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class="vector-toc-numb">2</span> <span>Direct volume rendering</span> </div> </a> <button aria-controls="toc-Direct_volume_rendering-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Direct volume rendering subsection</span> </button> <ul id="toc-Direct_volume_rendering-sublist" class="vector-toc-list"> <li id="toc-Volume_ray_casting" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Volume_ray_casting"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Volume ray casting</span> </div> </a> <ul id="toc-Volume_ray_casting-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Splatting" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Splatting"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Splatting</span> </div> </a> <ul id="toc-Splatting-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Shear_warp" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Shear_warp"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Shear warp</span> </div> </a> <ul id="toc-Shear_warp-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Texture-based_volume_rendering" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Texture-based_volume_rendering"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Texture-based volume rendering</span> </div> </a> <ul id="toc-Texture-based_volume_rendering-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Hardware-accelerated_volume_rendering" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Hardware-accelerated_volume_rendering"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Hardware-accelerated volume rendering</span> </div> </a> <ul id="toc-Hardware-accelerated_volume_rendering-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Optimization_techniques" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Optimization_techniques"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Optimization techniques</span> </div> </a> <button aria-controls="toc-Optimization_techniques-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Optimization techniques subsection</span> </button> <ul id="toc-Optimization_techniques-sublist" class="vector-toc-list"> <li id="toc-Empty_space_skipping" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Empty_space_skipping"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Empty space skipping</span> </div> </a> <ul id="toc-Empty_space_skipping-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Early_ray_termination" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Early_ray_termination"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Early ray termination</span> </div> </a> <ul id="toc-Early_ray_termination-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Octree_and_BSP_space_subdivision" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Octree_and_BSP_space_subdivision"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Octree and BSP space subdivision</span> </div> </a> <ul id="toc-Octree_and_BSP_space_subdivision-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Volume_segmentation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Volume_segmentation"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Volume segmentation</span> </div> </a> <ul id="toc-Volume_segmentation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Multiple_and_adaptive_resolution_representation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Multiple_and_adaptive_resolution_representation"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Multiple and adaptive resolution representation</span> </div> </a> <ul id="toc-Multiple_and_adaptive_resolution_representation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pre-integrated_volume_rendering" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pre-integrated_volume_rendering"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Pre-integrated volume rendering</span> </div> </a> <ul id="toc-Pre-integrated_volume_rendering-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Image-based_meshing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Image-based_meshing"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7</span> <span>Image-based meshing</span> </div> </a> <ul id="toc-Image-based_meshing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Temporal_reuse_of_voxels" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Temporal_reuse_of_voxels"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.8</span> <span>Temporal reuse of voxels</span> </div> </a> <ul id="toc-Temporal_reuse_of_voxels-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-List_of_related_software" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#List_of_related_software"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>List of related software</span> </div> </a> <ul id="toc-List_of_related_software-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </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 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </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 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-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" ><span class="vector-icon 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mw-list-item"><a href="https://de.wikipedia.org/wiki/Volumengrafik" title="Volumengrafik – German" lang="de" hreflang="de" data-title="Volumengrafik" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Volume_rendering" title="Volume rendering – Spanish" lang="es" hreflang="es" data-title="Volume rendering" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></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_%D8%AD%D8%AC%D9%85%DB%8C" title="رندرینگ حجمی – Persian" lang="fa" hreflang="fa" data-title="رندرینگ حجمی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Rendu_volumique_direct" title="Rendu volumique direct – French" lang="fr" hreflang="fr" data-title="Rendu volumique