%B9%80%E0%B8%94%E0%B8%AD%E0%B8%A3%E0%B9%8C" title="การเร็นเดอร์ – Thai" lang="th" hreflang="th" data-title="การเร็นเดอร์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C4%B0%C5%9Fleme" title="İşleme – Turkish" lang="tr" hreflang="tr" data-title="İşleme" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D0%B5%D0%BD%D0%B4%D0%B5%D1%80%D0%B8%D0%BD%D0%B3" title="Рендеринг – Ukrainian" lang="uk" hreflang="uk" data-title="Рендеринг" data-language-autonym="Українська" data-language-local-name="Ukrainian" 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engine">Rendering engine</a>)</div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Process of generating an image from a model</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Image synthesis" redirects here. Not to be confused with <a href="/wiki/Text-to-image_model" title="Text-to-image model">Text-to-image model</a>. For other uses, see <a href="/wiki/Computer_graphics#Image_types" title="Computer graphics">Computer graphics § Image types</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">For 3-dimensional rendering, see <a href="/wiki/3D_rendering" title="3D rendering">3D rendering</a>. For rendering of HTML, see <a href="/wiki/Browser_engine" title="Browser engine">browser engine</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></div></td><td class="mbox-text"><div class="mbox-text-span">This article needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a>. Please help <a href="/wiki/Special:EditPage/Rendering_(computer_graphics)" title="Special:EditPage/Rendering (computer graphics)">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed. Find sources: <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Rendering%22+computer+graphics">"Rendering" computer graphics</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Rendering%22+computer+graphics+-wikipedia&tbs=ar:1">news</a> · <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Rendering%22+computer+graphics&tbs=bkt:s&tbm=bks">newspapers</a> · <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Rendering%22+computer+graphics+-wikipedia">books</a> · <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Rendering%22+computer+graphics">scholar</a> · <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Rendering%22+computer+graphics&acc=on&wc=on">JSTOR</a> (May 2020) (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a>)</div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Render_Types.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Render_Types.png/220px-Render_Types.png" decoding="async" width="220" height="665" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Render_Types.png/330px-Render_Types.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/01/Render_Types.png/440px-Render_Types.png 2x" data-file-width="640" data-file-height="1935" /></a><figcaption>A variety of rendering techniques applied to a single 3D scene</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Glasses_800_edit.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Glasses_800_edit.png/220px-Glasses_800_edit.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Glasses_800_edit.png/330px-Glasses_800_edit.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Glasses_800_edit.png/440px-Glasses_800_edit.png 2x" data-file-width="2048" data-file-height="1536" /></a><figcaption>An image created by using <a href="/wiki/POV-Ray" title="POV-Ray">POV-Ray</a> 3.6</figcaption></figure> Rendering or image synthesis is the process of generating a <a href="/wiki/Physically-based_rendering" class="mw-redirect" title="Physically-based rendering">photorealistic</a> or <a href="/wiki/Non-photorealistic_rendering" title="Non-photorealistic rendering">non-photorealistic</a> image from a <a href="/wiki/2D_model" class="mw-redirect" title="2D model">2D</a> or <a href="/wiki/3D_model" class="mw-redirect" title="3D model">3D model</a> by means of a <a href="/wiki/Computer_program" title="Computer program">computer program</a>.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] The resulting image is referred to as a rendering. Multiple models can be defined in a scene file containing objects in a strictly defined language or <a href="/wiki/Data_structure" title="Data structure">data structure</a>. The scene file contains geometry, viewpoint, <a href="/wiki/Texture_mapping" title="Texture mapping">textures</a>, <a href="/wiki/Computer_graphics_lighting" title="Computer graphics lighting">lighting</a>, and <a href="/wiki/Shading" title="Shading">shading</a> information describing the virtual scene. The data contained in the scene file is then passed to a rendering program to be processed and output to a <a href="/wiki/Digital_image" title="Digital image">digital image</a> or <a href="/wiki/Raster_graphics" title="Raster graphics">raster graphics</a> image file. The term "rendering" is analogous to the concept of an <a href="/wiki/Artist%27s_impression" title="Artist's impression">artist's impression</a> of a scene. The term "rendering" is also used to describe the process of calculating effects in a video editing program to produce the final video output. A <a href="/wiki/Application_software" title="Application software">software application</a> or <a href="/wiki/Component-based_software_engineering" title="Component-based software engineering">component</a> that performs rendering is called a rendering <a href="/wiki/Software_engine" title="Software engine">engine</a>,<a href="#cite_note-1">[1]</a> render engine, <a href="/wiki/Category:Rendering_systems" title="Category:Rendering systems">rendering system</a>, graphics engine, or simply a renderer. Rendering is one of the major sub-topics of <a href="/wiki/3D_computer_graphics" title="3D computer graphics">3D computer graphics</a>, and in practice it is always connected to the others. It is the last major step in the <a href="/wiki/Graphics_pipeline" title="Graphics pipeline">graphics pipeline</a>, giving models and animation their final appearance. With the increasing sophistication of computer graphics since the 1970s, it has become a more distinct subject. Rendering has uses in <a href="/wiki/Architectural_rendering" title="Architectural rendering">architecture</a>, <a href="/wiki/Video_game" title="Video game">video games</a>, <a href="/wiki/Simulation" title="Simulation">simulators</a>, movie and TV <a href="/wiki/Visual_effects" title="Visual effects">visual effects</a>, and design visualization, each employing a different balance of features and techniques. A wide variety of renderers are available for use. Some are integrated into larger modeling and animation packages, some are stand-alone, and some are free open-source projects. On the inside, a renderer is a carefully engineered program based on multiple disciplines, including <a href="/wiki/Optics" title="Optics">light physics</a>, <a href="/wiki/Visual_system" title="Visual system">visual perception</a>, <a href="/wiki/Mathematics" title="Mathematics">mathematics</a>, and <a href="/wiki/Software_engineering" title="Software engineering">software development</a>. Though the technical details of rendering methods vary, the general challenges to overcome in producing a 2D image on a screen from a 3D representation stored in a scene file are handled by the <a href="/wiki/Graphics_pipeline" title="Graphics pipeline">graphics pipeline</a> in a rendering device such as a <a href="/wiki/Graphics_processing_unit" title="Graphics processing unit">GPU</a>. A GPU is a purpose-built device that assists a <a href="/wiki/Central_processing_unit" title="Central processing unit">CPU</a> in performing complex rendering calculations. If a scene is to look relatively realistic and predictable under virtual lighting, the rendering software must solve the <a href="/wiki/Rendering_equation" title="Rendering equation">rendering equation</a>. The rendering equation does not account for all lighting phenomena, but instead acts as a general lighting model for computer-generated imagery. In the case of 3D graphics, scenes can be <a href="/wiki/Pre-rendered" class="mw-redirect" title="Pre-rendered">pre-rendered</a> or generated in realtime. Pre-rendering is a slow, computationally intensive process that is typically used for movie creation, where scenes can be generated ahead of time, while <a href="/wiki/Real-time_computer_graphics" title="Real-time computer graphics">real-time</a> rendering is often done for 3D video games and other applications that must dynamically create scenes. 3D <a href="/wiki/Hardware_accelerators" class="mw-redirect" title="Hardware accelerators">hardware accelerators</a> can improve realtime rendering performance. <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Features">Features</h2>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=1" title="Edit section: Features">edit</a>]</div> A rendered image can be understood in terms of a number of visible features. Rendering <a href="/wiki/Research_and_development" title="Research and development">research and development</a> has been largely motivated by finding ways to simulate these efficiently. Some relate directly to particular algorithms and techniques, while others are produced together. <ul><li><a href="/wiki/Shading" title="Shading">Shading</a> – how the color and brightness of a surface varies with lighting</li> <li><a href="/wiki/Texture_mapping" title="Texture mapping">Texture-mapping</a> – a method of applying detail to surfaces</li> <li><a href="/wiki/Bump_mapping" title="Bump mapping">Bump-mapping</a> – a method of simulating small-scale bumpiness on surfaces</li> <li><a href="/wiki/Distance_fog" title="Distance fog">Fogging/participating medium</a> – how light dims when passing through non-clear atmosphere or air</li> <li><a href="/wiki/Shadow" title="Shadow">Shadows</a> – the effect of obstructing light</li> <li><a href="/wiki/Soft_shadows" class="mw-redirect" title="Soft shadows">Soft shadows</a> – varying darkness caused by partially obscured light sources</li> <li><a href="/wiki/Reflection_(computer_graphics)" title="Reflection (computer graphics)">Reflection</a> – mirror-like or highly glossy reflection</li> <li><a href="/wiki/Transparency_(optics)" class="mw-redirect" title="Transparency (optics)">Transparency (optics)</a>, <a href="/wiki/Transparency_(graphic)" title="Transparency (graphic)">transparency (graphic)</a> or <a href="/wiki/Opacity_(optics)" class="mw-redirect" title="Opacity (optics)">opacity</a> – sharp transmission of light through solid objects</li> <li><a href="/wiki/Translucency" class="mw-redirect" title="Translucency">Translucency</a> – highly scattered transmission of light through solid objects</li> <li><a href="/wiki/Refraction" title="Refraction">Refraction</a> – bending of light associated with transparency</li> <li><a href="/wiki/Diffraction" title="Diffraction">Diffraction</a> – bending, spreading, and interference of light passing by an object or aperture that disrupts the ray</li> <li><a href="/wiki/Global_illumination" title="Global illumination">Indirect illumination</a> – surfaces illuminated by light reflected off other surfaces, rather than directly from a light source (also known as global illumination)</li> <li><a href="/wiki/Caustic_(optics)" title="Caustic (optics)">Caustics</a> (a form of indirect illumination) – reflection of light off a shiny object, or focusing of light through a transparent object, to produce bright highlights on another object</li> <li><a href="/wiki/Depth_of_field" title="Depth of field">Depth of field</a> – objects appear blurry or out of focus when too far in front of or behind the object in focus</li> <li><a href="/wiki/Motion_blur" title="Motion blur">Motion blur</a> – objects appear blurry due to high-speed motion, or the motion of the camera</li> <li><a href="/wiki/Non-photorealistic_rendering" title="Non-photorealistic rendering">Non-photorealistic rendering</a> – rendering of scenes in an artistic style, intended to look like a painting or drawing</li></ul> <div class="mw-heading mw-heading2"><h2 id="Inputs">Inputs</h2>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=2" title="Edit section: Inputs">edit</a>]</div> Before a 3D scene or 2D image can be rendered, it must be described in a way that the rendering software can understand. Historically, inputs for both 2D and 3D rendering were usually <a href="/wiki/Text_file" title="Text file">text files</a>, which are easier than binary files for humans to edit and debug. For 3D graphics, text formats have largely been supplanted by more efficient <a href="/wiki/Binary_file" title="Binary file">binary formats</a>, and by <a href="/wiki/API" title="API">APIs</a> which allow interactive applications to communicate directly with a rendering component without generating a file on disk (although a scene description is usually still created in memory prior to rendering).<a href="#cite_note-Raghavachary2005-2">[2]</a>: 1.2, 3.2.6, 3.3.1, 3.3.7  Traditional rendering algorithms use geometric descriptions of 3D scenes or 2D images. Applications and algorithms that render <a href="/wiki/Visualization_(graphics)" title="Visualization (graphics)">visualizations</a> of data scanned from the real world, or scientific <a href="/wiki/Computer_simulation" title="Computer simulation">simulations</a>, may require different types of input data. The <a href="/wiki/PostScript" title="PostScript">PostScript</a> format (which is often credited with the rise of <a href="/wiki/Desktop_publishing" title="Desktop publishing">desktop publishing</a>) provides a standardized, interoperable way to describe 2D graphics and <a href="/wiki/Page_layout" title="Page layout">page layout</a>. The <a href="/wiki/SVG" title="SVG">Scalable Vector Graphics (SVG)</a> format is also text-based, and the <a href="/wiki/PDF" title="PDF">PDF</a> format uses the PostScript language internally. In contrast, although many 3D graphics file formats have been standardized (including text-based formats such as <a href="/wiki/VRML" title="VRML">VRML</a> and <a href="/wiki/X3D" title="X3D">X3D</a>), different rendering applications typically use formats tailored to their needs, and this has led to a proliferation of proprietary and open formats, with binary files being more common.<a href="#cite_note-Raghavachary2005-2">[2]</a>: 3.2.3, 3.2.5, 3.3.7 <a href="#cite_note-PSRef-3">[3]</a>: vii <a href="#cite_note-MDN_SVG-4">[4]</a><a href="#cite_note-Hughes2014-5">[5]</a>: 16.5.2. <a href="#cite_note-BlenderImportExport-6">[6]</a> <div class="mw-heading mw-heading3"><h3 id="2D_vector_graphics">2D vector graphics</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=3" title="Edit section: 2D vector graphics">edit</a>]</div> A <a href="/wiki/Vector_graphics" title="Vector graphics">vector graphics</a> image description may include:<a href="#cite_note-PSRef-3">[3]</a><a href="#cite_note-MDN_SVG-4">[4]</a> <ul><li><a href="/wiki/Cartesian_coordinate_system" title="Cartesian coordinate system">Coordinates</a> and <a href="/wiki/Curvature" title="Curvature">curvature</a> information for <a href="/wiki/Line_segments" class="mw-redirect" title="Line segments">line segments</a>, <a href="/wiki/Circular_arc" title="Circular arc">arcs</a>, and <a href="/wiki/B%C3%A9zier_curve" title="Bézier curve">Bézier curves</a> (which may be used as boundaries of filled shapes)</li> <li>Center coordinates, width, and height (or <a href="/wiki/Minimum_bounding_rectangle" title="Minimum bounding rectangle">bounding rectangle</a> coordinates) of <a href="/wiki/Geometric_primitive" title="Geometric primitive">basic</a> shapes such as <a href="/wiki/Rectangle" title="Rectangle">rectangles</a>, <a href="/wiki/Circle" title="Circle">circles</a> and <a href="/wiki/Ellipse" title="Ellipse">ellipses</a></li> <li>Color, width and pattern (such as dashed or dotted) for rendering lines</li> <li>Colors, patterns, and <a href="/wiki/Color_gradient" title="Color gradient">gradients</a> for filling shapes</li> <li><a href="/wiki/Bitmap" title="Bitmap">Bitmap</a> image data (either embedded or in an external file) along with scale and position information</li> <li><a href="/wiki/Font_rasterization" title="Font rasterization">Text to be rendered</a> (along with size, position, orientation, color, and font)</li> <li><a href="/wiki/Clipping_(computer_graphics)" title="Clipping (computer graphics)">Clipping</a> information, if only part of a shape or bitmap image should be rendered</li> <li>Transparency and <a href="/wiki/Compositing" title="Compositing">compositing</a> information for rendering overlapping shapes</li> <li><a href="/wiki/Color_space" title="Color space">Color space</a> information, allowing the image to be rendered consistently on different displays and printers</li></ul> <div class="mw-heading mw-heading3"><h3 id="3D_geometry">3D geometry</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=4" title="Edit section: 3D geometry">edit</a>]</div> A geometric scene description may include:<a href="#cite_note-Raghavachary2005-2">[2]</a>: Ch. 4-7, 8.7 <a href="#cite_note-pbrt4FF-7">[7]</a> <ul><li>Size, position, and orientation of <a href="/wiki/Geometric_primitive" title="Geometric primitive">geometric primitives</a> such as spheres and cones (which may be <a href="/wiki/Constructive_solid_geometry" title="Constructive solid geometry">combined in various ways</a> to create more complex objects)</li> <li><a href="/wiki/Vertex_(geometry)" title="Vertex (geometry)">Vertex</a> <a href="/wiki/Cartesian_coordinate_system" title="Cartesian coordinate system">coordinates</a> and <a href="/wiki/Normal_(geometry)" title="Normal (geometry)">surface normal</a> <a href="/wiki/Euclidean_vector" title="Euclidean vector">vectors</a> for <a href="/wiki/Polygon_mesh" title="Polygon mesh">meshes</a> of triangles or polygons (often rendered as smooth surfaces by <a href="/wiki/Subdivision_surface" title="Subdivision surface">subdividing</a> the mesh)</li> <li><a href="/wiki/Geometric_transformation" title="Geometric transformation">Transformations</a> for positioning, rotating, and scaling objects within a scene (allowing parts of the scene to use different local coordinate systems).</li> <li>"Camera" information describing how the scene is being viewed (position, direction, <a href="/wiki/Focal_length" title="Focal length">focal length</a>, and <a href="/wiki/Field_of_view" title="Field of view">field of view</a>)</li> <li>Light information (location, type, brightness, and color)</li> <li>Optical properties of surfaces, such as <a href="/wiki/Albedo" title="Albedo">albedo</a>, <a href="/wiki/Reflectance" title="Reflectance">reflectance</a>, and <a href="/wiki/Refractive_index" title="Refractive index">refractive index</a>,</li> <li>Optical properties of media through which light passes (transparent solids, liquids, clouds, smoke), e.g. <a href="/wiki/Absorption_cross_section" title="Absorption cross section">absorption</a> and <a href="/wiki/Cross_section_(physics)#Scattering_of_light" title="Cross section (physics)">scattering</a> cross sections</li> <li><a href="/wiki/Bitmap" title="Bitmap">Bitmap</a> image data used as <a href="/wiki/Texture_mapping" title="Texture mapping">texture maps</a> for surfaces</li> <li>Small scripts or programs for generating complex 3D shapes or scenes <a href="/wiki/Procedural_generation" title="Procedural generation">procedurally</a></li> <li>Description of how object and camera locations and other information change over time, for rendering an animation</li></ul> Many file formats exist for storing individual 3D objects or "<a href="/wiki/3D_modeling" title="3D modeling">models</a>". These can be imported into a larger scene, or loaded on-demand by rendering software or games. A realistic scene may require hundreds of items like household objects, vehicles, and trees, and <a href="/wiki/Environment_artist" title="Environment artist">3D artists</a> often utilize large libraries of models. In game production, these models (along with other data such as textures, audio files, and animations) are referred to as "<a href="/wiki/Digital_asset" title="Digital asset">assets</a>".<a href="#cite_note-BlenderImportExport-6">[6]</a><a href="#cite_note-Dunlop2014-8">[8]</a>: Ch. 4  <div class="mw-heading mw-heading3"><h3 id="Volumetric_data">Volumetric data</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=5" title="Edit section: Volumetric data">edit</a>]</div> Scientific and engineering <a href="/wiki/Visualization_(graphics)" title="Visualization (graphics)">visualization</a> often requires rendering <a href="/wiki/Voxel" title="Voxel">volumetric data</a> generated by 3D scans or <a href="/wiki/Computer_simulation" title="Computer simulation">simulations</a>. Perhaps the most common source of such data is medical <a href="/wiki/CT_scan" title="CT scan">CT</a> and <a href="/wiki/Magnetic_resonance_imaging" title="Magnetic resonance imaging">MRI</a> scans, which need to be rendered for diagnosis. Volumetric data can be extremely large, and requires <a href="/wiki/OpenVDB" title="OpenVDB">specialized data formats</a> to store it efficiently, particularly if the volume is <a href="/wiki/Sparse_matrix" title="Sparse matrix">sparse</a> (with empty regions that do not contain data).<a href="#cite_note-AkenineMöller2018-9">[9]</a>: 14.3.1 <a href="#cite_note-OpenVDBAbout-10">[10]</a><a href="#cite_note-Museth2013-11">[11]</a> Before rendering, <a href="/wiki/Level_set" title="Level set">level sets</a> for volumetric data can be extracted and converted into a mesh of triangles, e.g. by using the <a href="/wiki/Marching_cubes" title="Marching cubes">marching cubes</a> algorithm. Algorithms have also been developed that work directly with volumetric data, for example to render realistic depictions of the way light is scattered and absorbed by clouds and smoke, and this type of volumetric rendering is used extensively in visual effects for movies. When rendering lower-resolution volumetric data without interpolation, the individual cubes or "<a href="/wiki/Voxel" title="Voxel">voxels</a>" may be visible, an effect sometimes used deliberately for game graphics.<a href="#cite_note-Bridson2015-12">[12]</a>: 4.6 <a href="#cite_note-AkenineMöller2018-9">[9]</a>: 13.10, Ch. 14, 16.1  <div class="mw-heading mw-heading3"><h3 id="Photogrammetry_and_scanning">Photogrammetry and scanning</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=6" title="Edit section: Photogrammetry and scanning">edit</a>]</div> Photographs of real world objects can be incorporated into a rendered scene by using them as <a href="/wiki/Texture_mapping" title="Texture mapping">textures</a> for 3D objects. Photos of a scene can also be stitched together to create <a href="/wiki/Panorama" title="Panorama">panoramic images</a> or <a href="/wiki/Reflection_mapping" title="Reflection mapping">environment maps</a>, which allow the scene to be rendered very efficiently but only from a single viewpoint. Scanning of real objects and scenes using <a href="/wiki/Structured-light_3D_scanner" title="Structured-light 3D scanner">structured light</a> or <a href="/wiki/Lidar" title="Lidar">lidar</a> produces <a href="/wiki/Point_cloud" title="Point cloud">point clouds</a> consisting of the coordinates of millions of individual points in space, sometimes along with color information. These point clouds may either be rendered directly or <a href="/wiki/Point_cloud#Conversion_to_3D_surfaces" title="Point cloud">converted into meshes</a> before rendering. (Note: "point cloud" sometimes also refers to a minimalist rendering style that can be used for any 3D geometry, similar to wireframe rendering.)<a href="#cite_note-AkenineMöller2018-9">[9]</a>: 13.3, 13.9 <a href="#cite_note-Raghavachary2005-2">[2]</a>: 1.3  <div class="mw-heading mw-heading3"><h3 id="Neural_approximations_and_light_fields">Neural approximations and light fields</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=7" title="Edit section: Neural approximations and light fields">edit</a>]</div> A more recent, experimental approach is description of scenes using <a href="/wiki/Neural_radiance_field" title="Neural radiance field">radiance fields</a> which define the color, intensity, and direction of incoming light at each point in space. (This is conceptually similar to, but not identical to, the <a href="/wiki/Light_field" title="Light field">light field</a> recorded by a <a href="/wiki/Holography" title="Holography">hologram</a>.) For any useful resolution, the amount of data in a radiance field is so large that it is impractical to represent it directly as volumetric data, and an <a href="/wiki/Approximation" title="Approximation">approximation</a> function must be found. <a href="/wiki/Deep_learning" title="Deep learning">Neural networks</a> are typically used to generate and evaluate these approximations, sometimes using video frames, or a collection of photographs of a scene taken at different angles, as "<a href="/wiki/Training,_validation,_and_test_data_sets#Training_data_set" title="Training, validation, and test data sets">training data</a>".<a href="#cite_note-Schmid2023-13">[13]</a><a href="#cite_note-Mildenhall2020-14">[14]</a> Algorithms related to neural networks have recently been used to find approximations of a scene as <a href="/wiki/Gaussian_splatting" title="Gaussian splatting">3D Gaussians</a>. The resulting representation is similar to a <a href="/wiki/Point_cloud" title="Point cloud">point cloud</a>, except that it uses fuzzy, partially-transparent blobs of varying dimensions and orientations instead of points. As with <a href="/wiki/Neural_radiance_field" title="Neural radiance field">neural radiance fields</a>, these approximations are often generated from photographs or video frames.<a href="#cite_note-Kerbl2023-15">[15]</a> <div class="mw-heading mw-heading2"><h2 id="Outputs">Outputs</h2>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=8" title="Edit section: Outputs">edit</a>]</div> The output of rendering may be displayed immediately on the screen (many times a second, in the case of real-time rendering such as games) or saved in a <a href="/wiki/Raster_graphics" title="Raster graphics">raster graphics</a> file format such as <a href="/wiki/JPEG" title="JPEG">JPEG</a> or <a href="/wiki/PNG" title="PNG">PNG</a>. High-end rendering applications commonly use the <a href="/wiki/OpenEXR" title="OpenEXR">OpenEXR</a> file format, which can represent finer gradations of colors and <a href="/wiki/High_dynamic_range" title="High dynamic range">high dynamic range</a> lighting, allowing <a href="/wiki/Tone_mapping" title="Tone mapping">tone mapping</a> or other adjustments to be applied afterwards without loss of quality.<a href="#cite_note-pbrt4UG-16">[16]</a><a href="#cite_note-Brinkmann2008-17">[17]</a>: Ch. 14, Ap. B  Quickly rendered animations can be saved directly as video files, but for high-quality rendering, individual frames (which may be rendered by different computers in a <a href="/wiki/Computer_cluster" title="Computer cluster">cluster</a> or <a href="/wiki/Render_farm" title="Render farm">render farm</a> and may take hours or even days to render) are output as separate files and combined later into a video clip.<a href="#cite_note-BlenderRenderingAnimations-18">[18]</a><a href="#cite_note-Dunlop2014-8">[8]</a>: 1.5, 3.11, 8.11  The output of a renderer sometimes includes more than just <a href="/wiki/RGB_color_model#Numeric_representations" title="RGB color model">RGB color values</a>. For example, the spectrum can be sampled using multiple wavelengths of light, or additional information such as depth (distance from camera) or the material of each point in the image can be included (this data can be used during compositing or when generating <a href="/wiki/Texture_mapping" title="Texture mapping">texture maps</a> for real-time rendering, or used to assist in <a href="/wiki/Noise_reduction#In_images" title="Noise reduction">removing noise</a> from a path-traced image). Transparency information can be included, allowing rendered foreground objects to be composited with photographs or video. It is also sometimes useful to store the contributions of different lights, or of specular and diffuse lighting, as separate channels, so lighting can be adjusted after rendering. The <a href="/wiki/OpenEXR" title="OpenEXR">OpenEXR</a> format allows storing many channels of data in a single file.<a href="#cite_note-pbrt4UG-16">[16]</a><a href="#cite_note-Brinkmann2008-17">[17]</a>: Ch. 14, Ap. B  <div class="mw-heading mw-heading2"><h2 id="Techniques">Techniques</h2>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=9" title="Edit section: Techniques">edit</a>]</div> Choosing how to render a 3D scene usually involves trade-offs between speed, memory usage, and realism (although realism is not always desired). The <style data-mw-deduplicate="TemplateStyles:r1238216509">.mw-parser-output .vanchor>:target~.vanchor-text{background-color:#b1d2ff}@media screen{html.skin-theme-clientpref-night .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}</style>algorithms developed over the years follow a loose progression, with more advanced methods becoming practical as computing power and memory capacity increased. Multiple techniques may be used for a single final image. An important distinction is between <a href="/wiki/Image_and_object_order_rendering" title="Image and object order rendering">image order</a> algorithms, which iterate over pixels of the image plane, and <a href="/wiki/Image_and_object_order_rendering" title="Image and object order rendering">object order</a> algorithms, which iterate over objects in the scene. For simple scenes, object order is usually more efficient, as there are fewer objects than pixels.<a href="#cite_note-Marschner2022-19">[19]</a>: Ch. 4  <dl><dt><a href="/wiki/Vector_graphics" title="Vector graphics">2D vector graphics</a></dt> <dd>The <a href="/wiki/Vector_monitor" title="Vector monitor">vector displays</a> of the 1960s-1970s used deflection of an <a href="/wiki/Cathode_ray" title="Cathode ray">electron beam</a> to draw <a href="/wiki/Line_segment" title="Line segment">line segments</a> directly on the screen. Nowadays, <a href="/wiki/Vector_graphics" title="Vector graphics">vector graphics</a> are rendered by <a href="/wiki/Rasterization" class="mw-redirect" title="Rasterization">rasterization</a> algorithms that also support filled shapes. In principle, any 2D vector graphics renderer can be used to render 3D objects by first projecting them onto a 2D image plane. <a href="#cite_note-Foley82-20">[20]</a>: 93, 431, 505, 553 </dd> <dt><a href="/wiki/Rasterisation#3D_images" title="Rasterisation">3D rasterization</a></dt> <dd>Adapts 2D rasterization algorithms so they can be used more efficiently for 3D rendering, handling <a href="/wiki/Hidden-surface_determination" title="Hidden-surface determination">hidden surface removal</a> via <a href="/wiki/Scanline_rendering" title="Scanline rendering">scanline</a> or <a href="/wiki/Z-buffering" title="Z-buffering">z-buffer</a> techniques. Different realistic or stylized effects can be obtained by coloring the pixels covered by the objects in different ways. <a href="/wiki/Computer_representation_of_surfaces" title="Computer representation of surfaces">Surfaces</a> are typically divided into <a href="/wiki/Polygon_mesh" title="Polygon mesh">meshes</a> of triangles before being rasterized. Rasterization is usually synonymous with "object order" rendering (as described above).<a href="#cite_note-Foley82-20">[20]</a>: 560-561, 575-590 <a href="#cite_note-Raghavachary2005-2">[2]</a>: 8.5 <a href="#cite_note-Marschner2022-19">[19]</a>: Ch. 9 </dd> <dt><a href="/wiki/Ray_casting" title="Ray casting">Ray casting</a></dt> <dd>Uses geometric formulas to compute the first object that a <a href="/wiki/Line_(geometry)#Ray" title="Line (geometry)">ray</a> intersects.<a href="#cite_note-RayTracingGems_1-21">[21]</a>: 8  It can be used to implement "image order" rendering by casting a ray for each pixel, and finding a corresponding point in the scene. Ray casting is a fundamental operation used for both graphical and non-graphical purposes,<a href="#cite_note-RealTimeRayTracing-22">[22]</a>: 6  e.g. determining whether a point is in shadow, or checking what an enemy can see in a <a href="/wiki/Artificial_intelligence_in_video_games" title="Artificial intelligence in video games">game</a>.</dd> <dt><a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">Ray tracing</a></dt> <dd>Simulates the bouncing paths of light caused by <a href="/wiki/Specular_reflection" title="Specular reflection">specular reflection</a> and <a href="/wiki/Refraction" title="Refraction">refraction</a>, requiring a varying number of ray casting operations for each path. Advanced forms use <a href="/wiki/Monte_Carlo_method" title="Monte Carlo method">Monte Carlo techniques</a> to render effects such as area lights, <a href="/wiki/Depth_of_field" title="Depth of field">depth of field</a>, blurry reflections, and <a href="/wiki/Umbra,_penumbra_and_antumbra" title="Umbra, penumbra and antumbra">soft shadows</a>, but computing <a href="/wiki/Global_illumination" title="Global illumination">global illumination</a> is usually in the domain of path tracing.<a href="#cite_note-RayTracingGems_1-21">[21]</a>: 9-13 <a href="#cite_note-IntroToRTCh5-23">[23]</a></dd> <dt><a href="/wiki/Radiosity_(computer_graphics)" title="Radiosity (computer graphics)">Radiosity</a></dt> <dd>A <a href="/wiki/Finite_element_method" title="Finite element method">finite element analysis</a> approach that breaks surfaces in the scene into pieces, and estimates the amount of light that each piece receives from light sources, or indirectly from other surfaces. Once the <a href="/wiki/Irradiance" title="Irradiance">irradiance</a> of each surface is known, the scene can be rendered using rasterization or ray tracing.<a href="#cite_note-Glassner95-24">[24]</a>: 888-890, 1044-1045 </dd> <dt><a href="/wiki/Path_tracing" title="Path tracing">Path tracing</a></dt> <dd>Uses <a href="/wiki/Monte_Carlo_method" title="Monte Carlo method">Monte Carlo integration</a> with a simplified form of ray tracing, computing the average brightness of a <a href="/wiki/Sampling_(statistics)" title="Sampling (statistics)">sample</a> of the possible paths that a photon could take when traveling from a light source to the camera (for some images, thousands of paths need to be sampled per pixel<a href="#cite_note-RealTimeRayTracing-22">[22]</a>: 8 ). It was introduced as a <a href="/wiki/Unbiased_rendering" title="Unbiased rendering">statistically unbiased</a> way to solve the <a href="/wiki/Rendering_equation" title="Rendering equation">rendering equation</a>, giving ray tracing a rigorous mathematical foundation.<a href="#cite_note-Kajiya1986-25">[25]</a><a href="#cite_note-RayTracingGems_1-21">[21]</a>: 11-13 </dd></dl> Each of the above approaches has many variations, and there is some overlap. Path tracing may be considered either a distinct technique or a particular type of ray tracing.<a href="#cite_note-Glassner95-24">[24]</a>: 846, 1021  Note that the <a href="/wiki/Usage_(language)" title="Usage (language)">usage</a> of terminology related to ray tracing and path tracing has changed significantly over time.<a href="#cite_note-RayTracingGems_1-21">[21]</a>: 7  <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Real-time_Raymarched_Terrain.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Real-time_Raymarched_Terrain.png/220px-Real-time_Raymarched_Terrain.png" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Real-time_Raymarched_Terrain.png/330px-Real-time_Raymarched_Terrain.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Real-time_Raymarched_Terrain.png/440px-Real-time_Raymarched_Terrain.png 2x" data-file-width="590" data-file-height="393" /></a><figcaption>Rendering of a fractal terrain by <a href="/wiki/Ray_marching" title="Ray marching">ray marching</a></figcaption></figure> <a href="/wiki/Ray_marching" title="Ray marching">Ray marching</a> is a family of algorithms, used by ray casting, for finding intersections between a ray and a complex object, such as a <a href="/wiki/Volume_ray_casting" title="Volume ray casting">volumetric dataset</a> or a surface defined by a <a href="/wiki/Signed_distance_function" title="Signed distance function">signed distance function</a>. It is not, by itself, a rendering method, but it can be incorporated into ray tracing and path tracing, and is used by rasterization to implement screen-space reflection and other effects.<a href="#cite_note-RayTracingGems_1-21">[21]</a>: 13  A technique called <a href="/wiki/Photon_mapping" title="Photon mapping">photon mapping</a> traces paths of photons from a light source to an object, accumulating data about <a href="/wiki/Irradiance" title="Irradiance">irradiance</a> which is then used during conventional ray tracing or path tracing.<a href="#cite_note-Glassner95-24">[24]</a>: 1037-1039  Rendering a scene using only rays traced from the light source to the camera is impractical, even though it corresponds more closely to reality, because a huge number of photons would need to be simulated, only a tiny fraction of which actually hit the camera.<a href="#cite_note-IntroToRTCh1-26">[26]</a>: 7-9 <a href="#cite_note-Foley82-20">[20]</a>: 587  Some authors call conventional ray tracing "backward" ray tracing because it traces the paths of photons backwards from the camera to the light source, and call following paths from the light source (as in photon mapping) "forward" ray tracing.<a href="#cite_note-IntroToRTCh1-26">[26]</a>: 7-9  However sometimes the meaning of these terms is reversed.<a href="#cite_note-Arvo1986-27">[27]</a> Tracing rays starting at the light source can also be called particle tracing or light tracing, which avoids this ambiguity.<a href="#cite_note-Veach1997-28">[28]</a>: 92 <a href="#cite_note-Dutré2015-29">[29]</a>: 4.5.4  Real-time rendering, including video game graphics, typically uses rasterization, but increasingly combines it with ray tracing and path tracing.<a href="#cite_note-RealTimeRayTracing-22">[22]</a>: 2  To enable realistic <a href="/wiki/Global_illumination" title="Global illumination">global illumination</a>, real-time rendering often relies on pre-rendered ("baked") lighting for stationary objects. For moving objects, it may use a technique called light probes, in which lighting is recorded by rendering omnidirectional views of the scene at chosen points in space (often points on a grid to allow easier <a href="/wiki/Interpolation" title="Interpolation">interpolation</a>). These are similar to <a href="/wiki/Reflection_mapping" title="Reflection mapping">environment maps</a>, but typically use a very low resolution or an approximation such as <a href="/wiki/Spherical_harmonics" title="Spherical harmonics">spherical harmonics</a>.<a href="#cite_note-UnityLightProbes-30">[30]</a> (Note: <a href="/wiki/Blender_(software)" title="Blender (software)">Blender</a> uses the term 'light probes' for a more general class of pre-recorded lighting data, including reflection maps.<a href="#cite_note-BlenderSettingsLightProbes-31">[31]</a>) <style data-mw-deduplicate="TemplateStyles:r1248256098">@media all and (max-width:720px){.mw-parser-output .mod-gallery{width:100%!important}}.mw-parser-output .mod-gallery{display:table}.mw-parser-output .mod-gallery-default{background:transparent;margin-top:4px}.mw-parser-output .mod-gallery-center{margin-left:auto;margin-right:auto}.mw-parser-output .mod-gallery-left{float:left}.mw-parser-output .mod-gallery-right{float:right}.mw-parser-output .mod-gallery-none{float:none}.mw-parser-output .mod-gallery-collapsible{width:100%}.mw-parser-output .mod-gallery .title,.mw-parser-output .mod-gallery .main,.mw-parser-output .mod-gallery .footer{display:table-row}.mw-parser-output .mod-gallery .title>div{display:table-cell;padding:0 4px 4px;text-align:center;font-weight:bold}.mw-parser-output .mod-gallery .main>div{display:table-cell}.mw-parser-output .mod-gallery .gallery{line-height:1.35em}.mw-parser-output .mod-gallery .footer>div{display:table-cell;padding:4px;text-align:right;font-size:85%;line-height:1em}.mw-parser-output .mod-gallery .title>div *,.mw-parser-output .mod-gallery .footer>div *{overflow:visible}.mw-parser-output .mod-gallery .gallerybox img{background:none!important}.mw-parser-output .mod-gallery .bordered-images .thumb img{border:solid var(--background-color-neutral,#eaecf0)1px}.mw-parser-output .mod-gallery .whitebg .thumb{background:var(--background-color-base,#fff)!important}</style><div class="mod-gallery mod-gallery-default"><div class="title"><div>Examples comparing different rendering techniques</div></div><div class="main"><div><ul class="gallery mw-gallery-nolines nochecker bordered-images whitebg"> <li class="gallerybox" style="width: 185px"> <div class="thumb" style="width: 180px;"><a href="/wiki/File:Rendering_techniques_example,_rasterization,_low_quality,_Blender_EEVEE.png" class="mw-file-description" title="A low quality rasterized image, rendered by Blender's EEVEE renderer with low shadow map resolution and a low-resolution mesh"><img alt="3D rendered image showing three copies of a cartoon cow. The one on the left has a mirror surface, and the one on the right uses a transparent glass material. The shadows of the cows are blocky (like blurry pixels) due to low quality settings in the renderer." src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Rendering_techniques_example%2C_rasterization%2C_low_quality%2C_Blender_EEVEE.png/180px-Rendering_techniques_example%2C_rasterization%2C_low_quality%2C_Blender_EEVEE.png" decoding="async" width="180" height="135" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Rendering_techniques_example%2C_rasterization%2C_low_quality%2C_Blender_EEVEE.png/270px-Rendering_techniques_example%2C_rasterization%2C_low_quality%2C_Blender_EEVEE.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/Rendering_techniques_example%2C_rasterization%2C_low_quality%2C_Blender_EEVEE.png/360px-Rendering_techniques_example%2C_rasterization%2C_low_quality%2C_Blender_EEVEE.png 2x" data-file-width="1024" data-file-height="768" /></a></div> <div class="gallerytext">A low quality rasterized image, rendered by <a href="/wiki/Blender_(software)" title="Blender (software)">Blender</a>'s EEVEE renderer with low <a href="/wiki/Shadow_mapping" title="Shadow mapping">shadow map</a> resolution and a low-resolution mesh</div> </li> <li class="gallerybox" style="width: 185px"> <div class="thumb" style="width: 180px;"><a href="/wiki/File:Rendering_techniques_example,_path_tracing,_low_quality,_Blender_Cycles.png" class="mw-file-description" title="A low quality path traced image, rendered by Blender's Cycles renderer with only 16 sampled paths per pixel and a low-resolution mesh"><img alt="3D rendered image showing three copies of a cartoon cow. The one on the left has a mirror surface, and the one on the right uses a transparent glass material. The image is speckled with many white dots, especially in the shadowed areas, due to low quality settings in the renderer. The reflection, transparency, and lighting are realistic, but the speckles distract from this." src="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Rendering_techniques_example%2C_path_tracing%2C_low_quality%2C_Blender_Cycles.png/180px-Rendering_techniques_example%2C_path_tracing%2C_low_quality%2C_Blender_Cycles.png" decoding="async" width="180" height="135" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Rendering_techniques_example%2C_path_tracing%2C_low_quality%2C_Blender_Cycles.png/270px-Rendering_techniques_example%2C_path_tracing%2C_low_quality%2C_Blender_Cycles.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/95/Rendering_techniques_example%2C_path_tracing%2C_low_quality%2C_Blender_Cycles.png/360px-Rendering_techniques_example%2C_path_tracing%2C_low_quality%2C_Blender_Cycles.png 2x" data-file-width="1024" data-file-height="768" /></a></div> <div class="gallerytext">A low quality path traced image, rendered by Blender's Cycles renderer with only 16 sampled paths per pixel and a low-resolution mesh</div> </li> <li class="gallerybox" style="width: 185px"> <div class="thumb" style="width: 180px;"><a href="/wiki/File:Rendering_techniques_example,_ray_tracing,_low_quality,_POV-Ray.png" class="mw-file-description" title="A ray traced image, using the POV-Ray program (using only its ray tracing features) with a low-resolution mesh"><img alt="3D rendered image showing three copies of a cartoon cow. The one on the left has a mirror surface, and the one on the right uses a transparent glass material. The outlines are angular and there are some defects (due to the low-resolution mesh of the models), and the transparent cow has no shadow." src="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Rendering_techniques_example%2C_ray_tracing%2C_low_quality%2C_POV-Ray.png/180px-Rendering_techniques_example%2C_ray_tracing%2C_low_quality%2C_POV-Ray.png" decoding="async" width="180" height="135" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Rendering_techniques_example%2C_ray_tracing%2C_low_quality%2C_POV-Ray.png/270px-Rendering_techniques_example%2C_ray_tracing%2C_low_quality%2C_POV-Ray.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/49/Rendering_techniques_example%2C_ray_tracing%2C_low_quality%2C_POV-Ray.png/360px-Rendering_techniques_example%2C_ray_tracing%2C_low_quality%2C_POV-Ray.png 2x" data-file-width="1024" data-file-height="768" /></a></div> <div class="gallerytext">A ray traced image, using the <a href="/wiki/POV-Ray" title="POV-Ray">POV-Ray</a> program (using only its ray tracing features) with a low-resolution mesh</div> </li> <li class="gallerybox" style="width: 185px"> <div class="thumb" style="width: 180px;"><a href="/wiki/File:Rendering_techniques_example,_rasterization,_high_quality,_Blender_EEVEE.png" class="mw-file-description" title="A higher quality rasterized image, using Blender's EEVEE renderer with light probes"><img alt="3D rendered image showing three copies of a cartoon cow. The one on the left has a mirror surface, and the one on the right uses a transparent glass material. The outlines of the cows and the shadows are smooth with no blockiness or angular defects, and the reflection looks quite realistic, but the transparency does not look convincing, and the lighting in the shadowed areas of the cows is not quite realistic." src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Rendering_techniques_example%2C_rasterization%2C_high_quality%2C_Blender_EEVEE.png/180px-Rendering_techniques_example%2C_rasterization%2C_high_quality%2C_Blender_EEVEE.png" decoding="async" width="180" height="135" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Rendering_techniques_example%2C_rasterization%2C_high_quality%2C_Blender_EEVEE.png/270px-Rendering_techniques_example%2C_rasterization%2C_high_quality%2C_Blender_EEVEE.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Rendering_techniques_example%2C_rasterization%2C_high_quality%2C_Blender_EEVEE.png/360px-Rendering_techniques_example%2C_rasterization%2C_high_quality%2C_Blender_EEVEE.png 2x" data-file-width="2048" data-file-height="1536" /></a></div> <div class="gallerytext">A higher quality rasterized image, using <a href="/wiki/Blender_(software)" title="Blender (software)">Blender</a>'s EEVEE renderer with light probes</div> </li> <li class="gallerybox" style="width: 185px"> <div class="thumb" style="width: 180px;"><a href="/wiki/File:Rendering_techniques_example,_path_tracing,_high_quality,_Blender_Cycles.png" class="mw-file-description" title="A higher quality path traced image, using Blender's Cycles renderer with 2000 sampled paths per pixel"><img alt="3D rendered image showing three copies of a cartoon cow. The one on the left has a mirror surface, and the one on the right uses a transparent glass material. The outlines of the cows and the shadows are smooth with no blockiness or angular defects. There are a few speckles of white pixels, but far fewer than in the low-quality image. The reflection, transparency, and lighting look realistic." src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Rendering_techniques_example%2C_path_tracing%2C_high_quality%2C_Blender_Cycles.png/180px-Rendering_techniques_example%2C_path_tracing%2C_high_quality%2C_Blender_Cycles.png" decoding="async" width="180" height="135" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Rendering_techniques_example%2C_path_tracing%2C_high_quality%2C_Blender_Cycles.png/270px-Rendering_techniques_example%2C_path_tracing%2C_high_quality%2C_Blender_Cycles.