direct" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B3%BC%EB%A5%A8_%EB%A0%8C%EB%8D%94%EB%A7%81" title="볼륨 렌더링 – Korean" lang="ko" hreflang="ko" data-title="볼륨 렌더링" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Rendering_volumetrico" title="Rendering volumetrico – Italian" lang="it" hreflang="it" data-title="Rendering volumetrico" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Tilpuma_render%C4%93%C5%A1ana" title="Tilpuma renderēšana – Latvian" lang="lv" hreflang="lv" data-title="Tilpuma renderēšana" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Volumerendering" title="Volumerendering – Dutch" lang="nl" hreflang="nl" data-title="Volumerendering" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%9C%E3%83%AA%E3%83%A5%E3%83%BC%E3%83%A0%E3%83%AC%E3%83%B3%E3%83%80%E3%83%AA%E3%83%B3%E3%82%B0" title="ボリュームレンダリング – Japanese" lang="ja" hreflang="ja" data-title="ボリュームレンダリング" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9E%D0%B1%D1%8A%D1%91%D0%BC%D0%BD%D1%8B%D0%B9_%D1%80%D0%B5%D0%BD%D0%B4%D0%B5%D1%80%D0%B8%D0%BD%D0%B3" title="Объёмный рендеринг – Russian" lang="ru" hreflang="ru" data-title="Объёмный рендеринг" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Volumetrinen_render%C3%B6inti" title="Volumetrinen renderöinti – Finnish" lang="fi" hreflang="fi" data-title="Volumetrinen renderöinti" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-zh 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.sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar nomobile nowraplinks"><tbody><tr><th class="sidebar-title"><a href="/wiki/3D_computer_graphics" title="3D computer graphics">Three-dimensional (3D)<br />computer graphics</a></th></tr><tr><td class="sidebar-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Activemarker2.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Activemarker2.PNG/220px-Activemarker2.PNG" decoding="async" width="220" height="157" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Activemarker2.PNG/330px-Activemarker2.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/6/6d/Activemarker2.PNG 2x" data-file-width="400" data-file-height="285" /></a></span></td></tr><tr><th class="sidebar-heading"> Fundamentals</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/3D_modeling" title="3D modeling">Modeling</a></li> <li><a href="/wiki/3D_scanning" title="3D scanning">Scanning</a></li> <li><a href="/wiki/3D_rendering" title="3D rendering">Rendering</a></li> <li><a href="/wiki/3D_printing" title="3D printing">Printing</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Primary uses</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/3D_model" class="mw-redirect" title="3D model">3D models</a></li> <li><a href="/wiki/Computer-aided_design" title="Computer-aided design">Computer-aided design</a></li> <li><a href="/wiki/Graphic_design" title="Graphic design">Graphic design</a></li> <li><a href="/wiki/Video_game" title="Video game">Video games</a></li> <li><a href="/wiki/Visual_effects" title="Visual effects">Visual effects</a></li> <li><a href="/wiki/Visualization_(graphic)" class="mw-redirect" title="Visualization (graphic)">Visualization</a></li> <li><a href="/wiki/Virtual_engineering" title="Virtual engineering">Virtual engineering</a></li> <li><a href="/wiki/Virtual_reality" title="Virtual reality">Virtual reality</a></li> <li><a href="/wiki/Virtual_cinematography" title="Virtual cinematography">Virtual cinematography</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Related topics</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Computer-generated_imagery" title="Computer-generated imagery">Computer-generated imagery <span style="font-size:85%;">(CGI)</span></a></li> <li><a href="/wiki/Animation" title="Animation">Animation</a> <ul><li><a href="/wiki/Computer_animation" title="Computer animation">computer</a></li> <li><a href="/wiki/Skeletal_animation" title="Skeletal animation">skeletal</a></li></ul></li> <li><a href="/wiki/3D_display" title="3D display">3D display</a></li> <li><a href="/wiki/Wire-frame_model" title="Wire-frame model">Wire-frame model</a></li> <li><a href="/wiki/Texture_mapping" title="Texture mapping">Texture mapping</a></li> <li><a href="/wiki/Motion_capture" title="Motion capture">Motion capture</a></li> <li><a href="/wiki/Crowd_simulation" title="Crowd simulation">Crowd simulation</a></li> <li><a href="/wiki/Global_illumination" title="Global illumination">Global illumination</a></li> <li><a class="mw-selflink selflink">Volume rendering</a></li></ul></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:3D_computer_graphics" title="Template:3D computer graphics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:3D_computer_graphics" title="Template talk:3D computer graphics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:3D_computer_graphics" title="Special:EditPage/Template:3D computer graphics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Image_of_3D_volumetric_QCT_scan.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Image_of_3D_volumetric_QCT_scan.jpg/220px-Image_of_3D_volumetric_QCT_scan.jpg" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Image_of_3D_volumetric_QCT_scan.jpg/330px-Image_of_3D_volumetric_QCT_scan.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Image_of_3D_volumetric_QCT_scan.jpg/440px-Image_of_3D_volumetric_QCT_scan.jpg 2x" data-file-width="880" data-file-height="880" /></a><figcaption>Multiple <a href="/wiki/CT_scan" title="CT scan">X-ray tomographs</a> (with <a href="/wiki/Quantitative_computed_tomography" title="Quantitative computed tomography">quantitative mineral density calibration</a>) stacked to form a 3D model</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:CTWristImage.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/CTWristImage.png/250px-CTWristImage.png" decoding="async" width="250" height="199" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/CTWristImage.png/375px-CTWristImage.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/06/CTWristImage.png/500px-CTWristImage.png 2x" data-file-width="798" data-file-height="636" /></a><figcaption> Volume rendered <a href="/wiki/Computed_tomography" class="mw-redirect" title="Computed tomography">CT</a> scan of a forearm with different color schemes for muscle, fat, bone, and blood</figcaption></figure> <p>In <a href="/wiki/Scientific_visualization" title="Scientific visualization">scientific visualization</a> and <a href="/wiki/Computer_graphics" title="Computer graphics">computer graphics</a>, <b>volume rendering</b> is a set of techniques used to display a 2D projection of a 3D discretely <a href="/wiki/Sampling_(signal_processing)" title="Sampling (signal processing)">sampled</a> <a href="/wiki/Data_set" title="Data set">data set</a>, typically a 3D <a href="/wiki/Scalar_field" title="Scalar field">scalar field</a>. </p><p>A typical 3D data set is a group of 2D slice images acquired by a <a href="/wiki/Computed_axial_tomography" class="mw-redirect" title="Computed axial tomography">CT</a>, <a href="/wiki/Magnetic_resonance_imaging" title="Magnetic resonance imaging">MRI</a>, or <a href="/wiki/Microtomography" class="mw-redirect" title="Microtomography">MicroCT</a> <a href="/wiki/Image_scanner" title="Image scanner">scanner</a>. Usually these are acquired in a regular pattern (e.g., one slice for each millimeter of depth) and usually have a regular number of image <a href="/wiki/Pixel" title="Pixel">pixels</a> in a regular pattern. This is an example of a regular volumetric grid, with each volume element, or <a href="/wiki/Voxel" title="Voxel">voxel</a> represented by a single value that is obtained by sampling the immediate area surrounding the voxel. </p><p>To render a 2D projection of the 3D data set, one first needs to define a <a href="/wiki/Virtual_camera" class="mw-redirect" title="Virtual camera">camera</a> in space relative to the volume. Also, one needs to define the <a href="/wiki/Opacity_(optics)" class="mw-redirect" title="Opacity (optics)">opacity</a> and color of every voxel. This is usually defined using an <a href="/wiki/RGBA_color_space" class="mw-redirect" title="RGBA color space">RGBA</a> (for red, green, blue, alpha) transfer function that defines the RGBA value for every possible voxel value. </p><p>For example, a volume may be viewed by extracting <a href="/wiki/Isosurface" title="Isosurface">isosurfaces</a> (surfaces of equal values) from the volume and rendering them as <a href="/wiki/Polygon_mesh" title="Polygon mesh">polygonal meshes</a> or by rendering the volume directly as a block of data. The <a href="/wiki/Marching_cubes" title="Marching cubes">marching cubes</a> algorithm is a common technique for extracting an isosurface from volume data. Direct volume rendering is a computationally intensive task that may be performed in several ways. </p><p>Another method of volume rendering is <a href="/wiki/Ray_marching" title="Ray marching">Ray marching</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Scope">Scope</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=1" title="Edit section: Scope"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:CT_presentation_as_thin_slice,_projection_and_volume_rendering.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/CT_presentation_as_thin_slice%2C_projection_and_volume_rendering.jpg/220px-CT_presentation_as_thin_slice%2C_projection_and_volume_rendering.jpg" decoding="async" width="220" height="191" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/CT_presentation_as_thin_slice%2C_projection_and_volume_rendering.jpg/330px-CT_presentation_as_thin_slice%2C_projection_and_volume_rendering.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/CT_presentation_as_thin_slice%2C_projection_and_volume_rendering.jpg/440px-CT_presentation_as_thin_slice%2C_projection_and_volume_rendering.jpg 2x" data-file-width="1190" data-file-height="1035" /></a><figcaption>Types of presentations of <a href="/wiki/CT_scan" title="CT scan">CT scans</a>, with two examples of volume rendering</figcaption></figure> <p>Volume rendering is distinguished from thin slice <a href="/wiki/Tomography" title="Tomography">tomography</a> presentations, and is also generally distinguished from projections of 3D models, including <a href="/wiki/Maximum_intensity_projection" title="Maximum intensity projection">maximum intensity projection</a>.<sup id="cite_ref-FishmanNey2006_1-0" class="reference"><a href="#cite_note-FishmanNey2006-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Still, technically, all volume renderings become projections when viewed on a <a href="/wiki/Display_device#Full-area_2-dimensional_displays" title="Display device">2-dimensional display</a>, making the distinction between projections and volume renderings a bit vague. Nevertheless, the epitomes of volume rendering models feature a mix of for example coloring<sup id="cite_ref-SilversteinParsad2008_2-0" class="reference"><a href="#cite_note-SilversteinParsad2008-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> and shading<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> in order to create realistic and/or observable representations. </p> <div class="mw-heading mw-heading2"><h2 id="Direct_volume_rendering">Direct volume rendering</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=2" title="Edit section: Direct volume rendering"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A direct volume renderer<sup id="cite_ref-_188_4-0" class="reference"><a href="#cite_note-_188-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-dch88_5-0" class="reference"><a href="#cite_note-dch88-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> requires every sample value to be mapped to opacity and a color. This is done with a "<a href="/wiki/Transfer_function" title="Transfer function">transfer function</a>" which can be a simple ramp, a <a href="/wiki/Piecewise_linear_function" title="Piecewise linear function">piecewise linear