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Rendering_techniques_example%2C_path_tracing%2C_high_quality%2C_Blender_Cycles.png/360px-Rendering_techniques_example%2C_path_tracing%2C_high_quality%2C_Blender_Cycles.png 2x" data-file-width="2048" data-file-height="1536" /></a></div> <div class="gallerytext">A higher quality path traced image, using <a href="/wiki/Blender_(software)" title="Blender (software)">Blender</a>'s Cycles renderer with 2000 sampled paths per pixel</div> </li> <li class="gallerybox" style="width: 185px"> <div class="thumb" style="width: 180px;"><a href="/wiki/File:Rendering_techniques_example,_ray_tracing,_radiosity,_photon_mapping,_POV-Ray.png" class="mw-file-description" title="An image rendered using POV-Ray's ray tracing, radiosity and photon mapping features"><img alt="3D rendered image showing three copies of a cartoon cow. The one on the left has a mirror surface, and the one on the right uses a transparent glass material. The outlines of the cows and the shadows are smooth with no blockiness or angular defects. The lighting is realistic, including in the shadowed areas. The base surface is illuminated by bright spots and lines ("caustics") caused by light being focused by the reflective and transparent cows." src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Rendering_techniques_example%2C_ray_tracing%2C_radiosity%2C_photon_mapping%2C_POV-Ray.png/180px-Rendering_techniques_example%2C_ray_tracing%2C_radiosity%2C_photon_mapping%2C_POV-Ray.png" decoding="async" width="180" height="135" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Rendering_techniques_example%2C_ray_tracing%2C_radiosity%2C_photon_mapping%2C_POV-Ray.png/270px-Rendering_techniques_example%2C_ray_tracing%2C_radiosity%2C_photon_mapping%2C_POV-Ray.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Rendering_techniques_example%2C_ray_tracing%2C_radiosity%2C_photon_mapping%2C_POV-Ray.png/360px-Rendering_techniques_example%2C_ray_tracing%2C_radiosity%2C_photon_mapping%2C_POV-Ray.png 2x" data-file-width="2048" data-file-height="1536" /></a></div> <div class="gallerytext">An image rendered using <a href="/wiki/POV-Ray" title="POV-Ray">POV-Ray</a>'s <a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">ray tracing</a>, <a href="/wiki/Radiosity_(computer_graphics)" title="Radiosity (computer graphics)">radiosity</a> and <a href="/wiki/Photon_mapping" title="Photon mapping">photon mapping</a> features</div> </li> <li class="gallerybox" style="width: 185px"> <div class="thumb" style="width: 180px;"><a href="/wiki/File:Rendering_techniques_example,_path_tracing,_realistic,_Blender_Cycles.jpg" class="mw-file-description" title="A more realistic path traced image, using Blender's Cycles renderer with image-based lighting"><img alt="3D rendered image showing three copies of a cartoon cow. The one on the left has a metalic surface, and the one on the right uses a transparent glass material. The cow in the center appears made of glazed porcelain. The cows are standing on a wooden table. Lights and other background details from a cafe environment are reflected in the slightly glossy table and the cows." src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Rendering_techniques_example%2C_path_tracing%2C_realistic%2C_Blender_Cycles.jpg/180px-Rendering_techniques_example%2C_path_tracing%2C_realistic%2C_Blender_Cycles.jpg" decoding="async" width="180" height="135" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Rendering_techniques_example%2C_path_tracing%2C_realistic%2C_Blender_Cycles.jpg/270px-Rendering_techniques_example%2C_path_tracing%2C_realistic%2C_Blender_Cycles.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Rendering_techniques_example%2C_path_tracing%2C_realistic%2C_Blender_Cycles.jpg/360px-Rendering_techniques_example%2C_path_tracing%2C_realistic%2C_Blender_Cycles.jpg 2x" data-file-width="2048" data-file-height="1536" /></a></div> <div class="gallerytext">A more realistic path traced image, using <a href="/wiki/Blender_(software)" title="Blender (software)">Blender</a>'s Cycles renderer with <a href="/wiki/Image-based_lighting" title="Image-based lighting">image-based lighting</a></div> </li> <li class="gallerybox" style="width: 185px"> <div class="thumb" style="width: 180px;"><a href="/wiki/File:Rendering_techniques_example,_spectral,_photon_mapping,_POV-Ray.png" class="mw-file-description" title="A spectral rendered image, using POV-Ray's ray tracing, radiosity and photon mapping features"><img alt="3D rendered image showing three copies of a cartoon cow. The one on the left has a mirror surface, and the one on the right uses a transparent glass material. The base surface is illuminated by finely detailed bright spots and lines ("caustics") caused by light being focused by the reflective and transparent cows. The caustics are colorful in some places, due to chromatic dispersion." src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Rendering_techniques_example%2C_spectral%2C_photon_mapping%2C_POV-Ray.png/180px-Rendering_techniques_example%2C_spectral%2C_photon_mapping%2C_POV-Ray.png" decoding="async" width="180" height="135" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Rendering_techniques_example%2C_spectral%2C_photon_mapping%2C_POV-Ray.png/270px-Rendering_techniques_example%2C_spectral%2C_photon_mapping%2C_POV-Ray.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/Rendering_techniques_example%2C_spectral%2C_photon_mapping%2C_POV-Ray.png/360px-Rendering_techniques_example%2C_spectral%2C_photon_mapping%2C_POV-Ray.png 2x" data-file-width="2048" data-file-height="1536" /></a></div> <div class="gallerytext">A <a href="/wiki/Spectral_rendering" title="Spectral rendering">spectral rendered</a> image, using <a href="/wiki/POV-Ray" title="POV-Ray">POV-Ray</a>'s <a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">ray tracing</a>, <a href="/wiki/Radiosity_(computer_graphics)" title="Radiosity (computer graphics)">radiosity</a> and <a href="/wiki/Photon_mapping" title="Photon mapping">photon mapping</a> features</div> </li> </ul></div></div></div> <div class="mw-heading mw-heading3"><h3 id="Rasterization">Rasterization</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=10" title="Edit section: Rasterization">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Rasterization" class="mw-redirect" title="Rasterization">Rasterization</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Latest_Rendering_of_the_E-ELT.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Latest_Rendering_of_the_E-ELT.jpg/220px-Latest_Rendering_of_the_E-ELT.jpg" decoding="async" width="220" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Latest_Rendering_of_the_E-ELT.jpg/330px-Latest_Rendering_of_the_E-ELT.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/Latest_Rendering_of_the_E-ELT.jpg/440px-Latest_Rendering_of_the_E-ELT.jpg 2x" data-file-width="5000" data-file-height="2813" /></a><figcaption>Rendering of the <a href="/wiki/Extremely_Large_Telescope" title="Extremely Large Telescope">Extremely Large Telescope</a></figcaption></figure> The term rasterization (in a broad sense) encompasses many techniques used for 2D rendering and <a href="/wiki/Real-time_computer_graphics" title="Real-time computer graphics">real-time</a> 3D rendering. 3D <a href="/wiki/Computer_animation" title="Computer animation">animated films</a> were rendered by rasterization before <a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">ray tracing</a> and <a href="/wiki/Path_tracing" title="Path tracing">path tracing</a> became practical. A renderer combines rasterization with geometry processing (which is not specific to rasterization) and pixel processing which computes the <a href="/wiki/RGB_color_model" title="RGB color model">RGB color values</a> to be placed in the <a href="/wiki/Framebuffer" title="Framebuffer">framebuffer</a> for display.<a href="#cite_note-AkenineMöller2018-9">[9]</a>: 2.1 <a href="#cite_note-Marschner2022-19">[19]</a>: 9  The main tasks of rasterization (including pixel processing) are:<a href="#cite_note-AkenineMöller2018-9">[9]</a>: 2, 3.8, 23.1.1  <ul><li>Determining which pixels are covered by each geometric shape in the 3D scene or 2D image (this is the actual rasterization step, in the strictest sense)</li> <li>Blending between colors and depths defined at the <a href="/wiki/Vertex_(computer_graphics)" title="Vertex (computer graphics)">vertices</a> of shapes, e.g. using <a href="/wiki/Barycentric_coordinate_system" title="Barycentric coordinate system">barycentric coordinates</a> (interpolation)</li> <li>Determining if parts of shapes are hidden by other shapes, due to 2D layering or 3D depth (<a href="/wiki/Hidden-surface_determination" title="Hidden-surface determination">hidden surface removal</a>)</li> <li>Evaluating a function for each pixel covered by a shape (<a href="/wiki/Shading" title="Shading">shading</a>)</li> <li>Smoothing edges of shapes so pixels are less visible (<a href="/wiki/Spatial_anti-aliasing" title="Spatial anti-aliasing">anti-aliasing</a>)</li> <li>Blending overlapping transparent shapes (<a href="/wiki/Compositing" title="Compositing">compositing</a>)</li></ul> 3D rasterization is typically part of a <a href="/wiki/Graphics_pipeline" title="Graphics pipeline">graphics pipeline</a> in which an application provides <a href="/wiki/Triangle_mesh" title="Triangle mesh">lists of triangles</a> to be rendered, and the rendering system transforms and <a href="/wiki/3D_projection" title="3D projection">projects</a> their coordinates, determines which triangles are potentially visible in the <a href="/wiki/Viewport" title="Viewport">viewport</a>, and performs the above rasterization and pixel processing tasks before displaying the final result on the screen.<a href="#cite_note-AkenineMöller2018-9">[9]</a>: 2.1 <a href="#cite_note-Marschner2022-19">[19]</a>: 9  Historically, 3D rasterization used algorithms like the <a href="/wiki/Warnock_algorithm" title="Warnock algorithm">Warnock algorithm</a> and <a href="/wiki/Scanline_rendering" title="Scanline rendering">scanline rendering</a> (also called "scan-conversion"), which can handle arbitrary polygons and can rasterize many shapes simultaneously. Although such algorithms are still important for 2D rendering, 3D rendering now usually divides shapes into triangles and rasterizes them individually using simpler methods.<a href="#cite_note-Warnock1969-32">[32]</a><a href="#cite_note-Bouknight1970-33">[33]</a><a href="#cite_note-Foley82-20">[20]</a>: 456, 561–569  <a href="/wiki/Digital_differential_analyzer_(graphics_algorithm)" title="Digital differential analyzer (graphics algorithm)">High-performance algorithms</a> exist for rasterizing <a href="/wiki/Bresenham%27s_line_algorithm" title="Bresenham's line algorithm">2D lines</a>, including <a href="/wiki/Xiaolin_Wu%27s_line_algorithm" title="Xiaolin Wu's line algorithm">anti-aliased lines</a>, as well as <a href="/wiki/Midpoint_circle_algorithm" title="Midpoint circle algorithm">ellipses</a> and filled triangles. An important special case of 2D rasterization is <a href="/wiki/Font_rasterization" title="Font rasterization">text rendering</a>, which requires careful anti-aliasing and rounding of coordinates to avoid distorting the <a href="/wiki/Letterform" title="Letterform">letterforms</a> and preserve spacing, density, and sharpness.<a href="#cite_note-Marschner2022-19">[19]</a>: 9.1.1 <a href="#cite_note-RasterTragedy-34">[34]</a> After 3D coordinates have been <a href="/wiki/3D_projection" title="3D projection">projected</a> onto the <a href="/wiki/Image_plane" title="Image plane">image plane</a>, rasterization is primarily a 2D problem, but the 3rd dimension necessitates <a href="/wiki/Hidden-surface_determination" title="Hidden-surface determination">hidden surface removal</a>. Early computer graphics used <a href="/wiki/Computational_geometry" title="Computational geometry">geometric algorithms</a> or ray casting to remove the hidden portions of shapes, or used the <a href="/wiki/Painter%27s_algorithm" title="Painter's algorithm">painter's algorithm</a>, which sorts shapes by depth (distance from camera) and renders them from back to front. Depth sorting was later avoided by incorporating depth comparison into the <a href="/wiki/Scanline_rendering" title="Scanline rendering">scanline rendering</a> algorithm. The <a href="/wiki/Z-buffering" title="Z-buffering">z-buffer </a> algorithm performs the comparisons indirectly by including a depth or "z" value in the <a href="/wiki/Framebuffer" title="Framebuffer">framebuffer</a>. A pixel is only covered by a shape if that shape's z value is lower (indicating closer to the camera) than the z value currently in the buffer. The z-buffer requires additional memory (an expensive resource at the time it was invented) but simplifies the rasterization code and permits multiple passes. Memory is now faster and more plentiful, and a z-buffer is almost always used for real-time rendering.<a href="#cite_note-Watkins1970-35">[35]</a><a href="#cite_note-Catmull1974-36">[36]</a><a href="#cite_note-Foley82-20">[20]</a>: 553–570 <a href="#cite_note-AkenineMöller2018-9">[9]</a>: 2.5.2  A drawback of the basic <a href="/wiki/Z-buffering" title="Z-buffering">z-buffer algorithm</a> is that each pixel ends up either entirely covered by a single object or filled with the background color, causing jagged edges in the final image. Early <a href="/wiki/Spatial_anti-aliasing" title="Spatial anti-aliasing">anti-aliasing</a> approaches addressed this by detecting when a pixel is partially covered by a shape, and calculating the covered area. The <a href="/wiki/A-buffer" title="A-buffer">A-buffer</a> (and other <a href="/wiki/Subpixel_rendering" title="Subpixel rendering">sub-pixel</a> and <a href="/wiki/Multisample_anti-aliasing" title="Multisample anti-aliasing">multi-sampling</a> techniques) solve the problem less precisely but with higher performance. For real-time 3D graphics, it has become common to use <a href="/wiki/Fast_approximate_anti-aliasing" title="Fast approximate anti-aliasing">complicated heuristics</a> (and even <a href="/wiki/Deep_learning_anti-aliasing" title="Deep learning anti-aliasing"> neural-networks</a>) to perform anti-aliasing.<a href="#cite_note-Catmull1974-36">[36]</a><a href="#cite_note-Carpenter1984-37">[37]</a><a href="#cite_note-Marschner2022-19">[19]</a>: 9.3 <a href="#cite_note-AkenineMöller2018-9">[9]</a>: 5.4.2  In 3D rasterization, color is usually determined by a <a href="/wiki/Shader#Pixel_shaders" title="Shader">pixel shader</a> or fragment shader, a small program that is run for each pixel. The shader does not (or cannot) directly access 3D data for the entire scene (this would be very slow, and would result in an algorithm similar to ray tracing) and a variety of techniques have been developed to render effects like <a href="/wiki/Shadow_mapping" title="Shadow mapping">shadows</a> and <a href="/wiki/Reflection_(computer_graphics)" title="Reflection (computer graphics)">reflections</a> using only <a href="/wiki/Texture_mapping" title="Texture mapping">texture mapping</a> and multiple passes.<a href="#cite_note-Marschner2022-19">[19]</a>: 17.8  Older and more basic 3D rasterization implementations did not support shaders, and used simple shading techniques such as <a href="/wiki/Shading#Flat_shading" title="Shading">flat shading</a> (lighting is computed once for each triangle, which is then rendered entirely in one color), <a href="/wiki/Gouraud_shading" title="Gouraud shading">Gouraud shading</a> (lighting is computed using <a href="/wiki/Normal_(geometry)" title="Normal (geometry)">normal vectors</a> defined at vertices and then colors are interpolated across each triangle), or <a href="/wiki/Phong_shading" title="Phong shading">Phong shading</a> (normal vectors are interpolated across each triangle and lighting is computed for each pixel).<a href="#cite_note-Marschner2022-19">[19]</a>: 9.2  Until relatively recently, <a href="/wiki/Pixar" title="Pixar">Pixar</a> used rasterization for rendering its <a href="/wiki/Computer_animation" title="Computer animation">animated films</a>. Unlike the renderers commonly used for real-time graphics, the <a href="/wiki/Reyes_rendering" title="Reyes rendering">Reyes rendering system</a> in Pixar's <a href="/wiki/Pixar_RenderMan" title="Pixar RenderMan">RenderMan</a> software was optimized for rendering very small (pixel-sized) polygons, and incorporated <a href="/wiki/Stochastic" title="Stochastic">stochastic</a> sampling techniques more typically associated with <a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">ray tracing</a>.<a href="#cite_note-Raghavachary2005-2">[2]</a>: 2, 6.3 <a href="#cite_note-Cook1987-38">[38]</a> <div class="mw-heading mw-heading3"><h3 id="Ray_casting">Ray casting</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=11" title="Edit section: Ray casting">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Ray_casting" title="Ray casting">Ray casting</a></div> One of the simplest ways to render a 3D scene is to test if a <a href="/wiki/Line_(geometry)#Ray" title="Line (geometry)">ray</a> starting at the viewpoint (the "eye" or "camera") intersects any of the geometric shapes in the scene, repeating this test using a different ray direction for each pixel. This method, called ray casting, was important in early computer graphics, and is a fundamental building block for more advanced algorithms. Ray casting can be used to render shapes defined by <a href="/wiki/Constructive_solid_geometry" title="Constructive solid geometry">constructive solid geometry</a> (CSG) operations.<a href="#cite_note-RayTracingGems_1-21">[21]</a>: 8-9 <a href="#cite_note-IntroToRTCh6-39">[39]</a>: 246–249  Early ray casting experiments include the work of Arthur Appel in the 1960s. Appel rendered shadows by casting an additional ray from each visible surface point towards a light source. He also tried rendering the density of illumination by casting random rays from the light source towards the object and <a href="/wiki/Plotter" title="Plotter">plotting</a> the intersection points (similar to the later technique called <a href="/wiki/Photon_mapping" title="Photon mapping">photon mapping</a>).<a href="#cite_note-Appel1968-40">[40]</a> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Mandelbulb_p8a.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Mandelbulb_p8a.jpg/220px-Mandelbulb_p8a.jpg" decoding="async" width="220" height="215" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Mandelbulb_p8a.jpg/330px-Mandelbulb_p8a.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/Mandelbulb_p8a.jpg/440px-Mandelbulb_p8a.jpg 2x" data-file-width="3437" data-file-height="3365" /></a><figcaption><a href="/wiki/Ray_marching" title="Ray marching">Ray marching</a> can be used to find the first intersection of a ray with an intricate shape such as this <a href="/wiki/Mandelbulb" title="Mandelbulb">Mandelbulb</a> fractal.</figcaption></figure> When rendering scenes containing many objects, testing the intersection of a ray with every object becomes very expensive. Special <a href="/wiki/Data_structure" title="Data structure">data structures</a> are used to speed up this process by allowing large numbers of objects to be excluded quickly (such as objects behind the camera). These structures are analogous to <a href="/wiki/Database_index" title="Database index">database indexes</a> for finding the relevant objects. The most common are the <a href="/wiki/Bounding_volume_hierarchy" title="Bounding volume hierarchy">bounding volume hierarchy</a> (BVH), which stores a pre-computed <a href="/wiki/Bounding_volume" title="Bounding volume">bounding box or sphere</a> for each branch of a <a href="/wiki/Tree_(data_structure)" class="mw-redirect" title="Tree (data structure)">tree</a> of objects, and the <a href="/wiki/K-d_tree" title="K-d tree">k-d tree</a> which <a href="/wiki/Recursion_(computer_science)" title="Recursion (computer science)">recursively</a> divides space into two parts. Recent <a href="/wiki/GPU" class="mw-redirect" title="GPU">GPUs</a> include hardware acceleration for BVH intersection tests. K-d trees are a special case of <a href="/wiki/Binary_space_partitioning" title="Binary space partitioning">binary space partitioning</a>, which was frequently used in early computer graphics (it can also generate a rasterization order for the <a href="/wiki/Painter%27s_algorithm" title="Painter's algorithm">painter's algorithm</a>). <a href="/wiki/Octree" title="Octree">Octrees</a>, another historically popular technique, are still often used for volumetric data.<a href="#cite_note-RealTimeRayTracing-22">[22]</a>: 16–17 <a href="#cite_note-RayTracingGems_Forword_Stich-41">[41]</a><a href="#cite_note-IntroToRTCh6-39">[39]</a><a href="#cite_note-Hughes2014-5">[5]</a>: 36.2  Geometric formulas are sufficient for finding the intersection of a ray with shapes like <a href="/wiki/Sphere" title="Sphere">spheres</a>, <a href="/wiki/Polygon" title="Polygon">polygons</a>, and <a href="/wiki/Polyhedron" title="Polyhedron">polyhedra</a>, but for most curved surfaces there is no <a href="/wiki/Closed-form_expression#Analytic_expression" title="Closed-form expression">analytic solution</a>, or the intersection is difficult to compute accurately using limited precision <a href="/wiki/Floating-point_arithmetic" title="Floating-point arithmetic">floating point numbers</a>. <a href="/wiki/Root-finding_algorithm" title="Root-finding algorithm">Root-finding algorithms</a> such as <a href="/wiki/Newton%27s_method" title="Newton's method">Newton's method</a> can sometimes be used. To avoid these complications, curved surfaces are often approximated as <a href="/wiki/Triangle_mesh" title="Triangle mesh">meshes of triangles</a>. <a href="/wiki/Volume_rendering" title="Volume rendering">Volume rendering</a> (e.g. rendering clouds and smoke), and some surfaces such as <a href="/wiki/Fractal" title="Fractal">fractals</a>, may require <a href="/wiki/Ray_marching" title="Ray marching">ray marching</a> instead of basic ray casting.<a href="#cite_note-IntroToRTCh2-42">[42]</a><a href="#cite_note-RayTracingGems_1-21">[21]</a>: 13 <a href="#cite_note-AkenineMöller2018-9">[9]</a>: 14, 17.3  <div class="mw-heading mw-heading3"><h3 id="Ray_tracing">Ray tracing</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=12" title="Edit section: Ray tracing">edit</a>]</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:SpiralSphereAndJuliaDetail1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/SpiralSphereAndJuliaDetail1.jpg/250px-SpiralSphereAndJuliaDetail1.jpg" decoding="async" width="250" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/SpiralSphereAndJuliaDetail1.jpg/375px-SpiralSphereAndJuliaDetail1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/c/ca/SpiralSphereAndJuliaDetail1.jpg 2x" data-file-width="480" data-file-height="480" /></a><figcaption>Spiral Sphere and Julia, Detail, a computer-generated image created by visual artist Robert W. McGregor using only <a href="/wiki/POV-Ray" title="POV-Ray">POV-Ray</a> 3.6 and its built-in scene description language</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">Ray tracing (graphics)</a></div> Ray casting can be used to render an image by tracing <a href="/wiki/Ray_(optics)" title="Ray (optics)">light rays</a> backwards from a simulated camera. After finding a point on a surface where a ray originated, another ray is traced towards the light source to determine if anything is casting a shadow on that point. If not, a <a href="/wiki/Bidirectional_reflectance_distribution_function" title="Bidirectional reflectance distribution function">reflectance model</a> (such as <a href="/wiki/Lambertian_reflectance" title="Lambertian reflectance">Lambertian reflectance</a> for <a href="/wiki/Paint_sheen" title="Paint sheen">matte</a> surfaces, or the <a href="/wiki/Phong_reflection_model" title="Phong reflection model">Phong reflection model</a> for glossy surfaces) is used to compute the probability that a <a href="/wiki/Photon" title="Photon">photon</a> arriving from the light would be reflected towards the camera, and this is multiplied by the brightness of the light to determine the pixel brightness. If there are multiple light sources, brightness contributions of the lights are added together. For color images, calculations are repeated for multiple <a href="/wiki/Visible_spectrum" title="Visible spectrum">wavelengths</a> of light (e.g. red, green, and blue).