function</a> or an arbitrary table. Once converted to an <a href="/wiki/RGBA_color_model" title="RGBA color model">RGBA color model</a> (for red, green, blue, alpha) value, the composed RGBA result is projected on the corresponding pixel of the frame buffer. The way this is done depends on the rendering technique. </p><p>A combination of these techniques is possible. For instance, a shear warp implementation could use texturing hardware to draw the aligned slices in the <a href="/wiki/Off-screen_buffer" class="mw-redirect" title="Off-screen buffer">off-screen buffer</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Volume_ray_casting">Volume ray casting</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=3" title="Edit section: Volume ray casting"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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/Volume_ray_casting" title="Volume ray casting">Volume ray casting</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Croc.5.3.10.a_gb1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Croc.5.3.10.a_gb1.jpg/300px-Croc.5.3.10.a_gb1.jpg" decoding="async" width="300" height="166" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Croc.5.3.10.a_gb1.jpg/450px-Croc.5.3.10.a_gb1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Croc.5.3.10.a_gb1.jpg/600px-Croc.5.3.10.a_gb1.jpg 2x" data-file-width="3552" data-file-height="1968" /></a><figcaption>Volume Ray Casting. Crocodile mummy provided by the Phoebe A. Hearst Museum of Anthropology, UC Berkeley. CT data was acquired by Rebecca Fahrig, Department of Radiology, Stanford University, using a Siemens SOMATOM Definition, Siemens Healthcare. The image was rendered by Fovia's High Definition Volume Rendering® engine.</figcaption></figure> <p>The technique of volume ray casting can be derived directly from the <a href="/wiki/Rendering_equation" title="Rendering equation">rendering equation</a>. It provides results of very high quality, usually considered to provide the best image quality. Volume ray casting is classified as image based volume rendering technique, as the computation emanates from the output image, not the input volume data as is the case with object based techniques. In this technique, a ray is generated for each desired image pixel. Using a simple camera model, the ray starts at the center of projection of the camera (usually the eye point) and passes through the image pixel on the imaginary image plane floating in between the camera and the volume to be rendered. The ray is clipped by the boundaries of the volume in order to save time. Then the ray is sampled at regular or adaptive intervals throughout the volume. The data is interpolated at each sample point, the transfer function applied to form an RGBA sample, the sample is composited onto the accumulated RGBA of the ray, and the process repeated until the ray exits the volume. The RGBA color is converted to an RGB color and deposited in the corresponding image pixel. The process is repeated for every pixel on the screen to form the completed image. </p> <div class="mw-heading mw-heading3"><h3 id="Splatting">Splatting</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=4" title="Edit section: Splatting"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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/Gaussian_splatting" title="Gaussian splatting">Gaussian splatting</a></div> <p>This is a technique which trades quality for speed. Here, every volume element is <a href="/wiki/Texture_splatting" title="Texture splatting">splatted</a>, as Lee Westover said, like a snow ball, on to the viewing surface in back to front order. These splats are rendered as disks whose properties (color and transparency) vary diametrically in normal (<a href="/wiki/Gaussian_distribution" class="mw-redirect" title="Gaussian distribution">Gaussian</a>) manner. Flat disks and those with other kinds of property distribution are also used depending on the application.<sup id="cite_ref-splatting_6-0" class="reference"><a href="#cite_note-splatting-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-fastsplat_7-0" class="reference"><a href="#cite_note-fastsplat-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Shear_warp">Shear warp</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=5" title="Edit section: Shear warp"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:VolRenderShearWarp.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/VolRenderShearWarp.gif/250px-VolRenderShearWarp.gif" decoding="async" width="250" height="253" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/VolRenderShearWarp.gif/375px-VolRenderShearWarp.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/VolRenderShearWarp.gif/500px-VolRenderShearWarp.gif 2x" data-file-width="533" data-file-height="540" /></a><figcaption>Example of a mouse skull (CT) rendering using the shear warp algorithm</figcaption></figure> <p>The shear warp approach to volume rendering was developed by Cameron and Undrill, popularized by Philippe Lacroute and <a href="/wiki/Marc_Levoy" title="Marc Levoy">Marc Levoy</a>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> In this technique, the <a href="/wiki/Viewing_transformation" class="mw-redirect" title="Viewing transformation">viewing transformation</a> is transformed such that the nearest face of the volume becomes axis aligned with an off-screen image <a href="/wiki/Data_buffer" title="Data buffer">data buffer</a> with a fixed scale of voxels to pixels. The volume is then rendered into this buffer using the far more favorable memory alignment and fixed scaling and blending factors. Once all slices of the volume have been rendered, the buffer is then warped into the desired orientation and scaled in the displayed image. </p><p>This technique is relatively fast in software at the cost of less accurate sampling and potentially worse image quality compared to ray casting. There is memory overhead for storing multiple copies of the volume, for the ability to have near axis aligned volumes. This overhead can be mitigated using <a href="/wiki/Run_length_encoding" class="mw-redirect" title="Run length encoding">run length encoding</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Texture-based_volume_rendering">Texture-based volume rendering</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=6" title="Edit section: Texture-based volume rendering"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:CTSkullImage.