<a href="#cite_note-AkenineMöller2018-9">[9]</a>: 11.2.2 <a href="#cite_note-RayTracingGems_1-21">[21]</a>: 8  Classical ray tracing (also called Whitted-style or recursive ray tracing) extends this method so it can render mirrors and transparent objects. If a ray traced backwards from the camera originates at a point on a mirror, the <a href="/wiki/Specular_reflection" title="Specular reflection">reflection formula</a> from <a href="/wiki/Geometric_optics" class="mw-redirect" title="Geometric optics">geometric optics</a> is used to calculate the direction the reflected ray came from, and another ray is cast backwards in that direction. If a ray originates at a transparent surface, rays are cast backwards for both <a href="/wiki/Specular_reflection" title="Specular reflection">reflected</a> and <a href="/wiki/Refraction" title="Refraction">refracted</a> rays (using <a href="/wiki/Snell%27s_law" title="Snell's law">Snell's law</a> to compute the refracted direction), and so ray tracing needs to support a branching "tree" of rays. In simple implementations, a <a href="/wiki/Recursion_(computer_science)" title="Recursion (computer science)">recursive function</a> is called to trace each ray.<a href="#cite_note-AkenineMöller2018-9">[9]</a>: 11.2.2 <a href="#cite_note-RayTracingGems_1-21">[21]</a>: 9  Ray tracing usually performs <a href="/wiki/Spatial_anti-aliasing" title="Spatial anti-aliasing">anti-aliasing</a> by taking the average of multiple <a href="/wiki/Sampling_(statistics)" title="Sampling (statistics)">samples</a> for each pixel. It may also use multiple samples for effects like <a href="/wiki/Depth_of_field" title="Depth of field">depth of field</a> and <a href="/wiki/Motion_blur" title="Motion blur">motion blur</a>. If evenly-spaced ray directions or times are used for each of these features, many rays are required, and some aliasing will remain. Cook-style, stochastic, or Monte Carlo ray tracing avoids this problem by using <a href="/wiki/Monte_Carlo_method" title="Monte Carlo method">random sampling</a> instead of evenly-spaced samples. This type of ray tracing is commonly called <a href="/wiki/Distributed_ray_tracing" title="Distributed ray tracing">distributed ray tracing, or distribution ray tracing</a> because it samples rays from <a href="/wiki/Probability_distribution" title="Probability distribution">probability distributions</a>. Distribution ray tracing can also render realistic "soft" shadows from large lights by using a random sample of points on the light when testing for shadowing, and it can simulate <a href="/wiki/Chromatic_aberration" title="Chromatic aberration">chromatic aberration</a> by sampling multiple wavelengths from the <a href="/wiki/Visible_spectrum" title="Visible spectrum">spectrum of light</a>.<a href="#cite_note-RayTracingGems_1-21">[21]</a>: 10 <a href="#cite_note-IntroToRTCh1-26">[26]</a>: 25  Real surface materials reflect small amounts of light in almost every direction because they have small (or microscopic) bumps and grooves. A distribution ray tracer can simulate this by sampling possible ray directions, which allows rendering blurry reflections from glossy and metallic surfaces. However if this procedure is repeated <a href="/wiki/Recursion" title="Recursion">recursively</a> to simulate realistic indirect lighting, and if more than one sample is taken at each surface point, the tree of rays quickly becomes huge. Another kind of ray tracing, called path tracing, handles indirect light more efficiently, avoiding branching, and ensures that the distribution of all possible paths from a light source to the camera is sampled in an <a href="/wiki/Unbiased_rendering" title="Unbiased rendering">unbiased</a> way.<a href="#cite_note-IntroToRTCh1-26">[26]</a>: 25–27 <a href="#cite_note-Kajiya1986-25">[25]</a> Ray tracing was often used for rendering reflections in animated films, until path tracing became standard for film rendering. Films such as <a href="/wiki/Shrek_2" title="Shrek 2">Shrek 2</a> and <a href="/wiki/Monsters_University" title="Monsters University">Monsters University</a> also used distribution ray tracing or path tracing to precompute indirect illumination for a scene or frame prior to rendering it using rasterization.<a href="#cite_note-Christensen2016-43">[43]</a>: 118–121  Advances in GPU technology have made real-time ray tracing possible in games, although it is currently almost always used in combination with rasterization.<a href="#cite_note-RealTimeRayTracing-22">[22]</a>: 2  This enables visual effects that are difficult with only rasterization, including reflection from curved surfaces and interreflective objects,<a href="#cite_note-RayTracingGems_19-44">[44]</a>: 305  and shadows that are accurate over a wide range of distances and surface orientations.<a href="#cite_note-RayTracingGems_13-45">[45]</a>: 159-160  Ray tracing support is included in recent versions of the graphics APIs used by games, such as <a href="/wiki/DirectX_Raytracing" title="DirectX Raytracing">DirectX</a>, <a href="/wiki/Metal_(API)" title="Metal (API)">Metal</a>, and <a href="/wiki/Vulkan" title="Vulkan">Vulkan</a>.<a href="#cite_note-KhronosRTInVukan-46">[46]</a> Ray tracing has been used to render simulated <a href="/wiki/Black_hole" title="Black hole">black holes</a>, and the appearance of objects moving at close to the speed of light, by taking <a href="/wiki/Curved_spacetime" title="Curved spacetime">spacetime curvature</a> and <a href="/wiki/Special_relativity" title="Special relativity">relativistic effects</a> into account during light ray simulation.<a href="#cite_note-Riazuelo2019-47">[47]</a><a href="#cite_note-Howard1995-48">[48]</a> <div class="mw-heading mw-heading3"><h3 id="Radiosity">Radiosity</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=13" title="Edit section: Radiosity">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Radiosity_(computer_graphics)" title="Radiosity (computer graphics)">Radiosity (computer graphics)</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Classical_radiosity_example,_simple_scene,_no_interpolation,_direct_only_and_full.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Classical_radiosity_example%2C_simple_scene%2C_no_interpolation%2C_direct_only_and_full.png/220px-Classical_radiosity_example%2C_simple_scene%2C_no_interpolation%2C_direct_only_and_full.png" decoding="async" width="220" height="440" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Classical_radiosity_example%2C_simple_scene%2C_no_interpolation%2C_direct_only_and_full.png/330px-Classical_radiosity_example%2C_simple_scene%2C_no_interpolation%2C_direct_only_and_full.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Classical_radiosity_example%2C_simple_scene%2C_no_interpolation%2C_direct_only_and_full.png/440px-Classical_radiosity_example%2C_simple_scene%2C_no_interpolation%2C_direct_only_and_full.png 2x" data-file-width="512" data-file-height="1024" /></a><figcaption>Classical radiosity demonstration. Surfaces are divided into 16x16 or 16x32 meshes. Top: direct light only. Bottom: radiosity solution (for <a href="/wiki/Albedo" title="Albedo">albedo</a> 0.85).</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Classical_radiosity_comparison_with_path_tracing,_simple_scene,_interpolated.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Classical_radiosity_comparison_with_path_tracing%2C_simple_scene%2C_interpolated.png/220px-Classical_radiosity_comparison_with_path_tracing%2C_simple_scene%2C_interpolated.png" decoding="async" width="220" height="440" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Classical_radiosity_comparison_with_path_tracing%2C_simple_scene%2C_interpolated.png/330px-Classical_radiosity_comparison_with_path_tracing%2C_simple_scene%2C_interpolated.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/Classical_radiosity_comparison_with_path_tracing%2C_simple_scene%2C_interpolated.png/440px-Classical_radiosity_comparison_with_path_tracing%2C_simple_scene%2C_interpolated.png 2x" data-file-width="512" data-file-height="1024" /></a><figcaption>Top: the same scene with a finer radiosity mesh, smoothing the patches during final rendering using <a href="/wiki/Bilinear_interpolation" title="Bilinear interpolation">bilinear interpolation</a>. Bottom: the scene rendered with path tracing (using the PBRT renderer).</figcaption></figure> Radiosity (named after the <a href="/wiki/Radiosity_(radiometry)" title="Radiosity (radiometry)">radiometric quantity of the same name</a>) is a method for rendering objects illuminated by light <a href="/wiki/Diffuse_reflection" title="Diffuse reflection">bouncing off rough or matte surfaces</a>. This type of illumination is called indirect light, environment lighting, or diffuse lighting, and the problem of rendering it realistically is called global illumination. Rasterization and basic forms of ray tracing (other than distribution ray tracing and path tracing) can only roughly approximate indirect light, e.g. by adding a uniform "ambient" lighting amount chosen by the artist. Radiosity techniques are also suited to rendering scenes with area lights such as rectangular fluorescent lighting panels, which are difficult for rasterization and traditional ray tracing. Radiosity is considered a <a href="/wiki/Physically_based_rendering" title="Physically based rendering">physically-based method</a>, meaning that it aims to simulate the flow of light in an environment using equations and experimental data from physics, however it often assumes that all surfaces are opaque and perfectly <a href="/wiki/Lambertian_reflectance" title="Lambertian reflectance">Lambertian</a>, which reduces realism and limits its applicability.<a href="#cite_note-AkenineMöller2018-9">[9]</a>: 10, 11.2.1 <a href="#cite_note-Glassner95-24">[24]</a>: 888, 893 <a href="#cite_note-Goral1984-49">[49]</a> In the original radiosity method (first proposed in 1984) now called classical radiosity, surfaces and lights in the scene are split into pieces called patches, a process called <a href="/wiki/Mesh_generation" title="Mesh generation">meshing</a> (this step makes it a <a href="/wiki/Finite_element_method" title="Finite element method">finite element method</a>). The rendering code must then determine what fraction of the light being emitted or <a href="/wiki/Diffuse_reflection" title="Diffuse reflection">diffusely reflected</a> (scattered) by each patch is received by each other patch. These fractions are called form factors or <a href="/wiki/View_factor" title="View factor">view factors</a> (first used in engineering to model <a href="/wiki/Thermal_radiation" title="Thermal radiation">radiative heat transfer</a>). The form factors are multiplied by the <a href="/wiki/Albedo" title="Albedo">albedo</a> of the receiving surface and put in a <a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">matrix</a>. The lighting in the scene can then be expressed as a matrix equation (or equivalently a <a href="/wiki/System_of_linear_equations" title="System of linear equations">system of linear equations</a>) that can be solved by methods from <a href="/wiki/Linear_algebra" title="Linear algebra">linear algebra</a>.<a href="#cite_note-Goral1984-49">[49]</a><a href="#cite_note-Dutré2003-50">[50]</a>: 46 <a href="#cite_note-Glassner95-24">[24]</a>: 888, 896  Solving the radiosity equation gives the total amount of light emitted and reflected by each patch, which is divided by area to get a value called <a href="/wiki/Radiosity_(radiometry)" title="Radiosity (radiometry)">radiosity</a> that can be used when rasterizing or ray tracing to determine the color of pixels corresponding to visible parts of the patch. For real-time rendering, this value (or more commonly the <a href="/wiki/Irradiance" title="Irradiance">irradiance</a>, which does not depend on local surface albedo) can be pre-computed and stored in a texture (called an irradiance map) or stored as vertex data for 3D models. This feature was used in architectural visualization software to allow real-time walk-throughs of a building interior after computing the lighting.<a href="#cite_note-Glassner95-24">[24]</a>: 890 <a href="#cite_note-AkenineMöller2018-9">[9]</a>: 11.5.1 <a href="#cite_note-Cohen1993-51">[51]</a>: 332  The large size of the matrices used in classical radiosity (the square of the number of patches) causes problems for realistic scenes. Practical implementations may use <a href="/wiki/Jacobi_method" title="Jacobi method">Jacobi</a> or <a href="/wiki/Gauss%E2%80%93Seidel_method" title="Gauss–Seidel method">Gauss-Seidel</a> iterations, which is equivalent (at least in the Jacobi case) to simulating the propagation of light one bounce at a time until the amount of light remaining (not yet absorbed by surfaces) is insignificant. The number of iterations (bounces) required is dependent on the scene, not the number of patches, so the total work is proportional to the square of the number of patches (in contrast, solving the matrix equation using <a href="/wiki/Gaussian_elimination" title="Gaussian elimination">Gaussian elimination</a> requires work proportional to the cube of the number of patches). Form factors may be recomputed when they are needed, to avoid storing a complete matrix in memory.<a href="#cite_note-Glassner95-24">[24]</a>: 901, 907  The quality of rendering is often determined by the size of the patches, e.g. very fine meshes are needed to depict the edges of shadows accurately. An important improvement is hierarchical radiosity, which uses a coarser mesh (larger patches) for simulating the transfer of light between surfaces that are far away from one another, and adaptively sub-divides the patches as needed. This allows radiosity to be used for much larger and more complex scenes.<a href="#cite_note-Glassner95-24">[24]</a>: 975, 939  Alternative and extended versions of the radiosity method support non-Lambertian surfaces, such as glossy surfaces and mirrors, and sometimes use volumes or "clusters" of objects as well as surface patches. Stochastic or <a href="/wiki/Monte_Carlo_method" title="Monte Carlo method">Monte Carlo</a> radiosity uses <a href="/wiki/Sampling_(statistics)" title="Sampling (statistics)">random sampling</a> in various ways, e.g. taking samples of incident light instead of integrating over all patches, which can improve performance but adds noise (this noise can be reduced by using deterministic iterations as a final step, unlike path tracing noise). Simplified and partially precomputed versions of radiosity are widely used for real-time rendering, combined with techniques such as <a href="/wiki/Octree" title="Octree">octree</a> radiosity that store approximations of the <a href="/wiki/Light_field" title="Light field">light field</a>.<a href="#cite_note-Glassner95-24">[24]</a>: 979, 982 <a href="#cite_note-Dutré2003-50">[50]</a>: 49 <a href="#cite_note-Bekaert1999-52">[52]</a><a href="#cite_note-AkenineMöller2018-9">[9]</a>: 11.5  <div class="mw-heading mw-heading3"><h3 id="Path_tracing">Path tracing</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=14" title="Edit section: Path tracing">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Path_tracing" title="Path tracing">Path tracing</a></div> As part of the approach known as <a href="/wiki/Physically_based_rendering" title="Physically based rendering">physically based rendering</a>, <a href="/wiki/Path_tracing" title="Path tracing">path tracing</a> has become the dominant technique for rendering realistic scenes, including effects for movies.<a href="#cite_note-Pharr2023_1_6-53">[53]</a> For example, the popular open source 3D software <a href="/wiki/Blender_(software)" title="Blender (software)">Blender</a> uses path tracing in its Cycles renderer.<a href="#cite_note-BlenderCyclesIntro-54">[54]</a> Images produced using path tracing for <a href="/wiki/Global_illumination" title="Global illumination">global illumination</a> are generally noisier than when using <a href="/wiki/Radiosity_(computer_graphics)" title="Radiosity (computer graphics)">radiosity</a> (the main competing algorithm for realistic lighting), but radiosity can be difficult to apply to complex scenes and is prone to artifacts that arise from using a <a href="/wiki/Tessellation_(computer_graphics)" title="Tessellation (computer graphics)">tessellated</a> representation of <a href="/wiki/Irradiance" title="Irradiance">irradiance</a>.<a href="#cite_note-Pharr2023_1_6-53">[53]</a><a href="#cite_note-Glassner95-24">[24]</a>: 975-976, 1045  Like <a href="/wiki/Distributed_ray_tracing" title="Distributed ray tracing">distributed ray tracing</a>, path tracing is a kind of <a href="/wiki/Stochastic" title="Stochastic">stochastic</a> or <a href="/wiki/Randomized_algorithm" title="Randomized algorithm">randomized</a> <a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">ray tracing</a> that uses <a href="/wiki/Monte_Carlo_integration" title="Monte Carlo integration">Monte Carlo</a> or <a href="/wiki/Quasi-Monte_Carlo_method" title="Quasi-Monte Carlo method">Quasi-Monte Carlo</a> integration. It was proposed and named in 1986 by <a href="/wiki/Jim_Kajiya" title="Jim Kajiya">Jim Kajiya</a> in the same paper as the <a href="/wiki/Rendering_equation" title="Rendering equation">rendering equation</a>. Kajiya observed that much of the complexity of <a href="/wiki/Distributed_ray_tracing" title="Distributed ray tracing">distributed ray tracing</a> could be avoided by only tracing a single path from the camera at a time (in Kajiya's implementation, this "no branching" rule was broken by tracing additional rays from each surface intersection point to randomly chosen points on each light source). Kajiya suggested reducing the noise present in the output images by using <a href="/wiki/Stratified_sampling" title="Stratified sampling">stratified sampling</a> and <a href="/wiki/Importance_sampling" title="Importance sampling">importance sampling</a> for making random decisions such as choosing which ray to follow at each step of a path. Even with these techniques, path tracing would not have been practical for film rendering, using computers available at the time, because the computational cost of generating enough samples to reduce <a href="/wiki/Variance" title="Variance">variance</a> to an acceptable level was too high. <a href="/wiki/Monster_House_(film)" title="Monster House (film)">Monster House</a>, the first feature film rendered entirely using path tracing, was not released until 20 years later.<a href="#cite_note-Kajiya1986-25">[25]</a><a href="#cite_note-Pharr2023_1_6-53">[53]</a><a href="#cite_note-Kulla2017-55">[55]</a> In its basic form, path tracing is inefficient (requiring too many samples) for rendering <a href="/wiki/Caustic_(optics)" title="Caustic (optics)">caustics</a> and scenes where light enters indirectly through narrow spaces. Attempts were made to address these weaknesses in the 1990s. <a href="/wiki/Path_tracing#Bidirectional_path_tracing" title="Path tracing">Bidirectional path tracing</a> has similarities to <a href="/wiki/Photon_mapping" title="Photon mapping">photon mapping</a>, tracing rays from the light source and the camera separately, and then finding ways to connect these paths (but unlike photon mapping it usually samples new light paths for each pixel rather than using the same cached data for all pixels). <a href="/wiki/Metropolis_light_transport" title="Metropolis light transport">Metropolis light transport</a> samples paths by modifying paths that were previously traced, spending more time exploring paths that are similar to other "bright" paths, which increases the chance of discovering even brighter paths. Multiple importance sampling provides a way to reduce <a href="/wiki/Variance" title="Variance">variance</a> when combining samples from more than one sampling method, particularly when some samples are much noisier than the others.<a href="#cite_note-Pharr2023_1_6-53">[53]</a><a href="#cite_note-Veach1997-28">[28]</a> This later work was summarized and expanded upon in <a href="/wiki/Eric_Veach" title="Eric Veach">Eric Veach</a>'s 1997 PhD thesis, which helped raise interest in path tracing in the computer graphics community. The <a href="/wiki/Autodesk_Arnold" title="Autodesk Arnold">Arnold renderer</a>, first released in 1998, proved that path tracing was practical for rendering frames for films, and that there was a demand for <a href="/wiki/Unbiased_rendering" title="Unbiased rendering">unbiased</a> and <a href="/wiki/Physically_based_rendering" title="Physically based rendering">physically based</a> rendering in the film industry; other commercial and open source path tracing renderers began appearing. Computational cost was addressed by rapid advances in <a href="/wiki/CPU" class="mw-redirect" title="CPU">CPU</a> and <a href="/wiki/Computer_cluster" title="Computer cluster">cluster</a> performance.<a href="#cite_note-Pharr2023_1_6-53">[53]</a> Path tracing's relative simplicity and its nature as a <a href="/wiki/Monte_Carlo_method" title="Monte Carlo method">Monte Carlo method</a> (sampling hundreds or thousands of paths per pixel) have made it attractive to implement on a <a href="/wiki/Graphics_processing_unit" title="Graphics processing unit">GPU</a>, especially on recent GPUs that support ray tracing acceleration technology such as Nvidia's <a href="/wiki/Nvidia_RTX" title="Nvidia RTX">RTX</a> and <a href="/wiki/OptiX" title="OptiX">OptiX</a>.<a href="#cite_note-Pharr2023_15-56">[56]</a> However bidirectional path tracing and Metropolis light transport are more difficult to implement efficiently on a GPU.<a href="#cite_note-Otte2015-57">[57]</a><a href="#cite_note-Schmidt2016-58">[58]</a> Research into improving path tracing continues. Recent path guiding approaches construct approximations of the <a href="/wiki/Light_field" title="Light field">light field</a> probability distribution in each volume of space, so paths can be sampled more effectively.<a href="#cite_note-Pharr2023_13fr-59">[59]</a> Many techniques have been developed to <a href="/wiki/Noise_reduction" title="Noise reduction">denoise</a> the output of path tracing, reducing the number of paths required to achieve acceptable quality, at the risk of losing some detail or introducing small-scale artifacts that are more objectionable than noise;<a href="#cite_note-Pharr2023_5fr-60">[60]</a><a href="#cite_note-BlenderCyclesReducingNoise-61">[61]</a> <a href="/wiki/Artificial_neural_network" class="mw-redirect" title="Artificial neural network">neural networks</a> are now widely used for this purpose.<a href="#cite_note-BlenderSettingsDenoising-62">[62]</a><a href="#cite_note-OpenImageDenoise-63">[63]</a><a href="#cite_note-NvidiaOptiXDenoiser-64">[64]</a> <div class="mw-heading mw-heading3"><h3 id="Neural_rendering">Neural rendering</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=15" title="Edit section: Neural rendering">edit</a>]</div> Neural rendering is a rendering method using <a href="/wiki/Artificial_neural_network" class="mw-redirect" title="Artificial neural network">artificial neural networks</a>.<a href="#cite_note-Tewari-65">[65]</a><a href="#cite_note-66">[66]</a> Neural rendering includes <a href="/wiki/Image-based_rendering" class="mw-redirect" title="Image-based rendering">image-based rendering</a> methods that are used to <a href="/wiki/3D_reconstruction" title="3D reconstruction">reconstruct 3D models</a> from 2-dimensional images.<a href="#cite_note-Tewari-65">[65]</a>One of these methods are <a href="/wiki/Photogrammetry" title="Photogrammetry">photogrammetry</a>, which is a method in which a collection of images from multiple angles of an object are turned into a 3D model. There have also been recent developments in generating and rendering 3D models from text and coarse paintings by notably <a href="/wiki/Nvidia" title="Nvidia">Nvidia</a>, <a href="/wiki/Google" title="Google">Google</a> and various other companies. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Expand_section plainlinks metadata ambox mbox-small-left ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><a href="/wiki/File:Wiki_letter_w_cropped.svg" class="mw-file-description"><img alt="[icon]" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png" decoding="async" width="20" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/30px-Wiki_letter_w_cropped.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/40px-Wiki_letter_w_cropped.svg.png 2x" data-file-width="44" data-file-height="31" /></a></td><td class="mbox-text"><div class="mbox-text-span">This section needs expansion. You can help by <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=">adding to it</a>. (February 2022)</div></td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Scientific_and_mathematical_basis">Scientific and mathematical basis</h2>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=16" title="Edit section: Scientific and mathematical basis">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Unbiased_rendering" title="Unbiased rendering">Unbiased rendering</a></div> The implementation of a realistic renderer always has some basic element of physical simulation or emulation – some computation which resembles or abstracts a real physical process. The term "<a href="/wiki/Physically_based_rendering" title="Physically based rendering">physically based</a>" indicates the use of physical models and approximations that are more general and widely accepted outside rendering. A particular set of related techniques have gradually become established in the rendering community. The basic concepts are moderately straightforward, but intractable to calculate; and a single elegant algorithm or approach has been elusive for more general purpose renderers. In order to meet demands of robustness, accuracy and practicality, an implementation will be a complex combination of different techniques. Rendering research is concerned with both the adaptation of scientific models and their efficient application. Mathematics used in rendering includes: <a href="/wiki/Linear_algebra" title="Linear algebra">linear algebra</a>, <a href="/wiki/Calculus" title="Calculus">calculus</a>, <a href="/wiki/Numerical_analysis" title="Numerical analysis">numerical mathematics</a>, <a href="/wiki/Digital_signal_processing" title="Digital signal processing">signal processing</a>, and <a href="/wiki/Monte_Carlo_methods" class="mw-redirect" title="Monte Carlo methods">Monte Carlo methods</a>. <div class="mw-heading mw-heading3"><h3 id="The_rendering_equation">The rendering equation</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=17" title="Edit section: The rendering equation">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Rendering_equation" title="Rendering equation">Rendering equation</a></div> This is the key academic/theoretical concept in rendering. It serves as the most abstract formal expression of the non-perceptual aspect of rendering. All more complete algorithms can be seen as solutions to particular formulations of this equation. <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{o}(x,\omega )=L_{e}(x,\omega )+\int _{\Omega }L_{i}(x,\omega ')f_{r}(x,\omega ',\omega )(\omega '\cdot n)\,\mathrm {d} \omega '}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>+</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Ω</mi> </mrow> </msub> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <msup> <mi>ω</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <msup> <mi>ω</mi> <mo>′</mo> </msup> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi>ω</mi> <mo>′</mo> </msup> <mo>⋅</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msup> <mi>ω</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{o}(x,\omega )=L_{e}(x,\omega )+\int _{\Omega }L_{i}(x,\omega ')f_{r}(x,\omega ',\omega )(\omega '\cdot n)\,\mathrm {d} \omega '}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9588b27c7bdd91e73e3b732daee0285339f6b86d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:55.874ex; height:5.676ex;" alt="{\displaystyle L_{o}(x,\omega )=L_{e}(x,\omega )+\int _{\Omega }L_{i}(x,\omega ')f_{r}(x,\omega ',\omega )(\omega '\cdot n)\,\mathrm {d} \omega '}"></dd></dl> Meaning: at a particular position and direction, the outgoing light (Lo) is the sum of the emitted light (Le) and the reflected light. The reflected light being the sum of the incoming light (Li) from all directions, multiplied by the surface reflection and incoming angle. By connecting outward light to inward light, via an interaction point, this equation stands for the whole 'light transport' – all the movement of light – in a scene. <div class="mw-heading mw-heading3"><h3 id="The_bidirectional_reflectance_distribution_function">The bidirectional reflectance distribution function</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=18" title="Edit section: The bidirectional reflectance distribution function">edit</a>]</div> The <a href="/wiki/Bidirectional_reflectance_distribution_function" title="Bidirectional reflectance distribution function">bidirectional reflectance distribution function</a> (BRDF) expresses a simple model of light interaction with a surface as follows: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{r}(x,\omega ',\omega )={\frac {\mathrm {d} L_{r}(x,\omega )}{L_{i}(x,\omega ')(\omega '\cdot {\vec {n}})\mathrm {d} \omega '}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <msup> <mi>ω</mi> <mo>′</mo> </msup> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <msup> <mi>ω</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi>ω</mi> <mo>′</mo> </msup> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msup> <mi>ω</mi> <mo>′</mo> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{r}(x,\omega ',\omega )={\frac {\mathrm {d} L_{r}(x,\omega )}{L_{i}(x,\omega ')(\omega '\cdot {\vec {n}})\mathrm {d} \omega '}}}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc1c730f74b5644bff67af0156fbf81ddfe1b36f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:33.953ex; height:6.509ex;" alt="{\displaystyle f_{r}(x,\omega ',\omega )={\frac {\mathrm {d} L_{r}(x,\omega )}{L_{i}(x,\omega ')(\omega '\cdot {\vec {n}})\mathrm {d} \omega '}}}"></dd></dl> Light interaction is often approximated by the even simpler models: diffuse reflection and specular reflection, although both can ALSO be BRDFs. <div class="mw-heading mw-heading3"><h3 id="Geometric_optics">Geometric optics</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=19" title="Edit section: Geometric optics">edit</a>]</div> Rendering is practically exclusively concerned with the particle aspect of light physics – known as <a href="/wiki/Geometrical_optics" title="Geometrical optics">geometrical optics</a>. Treating light, at its basic level, as particles bouncing around is a simplification, but appropriate: the wave aspects of light are negligible in most scenes, and are significantly more difficult to simulate. Notable wave aspect phenomena include diffraction (as seen in the colours of <a href="/wiki/Compact_disc" title="Compact disc">CDs</a> and <a href="/wiki/DVD" title="DVD">DVDs</a>) and polarisation (as seen in <a href="/wiki/Liquid-crystal_display" title="Liquid-crystal display">LCDs</a>). Both types of effect, if needed, are made by appearance-oriented adjustment of the reflection model. <div class="mw-heading mw-heading3"><h3 id="Visual_perception">Visual perception</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=20" title="Edit section: Visual perception">edit</a>]</div> Though it receives less attention, an understanding of <a href="/wiki/Human_visual_perception" class="mw-redirect" title="Human visual perception">human visual perception</a> is valuable to rendering. This is mainly because image displays and human perception have restricted ranges. A renderer can simulate a wide range of light brightness and color, but current displays – movie screen, computer monitor, etc. – cannot handle so much, and something must be discarded or compressed. Human perception also has limits, and so does not need to be given large-range images to create realism. This can help solve the problem of fitting images into displays, and, furthermore, suggest what short-cuts could be used in the rendering simulation, since certain subtleties will not be noticeable. This related subject is <a href="/wiki/Tone_mapping" title="Tone mapping">tone mapping</a>. <div class="mw-heading mw-heading3"><h3 id="Sampling_and_filtering">Sampling and filtering</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=21" title="Edit section: Sampling and filtering">edit</a>]</div> One problem that any rendering system must deal with, no matter which approach it takes, is the sampling problem. Essentially, the rendering process tries to depict a <a href="/wiki/Continuous_function" title="Continuous function">continuous function</a> from image space to colors by using a finite number of pixels. As a consequence of the <a href="/wiki/Nyquist%E2%80%93Shannon_sampling_theorem" title="Nyquist–Shannon sampling theorem">Nyquist–Shannon sampling theorem</a> (or Kotelnikov theorem), any spatial waveform that can be displayed must consist of at least two pixels, which is proportional to <a href="/wiki/Image_resolution" title="Image resolution">image resolution</a>. In simpler terms, this expresses the idea that an image cannot display details, peaks or troughs in color or intensity, that are smaller than one pixel. If a naive rendering algorithm is used without any filtering, high frequencies in the image function will cause ugly <a href="/wiki/Aliasing" title="Aliasing">aliasing</a> to be present in the final image. Aliasing typically manifests itself as <a href="/wiki/Jaggies" title="Jaggies">jaggies</a>, or jagged edges on objects where the pixel grid is visible. In order to remove aliasing, all rendering algorithms (if they are to produce good-looking images) must use some kind of <a href="/wiki/Low-pass_filter" title="Low-pass filter">low-pass filter</a> on the image function to remove high frequencies, a process called <a href="/wiki/Spatial_anti-aliasing" title="Spatial anti-aliasing">antialiasing</a>. <div class="mw-heading mw-heading2"><h2 id="Hardware">Hardware</h2>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=22" title="Edit section: Hardware">edit</a>]</div> Rendering is usually limited by available computing power and memory <a href="/wiki/Bandwidth_(computing)" title="Bandwidth (computing)">bandwidth</a>, and so specialized <a href="/wiki/Computer_hardware" title="Computer hardware">hardware</a> has been developed to speed it up ("accelerate" it), particularly for <a href="/wiki/Real-time_computer_graphics" title="Real-time computer graphics">real-time rendering</a>. Hardware features such as a <a href="/wiki/Framebuffer" title="Framebuffer">framebuffer</a> for raster graphics are required to display the output of rendering smoothly in real time. <div class="mw-heading mw-heading3"><h3 id="History">History</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=23" title="Edit section: History">edit</a>]</div> In the era of <a href="/wiki/Vector_monitor" title="Vector monitor">vector monitors</a> (also called calligraphic displays), a display processing unit (DPU) was a dedicated <a href="/wiki/Central_processing_unit" title="Central processing unit">CPU</a> or <a href="/wiki/Coprocessor" title="Coprocessor">coprocessor</a> that maintained a list of visual elements and redrew them continuously on the screen by controlling an <a href="/wiki/Cathode_ray" title="Cathode ray">electron beam</a>. Advanced DPUs such as <a href="/wiki/Evans_%26_Sutherland" title="Evans & Sutherland">Evans & Sutherland</a>'s <a href="/wiki/Line_Drawing_System-1" title="Line Drawing System-1">Line Drawing System-1</a> (and later models produced into the 1980s) incorporated 3D coordinate transformation features to accelerate rendering of <a href="/wiki/Wire-frame_model" title="Wire-frame model">wire-frame images</a>.<a href="#cite_note-Foley82-20">[20]</a>: 93–94, 404–421 <a href="#cite_note-EandS1979-67">[67]</a> Evans & Sutherland also made the <a href="/wiki/Digistar" title="Digistar">Digistar</a> <a href="/wiki/Planetarium" title="Planetarium">planetarium</a> projection system, which was a vector display that could render both stars and wire-frame graphics (the vector-based Digistar and Digistar II were used in many planetariums, and a few may still be in operation).<a href="#cite_note-NagoyaCityScienceMuseum-68">[68]</a><a href="#cite_note-WorldwidePlanetariumsDatabase1-69">[69]</a><a href="#cite_note-WorldwidePlanetariumsDatabase2-70">[70]</a> A Digistar prototype was used for rendering 3D star fields for the film <a href="/wiki/Star_Trek_II:_The_Wrath_of_Khan" title="Star Trek II: The Wrath of Khan">Star Trek II: The Wrath of Khan</a> – some of the first 3D computer graphics sequences ever seen in a feature film.<a href="#cite_note-Smith1982-71">[71]</a> Shaded 3D graphics rendering in the 1970s and early 1980s was usually implemented on general-purpose computers, such as the <a href="/wiki/PDP-10" title="PDP-10">PDP-10</a> used by researchers at the University of Utah<a href="#cite_note-Phong1973-72">[72]</a><a href="#cite_note-Catmull1974-36">[36]</a>. It was difficult to speed up using specialized hardware because it involves a <a href="/wiki/Graphics_pipeline" title="Graphics pipeline">pipeline</a> of complex steps, requiring data addressing, decision-making, and computation capabilities typically only provided by CPUs (although dedicated circuits for speeding up particular operations were proposed <a href="#cite_note-Phong1973-72">[72]</a>). <a href="/wiki/Supercomputer" title="Supercomputer">Supercomputers</a> or specially designed multi-CPU computers or <a href="/wiki/Computer_cluster" title="Computer cluster">clusters</a> were sometimes used for ray tracing.<a href="#cite_note-IntroToRTCh6-39">[39]</a> In 1981, <a href="/wiki/James_H._Clark" title="James H. Clark">James H. Clark</a> and <a href="/wiki/Marc_Hannah" title="Marc Hannah">Marc Hannah</a> designed the Geometry Engine, a <a href="/wiki/Very-large-scale_integration" title="Very-large-scale integration">VLSI</a> chip for performing some of the steps of the 3D rasterization pipeline, and started the company <a href="/wiki/Silicon_Graphics" title="Silicon Graphics">Silicon Graphics</a> (SGI) to commercialize this technology.<a href="#cite_note-Peddie2020-73">[73]</a><a href="#cite_note-Clark1980-74">[74]</a> <a href="/wiki/Home_computer" title="Home computer">Home computers</a> and <a href="/wiki/Video_game_console" title="Video game console">game consoles</a> in the 1980s contained graphics <a href="/wiki/Coprocessor" title="Coprocessor">coprocessors</a> that were capable of scrolling and filling areas of the display, and drawing <a href="/wiki/Sprite_(computer_graphics)" title="Sprite (computer graphics)">sprites</a> and lines, though they were not useful for rendering realistic images.<a href="#cite_note-Fox2024-75">[75]</a><a href="#cite_note-NESDevPPU-76">[76]</a> Towards the end of the 1980s <a href="/wiki/Graphics_card" title="Graphics card">PC graphics cards</a> and <a href="/wiki/Arcade_video_game" title="Arcade video game">arcade games</a> with 3D rendering acceleration began to appear, and in the 1990s such technology became commonplace. Today, even low-power <a href="/wiki/Mobile_processor" title="Mobile processor">mobile processors</a> typically incorporate 3D graphics acceleration features.<a href="#cite_note-Peddie2020-73">[73]</a><a href="#cite_note-PowerVRAt25-77">[77]</a> <div class="mw-heading mw-heading3"><h3 id="GPUs">GPUs</h3>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=24" title="Edit section: GPUs">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Graphics_processing_unit" title="Graphics processing unit">Graphics processing unit</a></div> The <a href="/wiki/Graphics_card" title="Graphics card">3D graphics accelerators</a> of the 1990s evolved into modern GPUs. GPUs are general-purpose processors, like <a href="/wiki/Central_processing_unit" title="Central processing unit">CPUs</a>, but they are designed for tasks that can be broken into many small, similar, mostly independent sub-tasks (such as rendering individual pixels) and performed in <a href="/wiki/Parallel_computing" title="Parallel computing">parallel</a>. This means that a GPU can speed up any rendering algorithm that can be split into subtasks in this way, in contrast to 1990s 3D accelerators which were only designed to speed up specific rasterization algorithms and simple shading and lighting effects (although <a href="/wiki/Kludge#Computer_science" title="Kludge">tricks</a> could be used to perform more general computations).<a href="#cite_note-AkenineMöller2018-9">[9]</a>: ch3 <a href="#cite_note-Peercy2000-78">[78]</a> Due to their origins, GPUs typically still provide specialized hardware acceleration for some steps of a traditional 3D rasterization <a href="/wiki/Graphics_pipeline" title="Graphics pipeline">pipeline</a>, including hidden surface removal using a <a href="/wiki/Z-buffering" title="Z-buffering">z-buffer</a>, and <a href="/wiki/Texture_mapping" title="Texture mapping">texture mapping</a> with <a href="/wiki/Mipmap" title="Mipmap">mipmaps</a>, but these features are no longer always used.<a href="#cite_note-AkenineMöller2018-9">[9]</a>: ch3  Recent GPUs have features to accelerate finding the intersections of rays with a <a href="/wiki/Bounding_volume_hierarchy" title="Bounding volume hierarchy">bounding volume hierarchy</a>, to help speed up all variants of <a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">ray tracing</a> and <a href="/wiki/Path_tracing" title="Path tracing">path tracing</a>,<a href="#cite_note-RayTracingGems_Forword_Stich-41">[41]</a> as well as <a href="/wiki/Neural_network_(machine_learning)" title="Neural network (machine learning)">neural network</a> acceleration features sometimes useful for rendering.<a href="#cite_note-NvidiaDLSS-79">[79]</a> GPUs are usually integrated with <a href="/wiki/GDDR_SDRAM" title="GDDR SDRAM">high-bandwidth memory systems</a> to support the read and write <a href="/wiki/Memory_bandwidth" title="Memory bandwidth">bandwidth</a> requirements of high-resolution, real-time rendering, particularly when multiple passes are required to render a frame, however memory <a href="/wiki/Memory_latency" title="Memory latency">latency</a> may be higher than on a CPU, which can be a problem if the <a href="/wiki/Analysis_of_parallel_algorithms#Critical_path" title="Analysis of parallel algorithms">critical path</a> in an algorithm involves many memory accesses. GPU design accepts high latency as inevitable (in part because a large number of <a href="/wiki/Thread_(computing)" title="Thread (computing)">threads</a> are sharing the <a href="/wiki/Bus_(computing)#Memory_bus" title="Bus (computing)">memory bus</a>) and attempts to "hide" it by efficiently switching between threads, so a different thread can be performing computations while the first thread is waiting for a read or write to complete.<a href="#cite_note-AkenineMöller2018-9">[9]</a>: ch3 <a href="#cite_note-Lam2021-80">[80]</a><a href="#cite_note-Gong2019-81">[81]</a> Rendering algorithms will run efficiently on a GPU only if they can be implemented using small groups of threads that perform mostly the same operations. As an example of code that meets this requirement: when rendering a small square of pixels in a simple <a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">ray-traced</a> image, all threads will likely be intersecting rays with the same object and performing the same lighting computations. For performance and architectural reasons, GPUs run groups of around 16-64 threads called warps or wavefronts in <a href="/wiki/Single_instruction,_multiple_threads" title="Single instruction, multiple threads">lock-step</a> (all threads in the group are executing the same instructions at the same time). If not all threads in the group need to run particular blocks of code (due to conditions) then some threads will be idle, or the results of their computations will be discarded, causing degraded performance.<a href="#cite_note-AkenineMöller2018-9">[9]</a>: ch3 <a href="#cite_note-Gong2019-81">[81]</a> <div class="mw-heading mw-heading2"><h2 id="Chronology_of_algorithms_and_techniques">Chronology of algorithms and techniques</h2>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=25" title="Edit section: Chronology of algorithms and techniques">edit</a>]</div> The following is a rough timeline of frequently mentioned rendering techniques, including areas of current research. Note that even in cases where an idea was named in a specific paper, there were almost always multiple researchers or teams working in the same area (including earlier related work). When a method is first proposed it is often very inefficient, and it takes additional research and practical efforts to turn it into a useful technique.