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/CTSkullImage.png/250px-CTSkullImage.png" decoding="async" width="250" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/CTSkullImage.png/375px-CTSkullImage.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/CTSkullImage.png/500px-CTSkullImage.png 2x" data-file-width="580" data-file-height="580" /></a><figcaption> A volume rendered cadaver head using view-aligned <a href="/wiki/Texture_mapping" title="Texture mapping">texture mapping</a> and <a href="/wiki/Diffuse_reflection" title="Diffuse reflection">diffuse reflection</a></figcaption></figure> <p>Many 3D graphics systems use <a href="/wiki/Texture_mapping" title="Texture mapping">texture mapping</a> to apply images, or textures, to geometric objects. Commodity PC <a href="/wiki/Graphics_cards" class="mw-redirect" title="Graphics cards">graphics cards</a> are fast at texturing and can efficiently render slices of a 3D volume, with real time interaction capabilities. <a href="/wiki/Workstation" title="Workstation">Workstation</a> <a href="/wiki/GPU" class="mw-redirect" title="GPU">GPUs</a> are even faster, and are the basis for much of the production volume visualization used in <a href="/wiki/Medical_imaging" title="Medical imaging">medical imaging</a>, oil and gas, and other markets (2007). In earlier years, dedicated 3D texture mapping systems were used on graphics systems such as <a href="/wiki/Silicon_Graphics" title="Silicon Graphics">Silicon Graphics</a> <a href="/wiki/InfiniteReality" title="InfiniteReality">InfiniteReality</a>, <a href="/wiki/Hewlett-Packard" title="Hewlett-Packard">HP</a> Visualize FX <a href="/wiki/Graphics_accelerator" class="mw-redirect" title="Graphics accelerator">graphics accelerator</a>, and others. This technique was first described by <a href="/wiki/Bill_Hibbard" title="Bill Hibbard">Bill Hibbard</a> and Dave Santek.<sup id="cite_ref-HS89_9-0" class="reference"><a href="#cite_note-HS89-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>These slices can either be aligned with the volume and rendered at an angle to the viewer, or aligned with the viewing plane and sampled from unaligned slices through the volume. Graphics hardware support for 3D textures is needed for the second technique. </p><p>Volume aligned texturing produces images of reasonable quality, though there is often a noticeable transition when the volume is rotated. </p> <div class="mw-heading mw-heading2"><h2 id="Hardware-accelerated_volume_rendering">Hardware-accelerated volume rendering</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=7" title="Edit section: Hardware-accelerated volume rendering"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Due to the extremely parallel nature of direct volume rendering, special purpose volume rendering hardware was a rich research topic before <a href="/wiki/GPU" class="mw-redirect" title="GPU">GPU</a> volume rendering became fast enough. The most widely cited technology was the VolumePro real-time ray-casting system, developed by <a href="/wiki/Hanspeter_Pfister" title="Hanspeter Pfister">Hanspeter Pfister</a> and scientists at <a href="/wiki/Mitsubishi_Electric_Research_Laboratories" title="Mitsubishi Electric Research Laboratories">Mitsubishi Electric Research Laboratories</a>,<sup id="cite_ref-phi99_10-0" class="reference"><a href="#cite_note-phi99-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> which used high memory bandwidth and brute force to render using the ray casting algorithm. The technology was transferred to TeraRecon, Inc. and two generations of ASICs were produced and sold. The VP1000<sup id="cite_ref-VP1000_11-0" class="reference"><a href="#cite_note-VP1000-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> was released in 2002 and the VP2000<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> in 2007. </p><p>A recently exploited technique to accelerate traditional volume rendering algorithms such as ray-casting is the use of modern graphics cards. Starting with the programmable <a href="/wiki/Pixel_shader" class="mw-redirect" title="Pixel shader">pixel shaders</a>, people recognized the power of parallel operations on multiple pixels and began to perform <a href="/wiki/GPGPU" class="mw-redirect" title="GPGPU"><i>general-purpose computing on (the) graphics processing units</i></a> (GPGPU). The <a href="/wiki/Pixel_shader" class="mw-redirect" title="Pixel shader">pixel shaders</a> are able to read and write randomly from video memory and perform some basic mathematical and logical calculations. These <a href="/wiki/Single_instruction,_multiple_data" title="Single instruction, multiple data">SIMD</a> processors were used to perform general calculations such as rendering polygons and signal processing. In recent <a href="/wiki/GPU" class="mw-redirect" title="GPU">GPU</a> generations, the pixel shaders now are able to function as <a href="/wiki/Multiple_instruction,_multiple_data" title="Multiple instruction, multiple data">MIMD</a> processors (now able to independently branch) utilizing up to 1 GB of texture memory with floating point formats. With such power, virtually any algorithm with steps that can be performed in parallel, such as <a href="/wiki/Volume_ray_casting" title="Volume ray casting">volume ray casting</a> or <a href="/wiki/Tomographic_reconstruction" title="Tomographic reconstruction">tomographic reconstruction</a>, can be performed with tremendous acceleration. The programmable <a href="/wiki/Pixel_shaders" class="mw-redirect" title="Pixel shaders">pixel shaders</a> can be used to simulate variations in the characteristics of lighting, shadow, <a href="/wiki/Reflection_(computer_graphics)" title="Reflection (computer graphics)">reflection</a>, emissive color and so forth. Such simulations can be written using high level <a href="/wiki/Shading_language" title="Shading language">shading languages</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Optimization_techniques">Optimization techniques</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=8" title="Edit section: Optimization techniques"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The primary goal of optimization is to skip as much of the volume as possible. A typical medical data set can be 1 GB in size. To render that at 30 frame/s requires an extremely fast memory bus. Skipping voxels means less information needs to be processed. </p> <div class="mw-heading mw-heading3"><h3 id="Empty_space_skipping">Empty space skipping</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=9" title="Edit section: Empty space skipping"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Often, a volume rendering system will have a system for identifying regions of the volume containing no visible material. This information can be used to avoid rendering these transparent regions.<sup id="cite_ref-shn03_13-0" class="reference"><a href="#cite_note-shn03-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Early_ray_termination">Early ray termination</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=10" title="Edit section: Early ray termination"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This is a technique used when the volume is rendered in front to back order. For a ray through a pixel, once sufficient dense material has been encountered, further samples will make no significant contribution to the pixel and so may be neglected. </p> <div class="mw-heading mw-heading3"><h3 id="Octree_and_BSP_space_subdivision">Octree and BSP space subdivision</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=11" title="Edit section: Octree and BSP space subdivision"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The use of hierarchical structures such as <a href="/wiki/Octree" title="Octree">octree</a> and <a href="/wiki/Binary_space_partitioning" title="Binary space partitioning">BSP</a>-tree could be very helpful for both compression of volume data and speed optimization of volumetric ray casting process. </p> <div class="mw-heading mw-heading3"><h3 id="Volume_segmentation">Volume segmentation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=12" title="Edit section: Volume segmentation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="anchor" id="Bone_removal"></span></p><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:CT_angiography_of_the_head_without_and_with_bone_removal.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/CT_angiography_of_the_head_without_and_with_bone_removal.jpg/220px-CT_angiography_of_the_head_without_and_with_bone_removal.jpg" decoding="async" width="220" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/CT_angiography_of_the_head_without_and_with_bone_removal.jpg/330px-CT_angiography_of_the_head_without_and_with_bone_removal.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/95/CT_angiography_of_the_head_without_and_with_bone_removal.jpg/440px-CT_angiography_of_the_head_without_and_with_bone_removal.jpg 2x" data-file-width="2000" data-file-height="822" /></a><figcaption>Volume segmentation include automatic bone removal, such as used in the right image in this <a href="/wiki/Computed_tomography_angiography" title="Computed tomography angiography">CT angiography</a>.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:3D_CT_of_thorax.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/3D_CT_of_thorax.jpg/220px-3D_CT_of_thorax.jpg" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/3D_CT_of_thorax.jpg/330px-3D_CT_of_thorax.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bd/3D_CT_of_thorax.jpg/440px-3D_CT_of_thorax.jpg 2x" data-file-width="1082" data-file-height="1081" /></a><figcaption>Volume segmentation of a 3D-rendered <a href="/wiki/CT_scan" title="CT scan">CT scan</a> of the <a href="/wiki/Thorax" title="Thorax">thorax</a>: The anterior thoracic wall, the airways and the pulmonary vessels anterior to the root of the lung have been digitally removed in order to visualize thoracic contents: <br />- <style data-mw-deduplicate="TemplateStyles:r1239334494">@media screen{html.skin-theme-clientpref-night .mw-parser-output div:not(.notheme)>.tmp-color,html.skin-theme-clientpref-night .mw-parser-output p>.tmp-color,html.skin-theme-clientpref-night .mw-parser-output table:not(.notheme) .tmp-color{color:inherit!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output div:not(.notheme)>.tmp-color,html.skin-theme-clientpref-os .mw-parser-output p>.tmp-color,html.skin-theme-clientpref-os .mw-parser-output table:not(.notheme) .tmp-color{color:inherit!important}}</style><span class="tmp-color" style="color:blue">blue</span>: <a href="/wiki/Pulmonary_arteries" class="mw-redirect" title="Pulmonary arteries">pulmonary arteries</a> <br />- <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:red">red</span>: <a href="/wiki/Pulmonary_veins" class="mw-redirect" title="Pulmonary veins">pulmonary veins</a> (and also the <a href="/wiki/Abdominal_wall" title="Abdominal wall">abdominal wall</a>)<br />- <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:yellow">yellow</span>: the <a href="/wiki/Mediastinum" title="Mediastinum">mediastinum</a> <br />- <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:violet">violet</span>: the <a href="/wiki/Thoracic_diaphragm" title="Thoracic