<a href="#cite_note-Glassner95-24">[24]</a>: 887  The list focuses on academic research and does not include hardware. (For more history see <a href="#External_links">#External links</a>, as well as <a href="/wiki/Computer_graphics#History" title="Computer graphics">Computer graphics#History</a> and <a href="/wiki/Golden_age_of_arcade_video_games#Technology" title="Golden age of arcade video games">Golden_age_of_arcade_video_games#Technology</a>.) <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 20em;"> <ul><li>1760 - <a href="/wiki/Lambertian_reflectance" title="Lambertian reflectance">Lambertian reflectance model</a><a href="#cite_note-AkenineMöller2018-9">[9]</a>: 5.2 </li> <li>1968 - <a href="/wiki/Ray_casting" title="Ray casting">Ray casting</a><a href="#cite_note-Appel1968-40">[40]</a></li> <li>1968 - <a href="/wiki/Warnock_algorithm" title="Warnock algorithm">Warnock hidden surface removal</a><a href="#cite_note-Warnock1968-82">[82]</a><a href="#cite_note-Warnock1969-32">[32]</a></li> <li>1970 - <a href="/wiki/Scanline_rendering" title="Scanline rendering">Scanline rendering</a><a href="#cite_note-Bouknight1970-33">[33]</a><a href="#cite_note-Watkins1970-35">[35]</a></li> <li>1971 - <a href="/wiki/Gouraud_shading" title="Gouraud shading">Gouraud shading</a><a href="#cite_note-83">[83]</a></li> <li>1973 - <a href="/wiki/Phong_shading" title="Phong shading">Phong shading</a><a href="#cite_note-phong-84">[84]</a><a href="#cite_note-phong1975-85">[85]</a></li> <li>1973 - <a href="/wiki/Phong_reflection_model" title="Phong reflection model">Phong reflectance model</a><a href="#cite_note-phong-84">[84]</a><a href="#cite_note-phong1975-85">[85]</a></li> <li>1974 - <a href="/wiki/Texture_mapping" title="Texture mapping">Texture mapping</a><a href="#cite_note-Catmull1974-36">[36]</a></li> <li>1974 - <a href="/wiki/Z-buffering" title="Z-buffering">Z-buffering</a><a href="#cite_note-Catmull1974-36">[36]</a></li> <li>1976 - <a href="/wiki/Environment_mapping" class="mw-redirect" title="Environment mapping">Environment mapping</a><a href="#cite_note-86">[86]</a></li> <li>1977 - <a href="/wiki/Blinn-Phong_shading_model" class="mw-redirect" title="Blinn-Phong shading model">Blinn-Phong reflectance model</a><a href="#cite_note-87">[87]</a></li> <li>1977 - <a href="/wiki/Shadow_volume" title="Shadow volume">Shadow volumes</a><a href="#cite_note-88">[88]</a></li> <li>1978 - <a href="/wiki/Shadow_mapping" title="Shadow mapping">Shadow mapping</a><a href="#cite_note-89">[89]</a></li> <li>1978 - <a href="/wiki/Bump_mapping" title="Bump mapping">Bump mapping</a><a href="#cite_note-90">[90]</a></li> <li>1980 - <a href="/wiki/BSP_trees" class="mw-redirect" title="BSP trees">BSP trees</a><a href="#cite_note-91">[91]</a></li> <li>1980 - <a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">Ray tracing</a><a href="#cite_note-92">[92]</a></li> <li>1981 - <a href="/wiki/Specular_highlight#Cook–Torrance_model" title="Specular highlight">Cook-Torrance reflectance model</a><a href="#cite_note-93">[93]</a></li> <li>1983 - <a href="/wiki/Mipmap" title="Mipmap">MIP maps</a><a href="#cite_note-94">[94]</a></li> <li>1984 - <a href="/wiki/Octree" title="Octree">Octree</a> ray tracing<a href="#cite_note-95">[95]</a></li> <li>1984 - <a href="/wiki/Alpha_compositing" title="Alpha compositing">Alpha compositing</a><a href="#cite_note-96">[96]</a></li> <li>1984 - <a href="/wiki/Distributed_ray_tracing" title="Distributed ray tracing">Distributed ray tracing</a><a href="#cite_note-97">[97]</a></li> <li>1984 - <a href="/wiki/Radiosity_(computer_graphics)" title="Radiosity (computer graphics)">Radiosity</a><a href="#cite_note-98">[98]</a></li> <li>1984 - <a href="/wiki/A-buffer" title="A-buffer">A-buffer</a><a href="#cite_note-Carpenter1984-37">[37]</a></li> <li>1985 - <a href="/wiki/Hemicube_(computer_graphics)" title="Hemicube (computer graphics)">Hemicube</a> radiosity<a href="#cite_note-99">[99]</a></li> <li>1986 - Light source tracing<a href="#cite_note-100">[100]</a></li> <li>1986 - <a href="/wiki/Rendering_equation" title="Rendering equation">Rendering equation</a><a href="#cite_note-Kajiya1986-25">[25]</a></li> <li>1986 - <a href="/wiki/Path_tracing" title="Path tracing">Path tracing</a><a href="#cite_note-Kajiya1986-25">[25]</a></li> <li>1987 - <a href="/wiki/Reyes_rendering" title="Reyes rendering">Reyes rendering</a><a href="#cite_note-Cook1987-38">[38]</a></li> <li>1991 - <a href="/wiki/Xiaolin_Wu%27s_line_algorithm" title="Xiaolin Wu's line algorithm">Xiaolin Wu line anti-aliasing</a><a href="#cite_note-101">[101]</a><a href="#cite_note-102">[102]</a></li> <li>1991 - Hierarchical radiosity<a href="#cite_note-103">[103]</a></li> <li>1993 - <a href="/wiki/Oren%E2%80%93Nayar_reflectance_model" title="Oren–Nayar reflectance model">Oren–Nayar reflectance model</a><a href="#cite_note-oren-nayar-104">[104]</a></li> <li>1993 - <a href="/wiki/Tone_mapping" title="Tone mapping">Tone mapping</a><a href="#cite_note-105">[105]</a></li> <li>1993 - <a href="/wiki/Subsurface_scattering" title="Subsurface scattering">Subsurface scattering</a><a href="#cite_note-106">[106]</a></li> <li>1993 - <a href="/wiki/Path_tracing#Bidirectional_path_tracing" title="Path tracing">Bidirectional path tracing</a> (Lafortune & Willems formulation)<a href="#cite_note-107">[107]</a></li> <li>1994 - <a href="/wiki/Ambient_occlusion" title="Ambient occlusion">Ambient occlusion</a><a href="#cite_note-108">[108]</a></li> <li>1995 - <a href="/wiki/Photon_mapping" title="Photon mapping">Photon mapping</a><a href="#cite_note-109">[109]</a></li> <li>1995 - Multiple importance sampling<a href="#cite_note-110">[110]</a></li> <li>1997 - <a href="/wiki/Path_tracing#Bidirectional_path_tracing" title="Path tracing">Bidirectional path tracing</a> (Veach & Guibas formulation)<a href="#cite_note-111">[111]</a></li> <li>1997 - <a href="/wiki/Metropolis_light_transport" title="Metropolis light transport">Metropolis light transport</a><a href="#cite_note-112">[112]</a></li> <li>1997 - Instant Radiosity<a href="#cite_note-113">[113]</a></li> <li>2002 - <a href="/wiki/Precomputed_Radiance_Transfer" title="Precomputed Radiance Transfer">Precomputed Radiance Transfer</a><a href="#cite_note-114">[114]</a></li> <li>2003 - <a href="/wiki/Mitsubishi_Electric_Research_Laboratories" title="Mitsubishi Electric Research Laboratories">MERL</a> <a href="/wiki/Bidirectional_reflectance_distribution_function" title="Bidirectional reflectance distribution function">BRDF</a> database<a href="#cite_note-115">[115]</a></li> <li>2014 - <a href="/wiki/Michael_J._Black#Differentiable_rendering" title="Michael J. Black">Differentiable rendering</a><a href="#cite_note-116">[116]</a></li> <li>2017 - Path guiding (using adaptive SD-tree)<a href="#cite_note-Mueller2017-117">[117]</a></li> <li>2020 - Spatiotemporal <a href="/wiki/Reservoir_sampling" title="Reservoir sampling">reservoir</a> resampling (ReSTIR)<a href="#cite_note-118">[118]</a></li> <li>2020 - <a href="/wiki/Neural_radiance_field" title="Neural radiance field">Neural radiance fields</a><a href="#cite_note-Mildenhall2020-14">[14]</a></li> <li>2023 - 3D <a href="/wiki/Gaussian_splatting" title="Gaussian splatting">Gaussian splatting</a><a href="#cite_note-Kerbl2023-15">[15]</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=26" title="Edit section: See also">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col"> <ul><li><a href="/wiki/2D_computer_graphics" title="2D computer graphics">2D computer graphics</a> – Computer-based generation of digital images</li> <li><a href="/wiki/3D_computer_graphics" title="3D computer graphics">3D computer graphics</a> – Graphics that use a three-dimensional representation of geometric data</li> <li><a href="/wiki/3D_rendering" title="3D rendering">3D rendering</a> – Process of converting 3D scenes into 2D images</li> <li><a href="/wiki/Artistic_rendering" class="mw-redirect" title="Artistic rendering">Artistic rendering</a> – Style of renderingPages displaying short descriptions of redirect targets</li> <li><a href="/wiki/Architectural_rendering" title="Architectural rendering">Architectural rendering</a> – creating two-dimensional images or animations showing the attributes of a proposed architectural designPages displaying wikidata descriptions as a fallback</li> <li><a href="/wiki/Chromatic_aberration" title="Chromatic aberration">Chromatic aberration</a> – Failure of a lens to focus all colors on the same point</li> <li><a href="/wiki/Displacement_mapping" title="Displacement mapping">Displacement mapping</a> – Computer graphics technique</li> <li><a href="/wiki/Font_rasterization" title="Font rasterization">Font rasterization</a> – Process of converting text from vector to raster</li> <li><a href="/wiki/Global_illumination" title="Global illumination">Global illumination</a> – Group of rendering algorithms used in 3D computer graphics</li> <li><a href="/wiki/Graphics_pipeline" title="Graphics pipeline">Graphics pipeline</a> – Procedure to convert 3D scenes to 2D images</li> <li><a href="/wiki/Heightmap" title="Heightmap">Heightmap</a> – Type of raster image in computer graphics</li> <li><a href="/wiki/High-dynamic-range_rendering" title="High-dynamic-range rendering">High-dynamic-range rendering</a> – Rendering of computer graphics scenes by using lighting calculations done in high-dynamic-range</li> <li><a href="/wiki/Image-based_modeling_and_rendering" title="Image-based modeling and rendering">Image-based modeling and rendering</a></li> <li><a href="/wiki/List_of_3D_rendering_software" title="List of 3D rendering software">List of 3D rendering software</a></li> <li><a href="/wiki/Motion_blur" title="Motion blur">Motion blur</a> – Photography artifact from moving objects</li> <li><a href="/wiki/Non-photorealistic_rendering" title="Non-photorealistic rendering">Non-photorealistic rendering</a> – Style of rendering</li> <li><a href="/wiki/Normal_mapping" title="Normal mapping">Normal mapping</a> – Texture mapping technique</li> <li><a href="/wiki/Painter%27s_algorithm" title="Painter's algorithm">Painter's algorithm</a> – Algorithm for visible surface determination in 3D graphics</li> <li><a href="/wiki/Per-pixel_lighting" title="Per-pixel lighting">Per-pixel lighting</a></li> <li><a href="/wiki/Physically_based_rendering" title="Physically based rendering">Physically based rendering</a> – Computer graphics technique</li> <li><a href="/wiki/Pre-rendering" title="Pre-rendering">Pre-rendering</a> – Process in which video footage is not rendered in real-time</li> <li><a href="/wiki/Raster_image_processor" title="Raster image processor">Raster image processor</a> – component used in a printing system which produces a raster image also known as a bitmapPages displaying wikidata descriptions as a fallback</li> <li><a href="/wiki/Radiosity_(computer_graphics)" title="Radiosity (computer graphics)">Radiosity</a> – Computer graphics rendering method using diffuse reflection</li> <li><a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">Ray tracing</a> – Rendering method</li> <li><a href="/wiki/Real-time_computer_graphics" title="Real-time computer graphics">Real-time computer graphics</a> – Sub-field of computer graphics</li> <li><a href="/wiki/Reyes_rendering" title="Reyes rendering">Reyes</a> – Computer software architecture in 3D computer graphics</li> <li><a href="/wiki/Scanline_rendering" title="Scanline rendering">Scanline rendering/Scanline algorithm</a> – 3D computer graphics image rendering method</li> <li><a href="/wiki/Software_rendering" title="Software rendering">Software rendering</a> – Generating images by computer software</li> <li><a href="/wiki/Sprite_(computer_graphics)" title="Sprite (computer graphics)">Sprite (computer graphics)</a> – 2D bitmap displayed over a larger scene</li> <li><a href="/wiki/Unbiased_rendering" title="Unbiased rendering">Unbiased rendering</a> – Type of rendering in computer graphics</li> <li><a href="/wiki/Vector_graphics" title="Vector graphics">Vector graphics</a> – Computer graphics images defined by points, lines and curves</li> <li><a href="/wiki/VirtualGL" title="VirtualGL">VirtualGL</a></li> <li><a href="/wiki/Virtual_model" class="mw-redirect" title="Virtual model">Virtual model</a> – Form of computer-aided engineeringPages displaying short descriptions of redirect targets</li> <li><a href="/wiki/Virtual_studio" class="mw-redirect" title="Virtual studio">Virtual studio</a> – Technology for television and film productionPages displaying short descriptions of redirect targets</li> <li><a href="/wiki/Volume_rendering" title="Volume rendering">Volume rendering</a> – Representing a 3D-modeled object or dataset as a 2D projection</li> <li><a href="/wiki/Z-buffering" title="Z-buffering">Z-buffer algorithms</a> – Type of data buffer in computer graphics</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=27" title="Edit section: References">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output 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Focal Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-315-85827-2" title="Special:BookSources/978-1-315-85827-2"><bdi>978-1-315-85827-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Production+Pipeline+Fundamentals+for+Film+and+Games&rft.pub=Focal+Press&rft.date=2014&rft.isbn=978-1-315-85827-2&rft.aulast=Dunlop&rft.aufirst=Renee&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> <li id="cite_note-AkenineMöller2018-9">^ <a href="#cite_ref-AkenineMöller2018_9-0">a</a> <a href="#cite_ref-AkenineMöller2018_9-1">b</a> <a href="#cite_ref-AkenineMöller2018_9-2">c</a> <a href="#cite_ref-AkenineMöller2018_9-3">d</a> <a href="#cite_ref-AkenineMöller2018_9-4">e</a> <a href="#cite_ref-AkenineMöller2018_9-5">f</a> <a href="#cite_ref-AkenineMöller2018_9-6">g</a> <a href="#cite_ref-AkenineMöller2018_9-7">h</a> <a href="#cite_ref-AkenineMöller2018_9-8">i</a> <a href="#cite_ref-AkenineMöller2018_9-9">j</a> <a href="#cite_ref-AkenineMöller2018_9-10">k</a> <a href="#cite_ref-AkenineMöller2018_9-11">l</a> <a href="#cite_ref-AkenineMöller2018_9-12">m</a> <a href="#cite_ref-AkenineMöller2018_9-13">n</a> <a href="#cite_ref-AkenineMöller2018_9-14">o</a> <a href="#cite_ref-AkenineMöller2018_9-15">p</a> <a href="#cite_ref-AkenineMöller2018_9-16">q</a> <a href="#cite_ref-AkenineMöller2018_9-17">r</a> <a href="#cite_ref-AkenineMöller2018_9-18">s</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAkenine-MöllerHainesHoffmanPesce2018" class="citation book cs1">Akenine-Möller, Tomas; Haines, Eric; Hoffman, Naty; Pesce, Angelo; Iwanicki, Michał; Hillaire, Sébastien (2018). Real-Time Rendering (4th ed.). Boca Raton, FL: A K Peters/CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1138627000" title="Special:BookSources/978-1138627000"><bdi>978-1138627000</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Real-Time+Rendering&rft.place=Boca+Raton%2C+FL&rft.edition=4th&rft.pub=A+K+Peters%2FCRC+Press&rft.date=2018&rft.isbn=978-1138627000&rft.aulast=Akenine-M%C3%B6ller&rft.aufirst=Tomas&rft.au=Haines%2C+Eric&rft.au=Hoffman%2C+Naty&rft.au=Pesce%2C+Angelo&rft.au=Iwanicki%2C+Micha%C5%82&rft.au=Hillaire%2C+S%C3%A9bastien&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> <li id="cite_note-OpenVDBAbout-10"><a href="#cite_ref-OpenVDBAbout_10-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.openvdb.org/about/">"About OpenVDB"</a>. www.openvdb.org. Academy Software Foundation. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240903072553/https://www.openvdb.org/about/">Archived</a> from the original on 3 September 2024. Retrieved 31 August 2024.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.openvdb.org&rft.atitle=About+OpenVDB&rft_id=https%3A%2F%2Fwww.openvdb.org%2Fabout%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> <li id="cite_note-Museth2013-11"><a href="#cite_ref-Museth2013_11-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMuseth2013" class="citation journal cs1">Museth, Ken (June 2013). <a rel="nofollow" class="external text" href="https://www.museth.org/Ken/Publications_files/Museth_TOG13.pdf">"VDB: High-Resolution Sparse Volumes with Dynamic Topology"</a> (PDF). ACM Transactions on Graphics. 32 (3). <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F2487228.2487235">10.1145/2487228.2487235</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240415172843/https://www.museth.org/Ken/Publications_files/Museth_TOG13.pdf">Archived</a> (PDF) from the original on 15 April 2024. Retrieved 31 August 2024.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ACM+Transactions+on+Graphics&rft.atitle=VDB%3A+High-Resolution+Sparse+Volumes+with+Dynamic+Topology&rft.volume=32&rft.issue=3&rft.date=2013-06&rft_id=info%3Adoi%2F10.1145%2F2487228.2487235&rft.aulast=Museth&rft.aufirst=Ken&rft_id=https%3A%2F%2Fwww.museth.org%2FKen%2FPublications_files%2FMuseth_TOG13.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> <li id="cite_note-Bridson2015-12"><a href="#cite_ref-Bridson2015_12-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBridson2015" class="citation book cs1">Bridson, Robert (2015). Fluid Simulation for Computer Graphics (2nd ed.). A K Peters/CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-482-23283-7" title="Special:BookSources/978-1-482-23283-7"><bdi>978-1-482-23283-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fluid+Simulation+for+Computer+Graphics&rft.edition=2nd&rft.pub=A+K+Peters%2FCRC+Press&rft.date=2015&rft.isbn=978-1-482-23283-7&rft.aulast=Bridson&rft.aufirst=Robert&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> <li id="cite_note-Schmid2023-13"><a href="#cite_ref-Schmid2023_13-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchmid2023" class="citation web cs1">Schmid, Katrin (March 2, 2023). <a rel="nofollow" class="external text" href="https://radiancefields.com/history-of-neural-radiance-fields">"A short 170 year history of Neural Radiance Fields (NeRF), Holograms, and Light Fields"</a>. radiancefields.com. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240831194910/https://radiancefields.com/history-of-neural-radiance-fields">Archived</a> from the original on 31 August 2024. Retrieved 31 August 2024.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=radiancefields.com&rft.atitle=A+short+170+year+history+of+Neural+Radiance+Fields+%28NeRF%29%2C+Holograms%2C+and+Light+Fields&rft.date=2023-03-02&rft.aulast=Schmid&rft.aufirst=Katrin&rft_id=https%3A%2F%2Fradiancefields.com%2Fhistory-of-neural-radiance-fields&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> <li id="cite_note-Mildenhall2020-14">^ <a href="#cite_ref-Mildenhall2020_14-0">a</a> <a href="#cite_ref-Mildenhall2020_14-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMildenhallSrinivasanTancikBarron2020" class="citation web cs1">Mildenhall, Ben; Srinivasan, Pratul P.; Tancik, Matthew; Barron, Jonathan T.; Ramamoorthi, Ravi; Ng, Ren (2020). <a rel="nofollow" class="external text" href="https://www.matthewtancik.com/nerf">"NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis"</a>. 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ACM Transactions on Graphics. 42 (4): 1–14. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/2308.04079">2308.04079</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F3592433">10.1145/3592433</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240822130514/https://repo-sam.inria.fr/fungraph/3d-gaussian-splatting/">Archived</a> from the original on 22 August 2024. Retrieved 31 August 2024.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ACM+Transactions+on+Graphics&rft.atitle=3D+Gaussian+Splatting+for+Real-Time+Radiance+Field+Rendering&rft.volume=42&rft.issue=4&rft.pages=1-14&rft.date=2023-07&rft_id=info%3Aarxiv%2F2308.04079&rft_id=info%3Adoi%2F10.1145%2F3592433&rft.aulast=Kerbl&rft.aufirst=Bernhard&rft.au=Kopanas%2C+Georgios&rft.au=Leimk%C3%BChler%2C+Thomas&rft.au=Drettakis%2C+George&rft_id=https%3A%2F%2Frepo-sam.inria.fr%2Ffungraph%2F3d-gaussian-splatting%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> <li id="cite_note-pbrt4UG-16">^ <a href="#cite_ref-pbrt4UG_16-0">a</a> <a href="#cite_ref-pbrt4UG_16-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPharrJakobHumphreys2023" class="citation web cs1">Pharr, Matt; Jakob, Wenzel; Humphreys, Greg (2023). <a rel="nofollow" class="external text" href="https://pbrt.org/users-guide-v4">"pbrt-v4 User's Guide"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240903072555/https://pbrt.org/users-guide-v4">Archived</a> from the original on 3 September 2024. Retrieved 31 August 2024.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=pbrt-v4+User%27s+Guide&rft.date=2023&rft.aulast=Pharr&rft.aufirst=Matt&rft.au=Jakob%2C+Wenzel&rft.au=Humphreys%2C+Greg&rft_id=https%3A%2F%2Fpbrt.org%2Fusers-guide-v4&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> <li id="cite_note-Brinkmann2008-17">^ <a href="#cite_ref-Brinkmann2008_17-0">a</a> <a href="#cite_ref-Brinkmann2008_17-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrinkmann2008" class="citation book cs1">Brinkmann, Ron (2008). The Art and Science of Digital Compositing (2nd ed.). Morgan Kaufmann. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-370638-6" title="Special:BookSources/978-0-12-370638-6"><bdi>978-0-12-370638-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Art+and+Science+of+Digital+Compositing&rft.edition=2nd&rft.pub=Morgan+Kaufmann&rft.date=2008&rft.isbn=978-0-12-370638-6&rft.aulast=Brinkmann&rft.aufirst=Ron&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> <li id="cite_note-BlenderRenderingAnimations-18"><a href="#cite_ref-BlenderRenderingAnimations_18-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://docs.blender.org/manual/en/4.2/render/output/animation.html">"Blender 4.2 Manual: Rendering: Render Output: Rendering Animations"</a>. docs.blender.org. The Blender Foundation. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240831195034/https://docs.blender.org/manual/en/4.2/render/output/animation.html">Archived</a> from the original on 31 August 2024. Retrieved 31 August 2024.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=docs.blender.org&rft.atitle=Blender+4.2+Manual%3A+Rendering%3A+Render+Output%3A+Rendering+Animations&rft_id=https%3A%2F%2Fdocs.blender.org%2Fmanual%2Fen%2F4.2%2Frender%2Foutput%2Fanimation.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> <li id="cite_note-Marschner2022-19">^ <a href="#cite_ref-Marschner2022_19-0">a</a> <a href="#cite_ref-Marschner2022_19-1">b</a> <a href="#cite_ref-Marschner2022_19-2">c</a> <a href="#cite_ref-Marschner2022_19-3">d</a> <a href="#cite_ref-Marschner2022_19-4">e</a> <a href="#cite_ref-Marschner2022_19-5">f</a> <a href="#cite_ref-Marschner2022_19-6">g</a> <a href="#cite_ref-Marschner2022_19-7">h</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMarschnerShirley2022" class="citation book cs1">Marschner, Steve; Shirley, Peter (2022). Fundamentals of Computer Graphics (5th ed.). CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-003-05033-9" title="Special:BookSources/978-1-003-05033-9"><bdi>978-1-003-05033-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Computer+Graphics&rft.edition=5th&rft.pub=CRC+Press&rft.date=2022&rft.isbn=978-1-003-05033-9&rft.aulast=Marschner&rft.aufirst=Steve&rft.au=Shirley%2C+Peter&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> <li id="cite_note-Foley82-20">^ <a href="#cite_ref-Foley82_20-0">a</a> <a href="#cite_ref-Foley82_20-1">b</a> <a href="#cite_ref-Foley82_20-2">c</a> <a href="#cite_ref-Foley82_20-3">d</a> <a href="#cite_ref-Foley82_20-4">e</a> <a href="#cite_ref-Foley82_20-5">f</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFoleyVan_Dam1982" class="citation book cs1"><a href="/wiki/James_D._Foley" title="James D. 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Addison-Wesley Publishing Company, Inc. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-201-14468-9" title="Special:BookSources/0-201-14468-9"><bdi>0-201-14468-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Interactive+Computer+Graphics&rft.pub=Addison-Wesley+Publishing+Company%2C+Inc.&rft.date=1982&rft.isbn=0-201-14468-9&rft.aulast=Foley&rft.aufirst=James+D.&rft.au=Van+Dam%2C+Andries&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> <li id="cite_note-RayTracingGems_1-21">^ <a href="#cite_ref-RayTracingGems_1_21-0">a</a> <a href="#cite_ref-RayTracingGems_1_21-1">b</a> <a href="#cite_ref-RayTracingGems_1_21-2">c</a> <a href="#cite_ref-RayTracingGems_1_21-3">d</a> <a href="#cite_ref-RayTracingGems_1_21-4">e</a> <a href="#cite_ref-RayTracingGems_1_21-5">f</a> <a href="#cite_ref-RayTracingGems_1_21-6">g</a> <a href="#cite_ref-RayTracingGems_1_21-7">h</a> <a href="#cite_ref-RayTracingGems_1_21-8">i</a> <a href="#cite_ref-RayTracingGems_1_21-9">j</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHainesShirley2019" class="citation book cs1">Haines, Eric; Shirley, Peter (February 25, 2019). 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Berkeley, CA: Apress. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-1-4842-4427-2">10.1007/978-1-4842-4427-2</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4842-4427-2" title="Special:BookSources/978-1-4842-4427-2"><bdi>978-1-4842-4427-2</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:71144394">71144394</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240127220804/https://link.springer.com/book/10.1007/978-1-4842-4427-2">Archived</a> from the original on January 27, 2024. 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Berkeley, CA: Apress. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-1-4842-4427-2">10.1007/978-1-4842-4427-2</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4842-4427-2" title="Special:BookSources/978-1-4842-4427-2"><bdi>978-1-4842-4427-2</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:71144394">71144394</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240127220804/https://link.springer.com/book/10.1007/978-1-4842-4427-2">Archived</a> from the original on January 27, 2024. 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Berkeley, CA: Apress. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-1-4842-4427-2">10.1007/978-1-4842-4427-2</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4842-4427-2" title="Special:BookSources/978-1-4842-4427-2"><bdi>978-1-4842-4427-2</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:71144394">71144394</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240127220804/https://link.springer.com/book/10.1007/978-1-4842-4427-2">Archived</a> from the original on January 27, 2024. 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Cambridge, Massachusetts: The MIT Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0262048026" title="Special:BookSources/978-0262048026"><bdi>978-0262048026</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240127220804/https://pbr-book.org/4ed/contents">Archived</a> from the original on January 27, 2024. 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Retrieved 23 November 2024.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ACM+Transactions+on+Graphics+%28TOG%29&rft.atitle=A+Data-Driven+Reflectance+Model&rft.volume=22&rft.issue=3&rft.pages=759-769&rft.date=2003-07&rft_id=info%3Adoi%2F10.1145%2F882262.882343&rft.aulast=Matusik&rft.aufirst=W.&rft.au=Pfister%2C+H.&rft.au=Brand%2C+M.&rft.au=McMillan%2C+L.&rft_id=https%3A%2F%2Fwww.merl.com%2Fpublications%2FTR2003-83&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> <li id="cite_note-116"><a href="#cite_ref-116">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLoperBlack2014" class="citation conference cs1">Loper, Matthew M; Black, Michael J (6 September 2014). <a rel="nofollow" class="external text" href="http://files.is.tue.mpg.de/black/papers/OpenDR.pdf">"OpenDR: An approximate differentiable renderer"</a> (PDF). Computer Vision - ECCV 2014. Vol. 8695. Zurich, Switzerland: Springer International Publishing. pp. 154–169. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-319-10584-0_11">10.1007/978-3-319-10584-0_11</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240624151721/https://files.is.tue.mpg.de/black/papers/OpenDR.pdf">Archived</a> (PDF) from the original on 24 June 2024. Retrieved 2 September 2024.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.atitle=OpenDR%3A+An+approximate+differentiable+renderer&rft.btitle=Computer+Vision+-+ECCV+2014&rft.place=Zurich%2C+Switzerland&rft.pages=154-169&rft.pub=Springer+International+Publishing&rft.date=2014-09-06&rft_id=info%3Adoi%2F10.1007%2F978-3-319-10584-0_11&rft.aulast=Loper&rft.aufirst=Matthew+M&rft.au=Black%2C+Michael+J&rft_id=http%3A%2F%2Ffiles.is.tue.mpg.de%2Fblack%2Fpapers%2FOpenDR.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> <li id="cite_note-Mueller2017-117"><a href="#cite_ref-Mueller2017_117-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMüllerGrossNovák2017" class="citation journal cs1">Müller, Thomas; Gross, Markus; Novák, Jan (June 2017). <a rel="nofollow" class="external text" href="https://jannovak.info/publications/PathGuide/index.html">"Practical Path Guiding for Efficient Light-Transport Simulation"</a>. Computer Graphics Forum (Proceedings of EGSR). 36 (4). The Eurographs Association & John Wiley & Sons, Ltd.: 91–100. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fcgf.13227">10.1111/cgf.13227</a>. Retrieved 4 September 2024.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Computer+Graphics+Forum+%28Proceedings+of+EGSR%29&rft.atitle=Practical+Path+Guiding+for+Efficient+Light-Transport+Simulation&rft.volume=36&rft.issue=4&rft.pages=91-100&rft.date=2017-06&rft_id=info%3Adoi%2F10.1111%2Fcgf.13227&rft.aulast=M%C3%BCller&rft.aufirst=Thomas&rft.au=Gross%2C+Markus&rft.au=Nov%C3%A1k%2C+Jan&rft_id=https%3A%2F%2Fjannovak.info%2Fpublications%2FPathGuide%2Findex.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> <li id="cite_note-118"><a href="#cite_ref-118">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBitterliWymanPharrShirley2020" class="citation journal cs1">Bitterli, Benedikt; Wyman, Chris; Pharr, Matt; Shirley, Peter; Lefohn, Aaron; Jarosz, Wojciech (July 2020). <a rel="nofollow" class="external text" href="https://cs.dartmouth.edu/~wjarosz/publications/bitterli20spatiotemporal.html">"Spatiotemporal reservoir resampling for real-time ray tracing with dynamic direct lighting"</a>. ACM Transactions on Graphics. 39 (4). <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F3386569.3392481">10.1145/3386569.3392481</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240301064934/https://cs.dartmouth.edu/~wjarosz/publications/bitterli20spatiotemporal.html">Archived</a> from the original on 1 March 2024. Retrieved 2 September 2024.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ACM+Transactions+on+Graphics&rft.atitle=Spatiotemporal+reservoir+resampling+for+real-time+ray+tracing+with+dynamic+direct+lighting&rft.volume=39&rft.issue=4&rft.date=2020-07&rft_id=info%3Adoi%2F10.1145%2F3386569.3392481&rft.aulast=Bitterli&rft.aufirst=Benedikt&rft.au=Wyman%2C+Chris&rft.au=Pharr%2C+Matt&rft.au=Shirley%2C+Peter&rft.au=Lefohn%2C+Aaron&rft.au=Jarosz%2C+Wojciech&rft_id=https%3A%2F%2Fcs.dartmouth.edu%2F~wjarosz%2Fpublications%2Fbitterli20spatiotemporal.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=28" title="Edit section: Further reading">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col" style="column-width: 30em;"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAkenine-MöllerHainesHoffmanPesce2018" class="citation book cs1">Akenine-Möller, Tomas; Haines, Eric; Hoffman, Naty; Pesce, Angelo; Iwanicki, Micał; Hillaire, Sébastien (2018). <a rel="nofollow" class="external text" href="https://www.realtimerendering.com/">Real-time rendering</a> (4 ed.). Boca Raton, FL, USA.: AK Peters. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-13862-700-0" title="Special:BookSources/978-1-13862-700-0"><bdi>978-1-13862-700-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Real-time+rendering&rft.place=Boca+Raton%2C+FL%2C+USA.&rft.edition=4&rft.pub=AK+Peters&rft.date=2018&rft.isbn=978-1-13862-700-0&rft.aulast=Akenine-M%C3%B6ller&rft.aufirst=Tomas&rft.au=Haines%2C+Eric&rft.au=Hoffman%2C+Naty&rft.au=Pesce%2C+Angelo&rft.au=Iwanicki%2C+Mica%C5%82&rft.au=Hillaire%2C+S%C3%A9bastien&rft_id=https%3A%2F%2Fwww.realtimerendering.com%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBlinn1996" class="citation book cs1"><a href="/wiki/Jim_Blinn" title="Jim Blinn">Blinn, Jim</a> (1996). Jim Blinn's corner : a trip down the graphics pipeline. San Francisco, Calif.: Morgan Kaufmann Publishers. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-55860-387-5" title="Special:BookSources/978-1-55860-387-5"><bdi>978-1-55860-387-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Jim+Blinn%27s+corner+%3A+a+trip+down+the+graphics+pipeline&rft.place=San+Francisco%2C+Calif.&rft.pub=Morgan+Kaufmann+Publishers&rft.date=1996&rft.isbn=978-1-55860-387-5&rft.aulast=Blinn&rft.aufirst=Jim&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCohenWallace1998" class="citation book cs1">Cohen, Michael F.; Wallace, John R. (1998). Radiosity and realistic image synthesis (3 ed.). Boston, Mass. [u.a.]: Academic Press Professional. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-178270-2" title="Special:BookSources/978-0-12-178270-2"><bdi>978-0-12-178270-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Radiosity+and+realistic+image+synthesis&rft.place=Boston%2C+Mass.+%5Bu.a.%5D&rft.edition=3&rft.pub=Academic+Press+Professional&rft.date=1998&rft.isbn=978-0-12-178270-2&rft.aulast=Cohen&rft.aufirst=Michael+F.&rft.au=Wallace%2C+John+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPhilip_DutréBekaertBala2003" class="citation book cs1">Philip Dutré; Bekaert, Philippe; Bala, Kavita (2003). Advanced global illumination ([Online-Ausg.] ed.). Natick, Mass.: A K Peters. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-56881-177-2" title="Special:BookSources/978-1-56881-177-2"><bdi>978-1-56881-177-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Advanced+global+illumination&rft.place=Natick%2C+Mass.&rft.edition=%5BOnline-Ausg.%5D&rft.pub=A+K+Peters&rft.date=2003&rft.isbn=978-1-56881-177-2&rft.au=Philip+Dutr%C3%A9&rft.au=Bekaert%2C+Philippe&rft.au=Bala%2C+Kavita&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFoleyVan_DamFeinerHughes1990" class="citation book cs1"><a href="/wiki/James_D._Foley" title="James D. Foley">Foley, James D.</a>; Van Dam; Feiner; Hughes (1990). <a rel="nofollow" class="external text" href="https://archive.org/details/computergraphics00fole">Computer graphics : principles and practice</a> (2 ed.). Reading, Mass.: Addison-Wesley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-12110-0" title="Special:BookSources/978-0-201-12110-0"><bdi>978-0-201-12110-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computer+graphics+%3A+principles+and+practice&rft.place=Reading%2C+Mass.&rft.edition=2&rft.pub=Addison-Wesley&rft.date=1990&rft.isbn=978-0-201-12110-0&rft.aulast=Foley&rft.aufirst=James+D.&rft.au=Van+Dam&rft.au=Feiner&rft.au=Hughes&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcomputergraphics00fole&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAndrew_S._Glassner1989" class="citation book cs1">Andrew S. Glassner, ed. (1989). An introduction to ray tracing (3 ed.). London [u.a.]: Acad. Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-286160-4" title="Special:BookSources/978-0-12-286160-4"><bdi>978-0-12-286160-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+introduction+to+ray+tracing&rft.place=London+%5Bu.a.%5D&rft.edition=3&rft.pub=Acad.+Press&rft.date=1989&rft.isbn=978-0-12-286160-4&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGlassner2004" class="citation book cs1"><a href="/wiki/Andrew_Glassner" title="Andrew Glassner">Glassner, Andrew S.</a> (2004). Principles of digital image synthesis (2 ed.). San Francisco, Calif.: Kaufmann. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-55860-276-2" title="Special:BookSources/978-1-55860-276-2"><bdi>978-1-55860-276-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principles+of+digital+image+synthesis&rft.place=San+Francisco%2C+Calif.&rft.edition=2&rft.pub=Kaufmann&rft.date=2004&rft.isbn=978-1-55860-276-2&rft.aulast=Glassner&rft.aufirst=Andrew+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGoochGooch2001" class="citation book cs1">Gooch, Bruce; <a href="/wiki/Amy_Ashurst_Gooch" title="Amy Ashurst Gooch">Gooch, Amy</a> (2001). Non-photorealistic rendering. Natick, Mass.: A K Peters. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-56881-133-8" title="Special:BookSources/978-1-56881-133-8"><bdi>978-1-56881-133-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Non-photorealistic+rendering&rft.place=Natick%2C+Mass.&rft.pub=A+K+Peters&rft.date=2001&rft.isbn=978-1-56881-133-8&rft.aulast=Gooch&rft.aufirst=Bruce&rft.au=Gooch%2C+Amy&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJensen2001" class="citation book cs1">Jensen, Henrik Wann (2001). Realistic image synthesis using photon mapping ([Nachdr.] ed.). Natick, Mass.: AK Peters. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-56881-147-5" title="Special:BookSources/978-1-56881-147-5"><bdi>978-1-56881-147-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Realistic+image+synthesis+using+photon+mapping&rft.place=Natick%2C+Mass.&rft.edition=%5BNachdr.%5D&rft.pub=AK+Peters&rft.date=2001&rft.isbn=978-1-56881-147-5&rft.aulast=Jensen&rft.aufirst=Henrik+Wann&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPharrHumphreys2004" class="citation book cs1">Pharr, Matt; Humphreys, Greg (2004). Physically based rendering from theory to implementation. Amsterdam: Elsevier/Morgan Kaufmann. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-553180-1" title="Special:BookSources/978-0-12-553180-1"><bdi>978-0-12-553180-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physically+based+rendering+from+theory+to+implementation&rft.place=Amsterdam&rft.pub=Elsevier%2FMorgan+Kaufmann&rft.date=2004&rft.isbn=978-0-12-553180-1&rft.aulast=Pharr&rft.aufirst=Matt&rft.au=Humphreys%2C+Greg&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShirleyMorley2003" class="citation book cs1"><a href="/wiki/Peter_Shirley" title="Peter Shirley">Shirley, Peter</a>; Morley, R. Keith (2003). Realistic ray tracing (2 ed.). Natick, Mass.: AK Peters. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-56881-198-7" title="Special:BookSources/978-1-56881-198-7"><bdi>978-1-56881-198-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Realistic+ray+tracing&rft.place=Natick%2C+Mass.&rft.edition=2&rft.pub=AK+Peters&rft.date=2003&rft.isbn=978-1-56881-198-7&rft.aulast=Shirley&rft.aufirst=Peter&rft.au=Morley%2C+R.+Keith&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStrothotteSchlechtweg2002" class="citation book cs1">Strothotte, Thomas; Schlechtweg, Stefan (2002). Non-photorealistic computer graphics modeling, rendering, and animation (2 ed.). San Francisco, CA: Morgan Kaufmann. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-55860-787-3" title="Special:BookSources/978-1-55860-787-3"><bdi>978-1-55860-787-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Non-photorealistic+computer+graphics+modeling%2C+rendering%2C+and+animation&rft.place=San+Francisco%2C+CA&rft.edition=2&rft.pub=Morgan+Kaufmann&rft.date=2002&rft.isbn=978-1-55860-787-3&rft.aulast=Strothotte&rft.aufirst=Thomas&rft.au=Schlechtweg%2C+Stefan&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWard1994" class="citation book cs1">Ward, Gregory J. (July 1994). <a rel="nofollow" class="external text" href="http://radsite.lbl.gov/radiance/papers/sg94.1/">"The RADIANCE lighting simulation and rendering system"</a>. Proceedings of the 21st annual conference on Computer graphics and interactive techniques - SIGGRAPH '94. pp. 459–72. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F192161.192286">10.1145/192161.192286</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0897916670" title="Special:BookSources/0897916670"><bdi>0897916670</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:2487835">2487835</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+RADIANCE+lighting+simulation+and+rendering+system&rft.btitle=Proceedings+of+the+21st+annual+conference+on+Computer+graphics+and+interactive+techniques+-+SIGGRAPH+%2794&rft.pages=459-72&rft.date=1994-07&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A2487835%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1145%2F192161.192286&rft.isbn=0897916670&rft.aulast=Ward&rft.aufirst=Gregory+J.&rft_id=http%3A%2F%2Fradsite.lbl.gov%2Fradiance%2Fpapers%2Fsg94.1%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARendering+%28computer+graphics%29" class="Z3988"></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2>[<a href="/w/index.php?title=Rendering_(computer_graphics)&action=edit&section=29" title="Edit section: External links">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 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information</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Fields</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biological_data_visualization" title="Biological data visualization">Biological data visualization</a></li> <li><a href="/wiki/Chemical_imaging" title="Chemical imaging">Chemical imaging</a></li> <li><a href="/wiki/Crime_mapping" title="Crime mapping">Crime mapping</a></li> <li><a href="/wiki/Data_visualization" class="mw-redirect" title="Data visualization">Data visualization</a></li> <li><a href="/wiki/Visualization_(graphics)" title="Visualization (graphics)">Educational visualization</a></li> <li><a href="/wiki/Flow_visualization" title="Flow visualization">Flow visualization</a></li> <li><a href="/wiki/Geovisualization" title="Geovisualization">Geovisualization</a></li> <li><a href="/wiki/Information_visualization" class="mw-redirect" title="Information visualization">Information visualization</a></li> <li><a href="/wiki/Mathematical_diagram" title="Mathematical diagram">Mathematical visualization</a></li> <li><a href="/wiki/Medical_imaging" title="Medical imaging">Medical imaging</a></li> <li><a href="/wiki/Molecular_graphics" title="Molecular graphics">Molecular graphics</a></li> <li><a href="/wiki/Visualization_(graphics)" title="Visualization (graphics)">Product visualization</a></li> <li><a href="/wiki/Scientific_visualization" title="Scientific visualization">Scientific visualization</a></li> <li><a href="/wiki/Social_visualization" title="Social visualization">Social visualization</a></li> <li><a href="/wiki/Software_visualization" title="Software visualization">Software visualization</a></li> <li><a href="/wiki/Technical_drawing" title="Technical drawing">Technical drawing</a></li> <li><a href="/wiki/User_interface_design" title="User interface design">User interface design</a></li> <li><a href="/wiki/Visual_culture" title="Visual culture">Visual culture</a></li> <li><a href="/wiki/Volume_rendering" title="Volume rendering">Volume visualization</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Image types</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chart" title="Chart">Chart</a></li> <li><a href="/wiki/Diagram" title="Diagram">Diagram</a></li> <li><a href="/wiki/Engineering_drawing" title="Engineering drawing">Engineering drawing</a></li> <li><a href="/wiki/Graph_of_a_function" title="Graph of a function">Graph of a function</a></li> <li><a href="/wiki/Ideogram" title="Ideogram">Ideogram</a></li> <li><a href="/wiki/Map" title="Map">Map</a></li> <li><a href="/wiki/Photograph" title="Photograph">Photograph</a></li> <li><a href="/wiki/Pictogram" title="Pictogram">Pictogram</a></li> <li><a href="/wiki/Plot_(graphics)" title="Plot (graphics)">Plot</a></li> <li><a href="/wiki/Sankey_diagram" title="Sankey diagram">Sankey diagram</a></li> <li><a href="/wiki/Schematic" title="Schematic">Schematic</a></li> <li><a href="/wiki/Skeletal_formula" title="Skeletal formula">Skeletal formula</a></li> <li><a href="/wiki/Statistical_graphics" title="Statistical graphics">Statistical graphics</a></li> <li><a href="/wiki/Table_(information)" title="Table (information)">Table</a></li> <li><a href="/wiki/Technical_drawing" title="Technical drawing">Technical drawings</a></li> <li><a href="/wiki/Technical_illustration" title="Technical illustration">Technical illustration</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Pre-19th century</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Edmond_Halley" title="Edmond Halley">Edmond Halley</a></li> <li><a href="/wiki/Charles-Ren%C3%A9_de_Fourcroy" title="Charles-René de Fourcroy">Charles-René de Fourcroy</a></li> <li><a href="/wiki/Joseph_Priestley" title="Joseph Priestley">Joseph Priestley</a></li> <li><a href="/wiki/Gaspard_Monge" title="Gaspard Monge">Gaspard Monge</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">19th century</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Charles_Dupin" title="Charles Dupin">Charles Dupin</a></li> <li><a href="/wiki/Adolphe_Quetelet" title="Adolphe Quetelet">Adolphe Quetelet</a></li> <li><a href="/wiki/Andr%C3%A9-Michel_Guerry" title="André-Michel Guerry">André-Michel Guerry</a></li> <li><a href="/wiki/William_Playfair" title="William Playfair">William Playfair</a></li> <li><a href="/wiki/August_Kekul%C3%A9" title="August Kekulé">August Kekulé</a></li> <li><a href="/wiki/Charles_Joseph_Minard" title="Charles Joseph Minard">Charles Joseph Minard</a></li> <li><a href="/w/index.php?title=Luigi_Perozzo&action=edit&redlink=1" class="new" title="Luigi Perozzo (page does not exist)">Luigi Perozzo</a></li> <li><a href="/wiki/Francis_Amasa_Walker" title="Francis Amasa Walker">Francis Amasa Walker</a></li> <li><a href="/wiki/John_Venn" title="John Venn">John Venn</a></li> <li><a href="/wiki/Oliver_Byrne_(mathematician)" title="Oliver Byrne (mathematician)">Oliver Byrne</a></li> <li><a href="/wiki/Matthew_Henry_Phineas_Riall_Sankey" title="Matthew Henry Phineas Riall Sankey">Matthew Sankey</a></li> <li><a href="/wiki/Charles_Booth_(social_reformer)" title="Charles Booth (social reformer)">Charles Booth</a></li> <li><a href="/w/index.php?title=Georg_von_Mayr&action=edit&redlink=1" class="new" title="Georg von Mayr (page does not exist)">Georg von Mayr</a></li> <li><a href="/wiki/John_Snow" title="John Snow">John Snow</a></li> <li><a href="/wiki/Florence_Nightingale" title="Florence Nightingale">Florence Nightingale</a></li> <li><a href="/wiki/Karl_Wilhelm_Pohlke" title="Karl Wilhelm Pohlke">Karl Wilhelm Pohlke</a></li> <li><a href="/wiki/Toussaint_Loua" title="Toussaint Loua">Toussaint Loua</a></li> <li><a href="/wiki/Francis_Galton" title="Francis Galton">Francis Galton</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Early 20th century</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Edward_Walter_Maunder" title="Edward Walter Maunder">Edward Walter Maunder</a></li> <li><a href="/wiki/Otto_Neurath" title="Otto Neurath">Otto Neurath</a></li> <li><a href="/wiki/W._E._B._Du_Bois" title="W. E. B. Du Bois">W. E. B. Du Bois</a></li> <li><a href="/wiki/Henry_Gantt" title="Henry Gantt">Henry Gantt</a></li> <li><a href="/wiki/Arthur_Lyon_Bowley" title="Arthur Lyon Bowley">Arthur Lyon Bowley</a></li> <li><a href="/wiki/Howard_G._Funkhouser" title="Howard G. Funkhouser">Howard G. Funkhouser</a></li> <li><a href="/wiki/John_B._Peddle" title="John B. Peddle">John B. Peddle</a></li> <li><a href="/wiki/Ejnar_Hertzsprung" title="Ejnar Hertzsprung">Ejnar Hertzsprung</a></li> <li><a href="/wiki/Henry_Norris_Russell" title="Henry Norris Russell">Henry Norris Russell</a></li> <li><a href="/wiki/Max_O._Lorenz" title="Max O. Lorenz">Max O. Lorenz</a></li> <li><a href="/wiki/Fritz_Kahn" title="Fritz Kahn">Fritz Kahn</a></li> <li><a href="/wiki/Harry_Beck" title="Harry Beck">Harry Beck</a></li> <li><a href="/wiki/Erwin_Raisz" title="Erwin Raisz">Erwin Raisz</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mid 20th century</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Jacques_Bertin" title="Jacques Bertin">Jacques Bertin</a></li> <li><a href="/wiki/Rudolf_Modley" title="Rudolf Modley">Rudolf Modley</a></li> <li><a href="/wiki/Arthur_H._Robinson" title="Arthur H. Robinson">Arthur H. Robinson</a></li> <li><a href="/wiki/John_Tukey" title="John Tukey">John Tukey</a></li> <li><a href="/wiki/Mary_Eleanor_Spear" title="Mary Eleanor Spear">Mary Eleanor Spear</a></li> <li><a href="/wiki/Edgar_Anderson" title="Edgar Anderson">Edgar Anderson</a></li> <li><a href="/wiki/Howard_T._Fisher" title="Howard T. Fisher">Howard T. Fisher</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Late 20th century</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Borden_Dent" title="Borden Dent">Borden Dent</a></li> <li><a href="/wiki/Nigel_Holmes" title="Nigel Holmes">Nigel Holmes</a></li> <li><a href="/wiki/William_S._Cleveland" title="William S. Cleveland">William S. Cleveland</a></li> <li><a href="/wiki/George_G._Robertson" title="George G. Robertson">George G. Robertson</a></li> <li><a href="/wiki/Bruce_H._McCormick" title="Bruce H. McCormick">Bruce H. McCormick</a></li> <li><a href="/wiki/Catherine_Plaisant" title="Catherine Plaisant">Catherine Plaisant</a></li> <li><a href="/wiki/Stuart_Card" title="Stuart Card">Stuart Card</a></li> <li><a href="/wiki/Pat_Hanrahan" title="Pat Hanrahan">Pat Hanrahan</a></li> <li><a href="/wiki/Edward_Tufte" title="Edward Tufte">Edward Tufte</a></li> <li><a href="/wiki/Ben_Shneiderman" title="Ben Shneiderman">Ben Shneiderman</a></li> <li><a href="/wiki/Michael_Friendly" title="Michael Friendly">Michael Friendly</a></li> <li><a href="/wiki/Howard_Wainer" title="Howard Wainer">Howard Wainer</a></li> <li><a href="/wiki/Clifford_A._Pickover" title="Clifford A. Pickover">Clifford A. Pickover</a></li> <li><a href="/wiki/Lawrence_J._Rosenblum" title="Lawrence J. Rosenblum">Lawrence J. Rosenblum</a></li> <li><a href="/wiki/Thomas_A._DeFanti" title="Thomas A. DeFanti">Thomas A. DeFanti</a></li> <li><a href="/wiki/George_Furnas" title="George Furnas">George Furnas</a></li> <li><a href="/wiki/Sheelagh_Carpendale" title="Sheelagh Carpendale">Sheelagh Carpendale</a></li> <li><a href="/wiki/Cynthia_Brewer" title="Cynthia Brewer">Cynthia Brewer</a></li> <li><a href="/wiki/Jock_D._Mackinlay" title="Jock D. Mackinlay">Jock D. Mackinlay</a></li> <li><a href="/wiki/Alan_MacEachren" title="Alan MacEachren">Alan MacEachren</a></li> <li><a href="/wiki/David_Goodsell" title="David Goodsell">David Goodsell</a></li> <li><a href="/wiki/Kwan-Liu_Ma" title="Kwan-Liu Ma">Kwan-Liu Ma</a></li> <li><a href="/wiki/Michael_Maltz" class="mw-redirect" title="Michael Maltz">Michael Maltz</a></li> <li><a href="/wiki/Leland_Wilkinson" title="Leland Wilkinson">Leland Wilkinson</a></li> <li><a href="/wiki/Alfred_Inselberg" title="Alfred Inselberg">Alfred Inselberg</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Early 21st century</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Polo_Chau&action=edit&redlink=1" class="new" title="Polo Chau (page does not exist)">Polo Chau</a></li> <li><a href="/wiki/Ben_Fry" title="Ben Fry">Ben Fry</a></li> <li><a href="/wiki/Jeffrey_Heer" title="Jeffrey Heer">Jeffrey Heer</a></li> <li><a href="/wiki/Jessica_Hullman" title="Jessica Hullman">Jessica Hullman</a></li> <li><a href="/wiki/Gordon_Kindlmann" title="Gordon Kindlmann">Gordon Kindlmann</a></li> <li><a href="/wiki/Aaron_Koblin" title="Aaron Koblin">Aaron Koblin</a></li> <li><a href="/w/index.php?title=Martin_Krzywinski&action=edit&redlink=1" class="new" title="Martin Krzywinski (page does not exist)">Martin Krzywinski</a></li> <li><a href="/wiki/Christopher_R._Johnson" title="Christopher R. Johnson">Christopher R. Johnson</a></li> <li><a href="/wiki/Manuel_Lima" title="Manuel Lima">Manuel Lima</a></li> <li><a href="/wiki/David_McCandless" title="David McCandless">David McCandless</a></li> <li><a href="/wiki/Mauro_Martino" title="Mauro Martino">Mauro Martino</a></li> <li><a href="/wiki/John_Maeda" title="John Maeda">John Maeda</a></li> <li><a href="/wiki/Miriah_Meyer" title="Miriah Meyer">Miriah Meyer</a></li> <li><a href="/wiki/Tamara_Munzner" title="Tamara Munzner">Tamara