diaphragm">diaphragm</a> </figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Visible-human-leonardo-1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Visible-human-leonardo-1.jpg/220px-Visible-human-leonardo-1.jpg" decoding="async" width="220" height="278" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Visible-human-leonardo-1.jpg/330px-Visible-human-leonardo-1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Visible-human-leonardo-1.jpg/440px-Visible-human-leonardo-1.jpg 2x" data-file-width="2370" data-file-height="2995" /></a><figcaption>Visualization of the inner organs from the segmented <a href="/wiki/Visible_Human_Project" title="Visible Human Project">Visible Human</a> data set rendered by <a href="/wiki/Voxel-Man" title="Voxel-Man">Voxel-Man</a>, aside with a drawing of <a href="/wiki/Leonardo_da_Vinci" title="Leonardo da Vinci">Leonardo da Vinci</a> (1998)</figcaption></figure> <p><a href="/wiki/Image_segmentation" title="Image segmentation">Image segmentation</a> is a manual or automatic procedure that can be used to section out large portions of the volume that one considers uninteresting before rendering, the amount of calculations that have to be made by ray casting or texture blending can be significantly reduced. This reduction can be as much as from O(n) to O(log n) for n sequentially indexed voxels. Volume segmentation also has significant performance benefits for other <a href="/wiki/Ray_tracing_(graphics)" title="Ray tracing (graphics)">ray tracing</a> algorithms. Volume segmentation can subsequently be used to highlight or expose<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> structures of interest. </p> <div class="mw-heading mw-heading3"><h3 id="Multiple_and_adaptive_resolution_representation">Multiple and adaptive resolution representation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=13" title="Edit section: Multiple and adaptive resolution representation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>By representing less interesting regions of the volume in a coarser resolution, the data input overhead can be reduced. On closer observation, the data in these regions can be populated either by reading from memory or disk, or by <a href="/wiki/Interpolation" title="Interpolation">interpolation</a>. The coarser resolution volume is resampled to a smaller size in the same way as a 2D mipmap image is created from the original. These smaller volume are also used by themselves while rotating the volume to a new orientation. </p> <div class="mw-heading mw-heading3"><h3 id="Pre-integrated_volume_rendering">Pre-integrated volume rendering</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=14" title="Edit section: Pre-integrated volume rendering"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pre-integrated volume rendering<sup id="cite_ref-mhc90_15-0" class="reference"><a href="#cite_note-mhc90-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> is a method that can reduce sampling artifacts by pre-computing much of the required data. It is especially useful in hardware-accelerated applications<sup id="cite_ref-eke01_16-0" class="reference"><a href="#cite_note-eke01-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-lwm04_17-0" class="reference"><a href="#cite_note-lwm04-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> because it improves quality without a large performance impact. Unlike most other optimizations, this does not skip voxels. Rather it reduces the number of samples needed to accurately display a region of voxels. The idea is to render the intervals between the samples instead of the samples themselves. This technique captures rapidly changing material, for example the transition from muscle to bone with much less computation. </p> <div class="mw-heading mw-heading3"><h3 id="Image-based_meshing">Image-based meshing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=15" title="Edit section: Image-based meshing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Image-based_meshing" title="Image-based meshing">Image-based meshing</a> is the automated process of creating computer models from 3D image data (such as <a href="/wiki/MRI" class="mw-redirect" title="MRI">MRI</a>, <a href="/wiki/X-ray_computed_tomography" class="mw-redirect" title="X-ray computed tomography">CT</a>, <a href="/wiki/Industrial_CT_scanning" class="mw-redirect" title="Industrial CT scanning">Industrial CT</a> or <a href="/wiki/Microtomography" class="mw-redirect" title="Microtomography">microtomography</a>) for computational analysis and design, e.g. CAD, CFD, and FEA. </p> <div class="mw-heading mw-heading3"><h3 id="Temporal_reuse_of_voxels">Temporal reuse of voxels</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=16" title="Edit section: Temporal reuse of voxels"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For a complete display view, only one voxel per pixel (the front one) is required to be shown (although more can be used for smoothing the image), if animation is needed, the front voxels to be shown can be cached and their location relative to the camera can be recalculated as it moves. Where display voxels become too far apart to cover all the pixels, new front voxels can be found by ray casting or similar, and where two voxels are in one pixel, the front one can be kept. </p> <div class="mw-heading mw-heading2"><h2 id="List_of_related_software">List of related software</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=17" title="Edit section: List of related software"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dt>Open source</dt></dl> <ul><li><a href="/wiki/3D_Slicer" title="3D Slicer">3D Slicer</a> – a software package for scientific visualization and image analysis</li> <li><a href="/wiki/ClearVolume" title="ClearVolume">ClearVolume</a> – a GPU ray-casting based, live 3D visualization library designed for high-end volumetric light sheet microscopes.</li> <li><a href="/wiki/ParaView" title="ParaView">ParaView</a> – a cross-platform, large data analysis and visualization application. ParaView users can quickly build visualizations to analyze their data using qualitative and quantitative techniques. ParaView is built on VTK (below).