Munzner</a></li> <li><a href="/wiki/Ade_Olufeko" class="mw-redirect" title="Ade Olufeko">Ade Olufeko</a></li> <li><a href="/wiki/Hanspeter_Pfister" title="Hanspeter Pfister">Hanspeter Pfister</a></li> <li><a href="/wiki/Hans_Rosling" title="Hans Rosling">Hans Rosling</a></li> <li><a href="/wiki/Claudio_Silva_(computer_scientist)" title="Claudio Silva (computer scientist)">Claudio Silva</a></li> <li><a href="/wiki/Moritz_Stefaner" title="Moritz Stefaner">Moritz Stefaner</a></li> <li><a href="/wiki/Fernanda_Vi%C3%A9gas" title="Fernanda Viégas">Fernanda Viégas</a></li> <li><a href="/wiki/Martin_M._Wattenberg" title="Martin M. Wattenberg">Martin Wattenberg</a></li> <li><a href="/wiki/Bang_Wong" title="Bang Wong">Bang Wong</a></li> <li><a href="/wiki/Hadley_Wickham" title="Hadley Wickham">Hadley Wickham</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cartography" title="Cartography">Cartography</a></li> <li><a href="/wiki/Chartjunk" title="Chartjunk">Chartjunk</a></li> <li><a href="/wiki/Color_coding_in_data_visualization" class="mw-redirect" title="Color coding in data visualization">Color coding</a></li> <li><a href="/wiki/Computer_graphics" title="Computer graphics">Computer graphics</a> <ul><li><a href="/wiki/Computer_graphics_(computer_science)" title="Computer graphics (computer science)">in computer science</a></li></ul></li> <li><a href="/wiki/CPK_coloring" title="CPK coloring">CPK coloring</a></li> <li><a href="/wiki/Graph_drawing" title="Graph drawing">Graph drawing</a></li> <li><a href="/wiki/Graphic_design" title="Graphic design">Graphic design</a></li> <li><a href="/wiki/Graphic_organizer" title="Graphic organizer">Graphic organizer</a></li> <li><a href="/wiki/Imaging_science" class="mw-redirect" title="Imaging science">Imaging science</a></li> <li><a href="/wiki/Infographic" title="Infographic">Information graphics</a></li> <li><a href="/wiki/Information_science" title="Information science">Information science</a></li> <li><a href="/wiki/Misleading_graph" title="Misleading graph">Misleading graph</a></li> <li><a href="/wiki/Neuroimaging" title="Neuroimaging">Neuroimaging</a></li> <li><a href="/wiki/Patent_drawing" title="Patent drawing">Patent drawing</a></li> <li><a href="/wiki/Scientific_modelling" title="Scientific modelling">Scientific modelling</a></li> <li><a href="/wiki/Spatial_analysis" title="Spatial analysis">Spatial analysis</a></li> <li><a href="/wiki/Visual_analytics" title="Visual analytics">Visual analytics</a></li> <li><a href="/wiki/Visual_perception" title="Visual perception">Visual perception</a></li> <li><a href="/wiki/Volume_cartography" title="Volume cartography">Volume cartography</a></li> <li><a href="/wiki/Volume_rendering" title="Volume rendering">Volume rendering</a></li> <li><a href="/wiki/Information_art" title="Information art">Information art</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Computer_graphics" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Computer_graphics" title="Template:Computer graphics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Computer_graphics" title="Template talk:Computer graphics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Computer_graphics" title="Special:EditPage/Template:Computer graphics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Computer_graphics" style="font-size:114%;margin:0 4em"><a href="/wiki/Computer_graphics_(computer_science)" title="Computer graphics (computer science)">Computer graphics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Vector_graphics" title="Vector graphics">Vector graphics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Diffusion_curve" title="Diffusion curve">Diffusion curve</a></li> <li><a href="/wiki/Pixel" title="Pixel">Pixel</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/2D_computer_graphics" title="2D computer graphics">2D graphics</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alpha_compositing" title="Alpha compositing">Alpha compositing</a></li> <li><a href="/wiki/Layers_(digital_image_editing)" title="Layers (digital image editing)">Layers</a></li> <li><a href="/wiki/Text-to-image_model" title="Text-to-image model">Text-to-image</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="2.5D" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/2.5D" title="2.5D">2.5D</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Isometric_video_game_graphics" title="Isometric video game graphics">Isometric graphics</a></li> <li><a href="/wiki/Mode_7" title="Mode 7">Mode 7</a></li> <li><a href="/wiki/Parallax_scrolling" title="Parallax scrolling">Parallax scrolling</a></li> <li><a href="/wiki/Ray_casting" title="Ray casting">Ray casting</a></li> <li><a href="/wiki/Skybox_(video_games)" title="Skybox (video games)">Skybox</a></li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/3D_computer_graphics" title="3D computer graphics">3D graphics</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/3D_projection" title="3D projection">3D projection</a></li> <li><a href="/wiki/3D_rendering" title="3D rendering">3D rendering</a></li> <li>(<a href="/wiki/Image-based_modeling_and_rendering" title="Image-based modeling and rendering">Image-based</a></li> <li><a href="/wiki/Spectral_rendering" title="Spectral rendering">Spectral</a></li> <li><a href="/wiki/Unbiased_rendering" title="Unbiased rendering">Unbiased</a>)</li> <li><a href="/wiki/Aliasing" title="Aliasing">Aliasing</a></li> <li><a href="/wiki/Anisotropic_filtering" title="Anisotropic filtering">Anisotropic filtering</a></li> <li><a href="/wiki/Cel_shading" title="Cel shading">Cel shading</a></li> <li><a href="/wiki/Fluid_animation" title="Fluid animation">Fluid animation</a></li> <li><a href="/wiki/Computer_graphics_lighting" title="Computer graphics lighting">Lighting</a> <ul><li><a href="/wiki/Global_illumination" title="Global illumination">Global illumination</a></li></ul></li> <li><a href="/wiki/Hidden-surface_determination" title="Hidden-surface determination">Hidden-surface determination</a></li> <li><a href="/wiki/Polygon_mesh" title="Polygon mesh">Polygon mesh</a></li> <li>(<a href="/wiki/Triangle_mesh" title="Triangle mesh">Triangle mesh</a>)</li> <li><a href="/wiki/Shading" title="Shading">Shading</a> <ul><li><a href="/wiki/Deferred_shading" title="Deferred shading">Deferred</a></li></ul></li> <li><a href="/wiki/Surface_triangulation" title="Surface triangulation">Surface triangulation</a></li> <li><a href="/wiki/Wire-frame_model" title="Wire-frame model">Wire-frame model</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Affine_transformation" title="Affine transformation">Affine transformation</a></li> <li><a href="/wiki/Back-face_culling" title="Back-face culling">Back-face culling</a></li> <li><a href="/wiki/Clipping_(computer_graphics)" title="Clipping (computer graphics)">Clipping</a></li> <li><a href="/wiki/Collision_detection" title="Collision detection">Collision detection</a></li> <li><a href="/wiki/Planar_projection" title="Planar projection">Planar projection</a></li> <li><a href="/wiki/Reflection_(computer_graphics)" title="Reflection (computer graphics)">Reflection</a></li> <li><a class="mw-selflink selflink">Rendering</a> <ul><li><a href="/wiki/Beam_tracing" title="Beam tracing">Beam tracing</a></li> <li><a href="/wiki/Cone_tracing" title="Cone tracing">Cone tracing</a></li> <li><a href="/wiki/Checkerboard_rendering" title="Checkerboard rendering">Checkerboard rendering</a></li> <li><a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">Ray tracing</a></li> <li><a href="/wiki/Path_tracing" title="Path tracing">Path tracing</a></li> <li><a href="/wiki/Ray_casting" title="Ray casting">Ray casting</a></li> <li><a href="/wiki/Scanline_rendering" title="Scanline rendering">Scanline rendering</a></li></ul></li> <li><a href="/wiki/Rotation_(mathematics)" title="Rotation (mathematics)">Rotation</a></li> <li><a href="/wiki/Scaling_(geometry)" title="Scaling (geometry)">Scaling</a></li> <li><a href="/wiki/Shadow_mapping" title="Shadow mapping">Shadow mapping</a></li> <li><a href="/wiki/Shadow_volume" title="Shadow volume">Shadow volume</a></li> <li><a href="/wiki/Shear_matrix" class="mw-redirect" title="Shear matrix">Shear matrix</a></li> <li><a href="/wiki/Shader" title="Shader">Shader</a></li> <li><a href="/wiki/Texel_(graphics)" title="Texel (graphics)">Texel</a></li> <li><a href="/wiki/Translation_(geometry)" title="Translation (geometry)">Translation</a></li> <li><a href="/wiki/Volume_rendering" title="Volume rendering">Volume rendering</a></li> <li><a href="/wiki/Voxel" title="Voxel">Voxel</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Graphics_software" title="Graphics software">Graphics software</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_3D_computer_graphics_software" title="List of 3D computer graphics software">3D computer graphics software</a> <ul><li><a href="/wiki/List_of_3D_animation_software" title="List of 3D animation software">animation</a></li> <li><a href="/wiki/List_of_3D_modeling_software" title="List of 3D modeling software">modeling</a></li> <li><a href="/wiki/List_of_3D_rendering_software" title="List of 3D rendering software">rendering</a></li></ul></li> <li><a href="/wiki/Raster_graphics_editor" title="Raster graphics editor">Raster graphics editors</a></li> <li><a href="/wiki/Comparison_of_vector_graphics_editors" title="Comparison of vector graphics editors">Vector graphics editors</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Algorithms</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_computer_graphics_algorithms" class="mw-redirect" title="List of computer graphics algorithms">List of computer graphics algorithms</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Computer_science" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Computer_science" title="Template:Computer science"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Computer_science" title="Template talk:Computer science"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Computer_science" title="Special:EditPage/Template:Computer science"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Computer_science" style="font-size:114%;margin:0 4em"><a href="/wiki/Computer_science" title="Computer science">Computer science</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div>Note: This template roughly follows the 2012 <a href="/wiki/ACM_Computing_Classification_System" title="ACM Computing Classification System">ACM Computing Classification System</a>.</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computer_hardware" title="Computer hardware">Hardware</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Printed_circuit_board" title="Printed circuit board">Printed circuit board</a></li> <li><a href="/wiki/Peripheral" title="Peripheral">Peripheral</a></li> <li><a href="/wiki/Integrated_circuit" title="Integrated circuit">Integrated circuit</a></li> <li><a href="/wiki/Very_Large_Scale_Integration" class="mw-redirect" title="Very Large Scale Integration">Very Large Scale Integration</a></li> <li><a href="/wiki/System_on_a_chip" title="System on a chip">Systems on Chip (SoCs)</a></li> <li><a href="/wiki/Green_computing" title="Green computing">Energy consumption (Green computing)</a></li> <li><a href="/wiki/Electronic_design_automation" title="Electronic design automation">Electronic design automation</a></li> <li><a href="/wiki/Hardware_acceleration" title="Hardware acceleration">Hardware acceleration</a></li> <li><a href="/wiki/Processor_(computing)" title="Processor (computing)">Processor</a></li> <li><a href="/wiki/List_of_computer_size_categories" title="List of computer size categories">Size</a> / <a href="/wiki/Form_factor_(design)" title="Form factor (design)">Form</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Computer systems organization</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Computer_architecture" title="Computer architecture">Computer architecture</a></li> <li><a href="/wiki/Computational_complexity" title="Computational complexity">Computational complexity</a></li> <li><a href="/wiki/Dependability" title="Dependability">Dependability</a></li> <li><a href="/wiki/Embedded_system" title="Embedded system">Embedded system</a></li> <li><a href="/wiki/Real-time_computing" title="Real-time computing">Real-time computing</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computer_network" title="Computer network">Networks</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Network_architecture" title="Network architecture">Network architecture</a></li> <li><a href="/wiki/Network_protocol" class="mw-redirect" title="Network protocol">Network protocol</a></li> <li><a href="/wiki/Networking_hardware" title="Networking hardware">Network components</a></li> <li><a href="/wiki/Network_scheduler" title="Network scheduler">Network scheduler</a></li> <li><a href="/wiki/Network_performance" title="Network performance">Network performance evaluation</a></li> <li><a href="/wiki/Network_service" title="Network service">Network service</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Software organization</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Interpreter_(computing)" title="Interpreter (computing)">Interpreter</a></li> <li><a href="/wiki/Middleware" title="Middleware">Middleware</a></li> <li><a href="/wiki/Virtual_machine" title="Virtual machine">Virtual machine</a></li> <li><a href="/wiki/Operating_system" title="Operating system">Operating system</a></li> <li><a href="/wiki/Software_quality" title="Software quality">Software quality</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Programming_language_theory" title="Programming language theory">Software notations</a> and <a href="/wiki/Programming_tool" title="Programming tool">tools</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Programming_paradigm" title="Programming paradigm">Programming paradigm</a></li> <li><a href="/wiki/Programming_language" title="Programming language">Programming language</a></li> <li><a href="/wiki/Compiler_construction" class="mw-redirect" title="Compiler construction">Compiler</a></li> <li><a href="/wiki/Domain-specific_language" title="Domain-specific language">Domain-specific language</a></li> <li><a href="/wiki/Modeling_language" title="Modeling language">Modeling language</a></li> <li><a href="/wiki/Software_framework" title="Software framework">Software framework</a></li> <li><a href="/wiki/Integrated_development_environment" title="Integrated development environment">Integrated development environment</a></li> <li><a href="/wiki/Software_configuration_management" title="Software configuration management">Software configuration management</a></li> <li><a href="/wiki/Library_(computing)" title="Library (computing)">Software library</a></li> <li><a href="/wiki/Software_repository" title="Software repository">Software repository</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Software_development" title="Software development">Software development</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Control_variable_(programming)" class="mw-redirect" title="Control variable (programming)">Control variable</a></li> <li><a href="/wiki/Software_development_process" title="Software development process">Software development process</a></li> <li><a href="/wiki/Requirements_analysis" title="Requirements analysis">Requirements analysis</a></li> <li><a href="/wiki/Software_design" title="Software design">Software design</a></li> <li><a href="/wiki/Software_construction" title="Software construction">Software construction</a></li> <li><a href="/wiki/Software_deployment" title="Software deployment">Software deployment</a></li> <li><a href="/wiki/Software_engineering" title="Software engineering">Software engineering</a></li> <li><a href="/wiki/Software_maintenance" title="Software maintenance">Software maintenance</a></li> <li><a href="/wiki/Programming_team" title="Programming team">Programming team</a></li> <li><a href="/wiki/Open-source_software" title="Open-source software">Open-source model</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Theory_of_computation" title="Theory of computation">Theory of computation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Model_of_computation" title="Model of computation">Model of computation</a> <ul><li><a href="/wiki/Stochastic_computing" title="Stochastic computing">Stochastic</a></li></ul></li> <li><a href="/wiki/Formal_language" title="Formal language">Formal language</a></li> <li><a href="/wiki/Automata_theory" title="Automata theory">Automata theory</a></li> <li><a href="/wiki/Computability_theory" title="Computability theory">Computability theory</a></li> <li><a href="/wiki/Computational_complexity_theory" title="Computational complexity theory">Computational complexity theory</a></li> <li><a href="/wiki/Logic_in_computer_science" title="Logic in computer science">Logic</a></li> <li><a href="/wiki/Semantics_(computer_science)" title="Semantics (computer science)">Semantics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Algorithm" title="Algorithm">Algorithms</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algorithm_design" class="mw-redirect" title="Algorithm design">Algorithm design</a></li> <li><a href="/wiki/Analysis_of_algorithms" title="Analysis of algorithms">Analysis of algorithms</a></li> <li><a href="/wiki/Algorithmic_efficiency" title="Algorithmic efficiency">Algorithmic efficiency</a></li> <li><a href="/wiki/Randomized_algorithm" title="Randomized algorithm">Randomized algorithm</a></li> <li><a href="/wiki/Computational_geometry" title="Computational geometry">Computational geometry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mathematics of <a href="/wiki/Computing" title="Computing">computing</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Discrete_mathematics" title="Discrete mathematics">Discrete mathematics</a></li> <li><a href="/wiki/Probability" title="Probability">Probability</a></li> <li><a href="/wiki/Statistics" title="Statistics">Statistics</a></li> <li><a href="/wiki/Mathematical_software" title="Mathematical 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title="Enterprise information system">Enterprise information system</a></li> <li><a href="/wiki/Social_software" title="Social software">Social information systems</a></li> <li><a href="/wiki/Geographic_information_system" title="Geographic information system">Geographic information system</a></li> <li><a href="/wiki/Decision_support_system" title="Decision support system">Decision support system</a></li> <li><a href="/wiki/Process_control" class="mw-redirect" title="Process control">Process control system</a></li> <li><a href="/wiki/Multimedia_database" title="Multimedia database">Multimedia information system</a></li> <li><a href="/wiki/Data_mining" title="Data mining">Data mining</a></li> <li><a href="/wiki/Digital_library" title="Digital library">Digital library</a></li> <li><a href="/wiki/Computing_platform" title="Computing platform">Computing platform</a></li> <li><a href="/wiki/Digital_marketing" title="Digital marketing">Digital marketing</a></li> <li><a href="/wiki/World_Wide_Web" title="World Wide Web">World Wide Web</a></li> <li><a href="/wiki/Information_retrieval" title="Information retrieval">Information retrieval</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computer_security" title="Computer security">Security</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cryptography" title="Cryptography">Cryptography</a></li> <li><a href="/wiki/Formal_methods" title="Formal methods">Formal methods</a></li> <li><a href="/wiki/Security_hacker" title="Security hacker">Security hacker</a></li> <li><a href="/wiki/Security_service_(telecommunication)" title="Security service (telecommunication)">Security services</a></li> <li><a href="/wiki/Intrusion_detection_system" title="Intrusion detection system">Intrusion detection system</a></li> <li><a href="/wiki/Hardware_security" title="Hardware security">Hardware security</a></li> <li><a href="/wiki/Network_security" title="Network security">Network security</a></li> <li><a href="/wiki/Information_security" title="Information security">Information security</a></li> <li><a href="/wiki/Application_security" title="Application security">Application security</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Human%E2%80%93computer_interaction" title="Human–computer interaction">Human–computer interaction</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Interaction_design" title="Interaction design">Interaction design</a></li> <li><a href="/wiki/Social_computing" title="Social computing">Social computing</a></li> <li><a href="/wiki/Ubiquitous_computing" title="Ubiquitous computing">Ubiquitous computing</a></li> <li><a href="/wiki/Visualization_(graphics)" title="Visualization 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class="navbox-group" style="width:1%"><a href="/wiki/Artificial_intelligence" title="Artificial intelligence">Artificial intelligence</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Natural_language_processing" title="Natural language processing">Natural language processing</a></li> <li><a href="/wiki/Knowledge_representation_and_reasoning" title="Knowledge representation and reasoning">Knowledge representation and reasoning</a></li> <li><a href="/wiki/Computer_vision" title="Computer vision">Computer vision</a></li> <li><a href="/wiki/Automated_planning_and_scheduling" title="Automated planning and scheduling">Automated planning and scheduling</a></li> <li><a href="/wiki/Mathematical_optimization" title="Mathematical optimization">Search methodology</a></li> <li><a href="/wiki/Control_theory" title="Control theory">Control method</a></li> <li><a href="/wiki/Philosophy_of_artificial_intelligence" title="Philosophy of artificial intelligence">Philosophy of artificial intelligence</a></li> <li><a href="/wiki/Distributed_artificial_intelligence" title="Distributed artificial intelligence">Distributed artificial intelligence</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Machine_learning" title="Machine learning">Machine learning</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Supervised_learning" title="Supervised learning">Supervised learning</a></li> <li><a href="/wiki/Unsupervised_learning" title="Unsupervised learning">Unsupervised learning</a></li> <li><a href="/wiki/Reinforcement_learning" title="Reinforcement learning">Reinforcement learning</a></li> <li><a href="/wiki/Multi-task_learning" title="Multi-task learning">Multi-task learning</a></li> <li><a href="/wiki/Cross-validation_(statistics)" title="Cross-validation (statistics)">Cross-validation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computer_graphics" title="Computer graphics">Graphics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Computer_animation" title="Computer animation">Animation</a></li> <li><a class="mw-selflink selflink">Rendering</a></li> <li><a href="/wiki/Photograph_manipulation" title="Photograph manipulation">Photograph manipulation</a></li> <li><a href="/wiki/Graphics_processing_unit" title="Graphics processing unit">Graphics processing unit</a></li> <li><a href="/wiki/Mixed_reality" title="Mixed reality">Mixed reality</a></li> <li><a href="/wiki/Virtual_reality" title="Virtual reality">Virtual reality</a></li> <li><a href="/wiki/Image_compression" title="Image compression">Image compression</a></li> <li><a href="/wiki/Solid_modeling" title="Solid modeling">Solid modeling</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Applied computing</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_Computing" class="mw-redirect" title="Quantum Computing">Quantum Computing</a></li> <li><a href="/wiki/E-commerce" title="E-commerce">E-commerce</a></li> <li><a href="/wiki/Enterprise_software" title="Enterprise software">Enterprise software</a></li> <li><a href="/wiki/Computational_mathematics" title="Computational mathematics">Computational mathematics</a></li> <li><a href="/wiki/Computational_physics" title="Computational physics">Computational physics</a></li> <li><a href="/wiki/Computational_chemistry" title="Computational chemistry">Computational chemistry</a></li> <li><a href="/wiki/Computational_biology" title="Computational 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