</li> <li><a href="/wiki/Studierfenster" title="Studierfenster">Studierfenster (StudierFenster)</a> – a free, non-commercial Open Science client/server-based Medical Imaging Processing (MIP) online framework.</li> <li><a href="/wiki/Vaa3D" title="Vaa3D">Vaa3D</a> – a 3D, 4D and 5D volume rendering and image analysis platform for gigabytes and terabytes of large images (based on OpenGL) especially in the microscopy image field. Also cross-platform with Mac, Windows, and Linux versions. Include a comprehensive plugin interface and 100 plugins for image analysis. Also render multiple types of surface objects.</li> <li><a href="/wiki/VisIt" title="VisIt">VisIt</a> – a cross-platform interactive parallel visualization and graphical analysis tool for viewing scientific data.</li> <li><a href="/wiki/Volume_cartography" title="Volume cartography">Volume cartography</a> – an open source software used in recovering the <a href="/wiki/En-Gedi_Scroll" title="En-Gedi Scroll">En-Gedi Scroll</a>.</li> <li><a href="/wiki/Voreen" title="Voreen">Voreen</a> – a cross-platform rapid application development framework for the interactive visualization and analysis of multi-modal volumetric data sets. It provides GPU-based volume rendering and data analysis techniques</li> <li><a href="/wiki/VTK" title="VTK">VTK</a> – a general-purpose C++ toolkit for data processing, visualization, 3D interaction, computational geometry, with Python and Java bindings. Also, VTK.js provides a JavaScript implementation.</li></ul> <dl><dt>Commercial</dt></dl> <ul><li><a href="/wiki/Amira_(Software)" class="mw-redirect" title="Amira (Software)">Amira</a> – a 3D visualization and analysis software for scientists and researchers (in life sciences and biomedical)</li> <li><a href="/wiki/Imaris" class="mw-redirect" title="Imaris">Imaris</a> – a scientific software module that delivers all the necessary functionality for data management, visualization, analysis, segmentation and interpretation of 3D and 4D microscopy datasets</li> <li><a href="/wiki/MeVisLab" title="MeVisLab">MeVisLab</a> – cross-platform software for medical image processing and visualization (based on OpenGL and Open Inventor)</li> <li><a href="/wiki/Open_Inventor" title="Open Inventor">Open Inventor</a> – a high-level 3D API for 3D graphics software development (C++, .NET, Java)</li> <li><a href="/wiki/ScanIP" title="ScanIP">ScanIP</a> – an image processing and <a href="/wiki/Image-based_meshing" title="Image-based meshing">image-based meshing</a> platform that can render scan data (MRI, CT, Micro-CT...) in 3D directly after import.</li></ul> <figure typeof="mw:File/Thumb"><a href="/wiki/File:V3d-display_01.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/V3d-display_01.png/250px-V3d-display_01.png" decoding="async" width="250" height="179" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/V3d-display_01.png/375px-V3d-display_01.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5a/V3d-display_01.png/500px-V3d-display_01.png 2x" data-file-width="584" data-file-height="419" /></a><figcaption>Example of a fly brain rendered with its compartments' surface models using Vaa3D</figcaption></figure> <ul><li><a href="/wiki/Tomviz" title="Tomviz">tomviz</a> – a 3D visualization platform for scientists and researchers that can utilize Python scripts for advanced 3D data processing.</li> <li><a href="/wiki/VoluMedic" title="VoluMedic">VoluMedic</a> – a volume slicing and rendering software</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=18" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Volume_rendering" class="extiw" title="commons:Category:Volume rendering">Volume rendering</a></span>.</div></div> </div> <ul><li><a href="/wiki/Isosurface" title="Isosurface">Isosurface</a>, a surface that represents points of a constant value (e.g. pressure, temperature, velocity, density) within a volume of space</li> <li><a href="/wiki/Flow_visualization" title="Flow visualization">Flow visualization</a>, a technique for the visualization of <a href="/wiki/Vector_field" title="Vector field">vector fields</a></li> <li><a href="/wiki/Volume_mesh" class="mw-redirect" title="Volume mesh">Volume mesh</a>, a polygonal representation of the interior volume of an object</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=19" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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 .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width reflist-columns-2"> <ol class="references"> <li id="cite_note-FishmanNey2006-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-FishmanNey2006_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFFishmanNeyHeathCorl2006" class="citation journal cs1"><a href="/wiki/Elliot_K._Fishman" title="Elliot K. Fishman">Fishman, Elliot K.</a>; Ney, Derek R.; Heath, David G.; Corl, Frank M.; Horton, Karen M.; Johnson, Pamela T. (2006). <a rel="nofollow" class="external text" href="https://doi.org/10.1148%2Frg.263055186">"Volume Rendering versus Maximum Intensity Projection in CT Angiography: What Works Best, When, and Why"</a>. <i>RadioGraphics</i>. <b>26</b> (3): 905–922. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1148%2Frg.263055186">10.1148/rg.263055186</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0271-5333">0271-5333</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16702462">16702462</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=RadioGraphics&rft.atitle=Volume+Rendering+versus+Maximum+Intensity+Projection+in+CT+Angiography%3A+What+Works+Best%2C+When%2C+and+Why&rft.volume=26&rft.issue=3&rft.pages=905-922&rft.date=2006&rft.issn=0271-5333&rft_id=info%3Apmid%2F16702462&rft_id=info%3Adoi%2F10.1148%2Frg.263055186&rft.aulast=Fishman&rft.aufirst=Elliot+K.&rft.au=Ney%2C+Derek+R.&rft.au=Heath%2C+David+G.&rft.au=Corl%2C+Frank+M.&rft.au=Horton%2C+Karen+M.&rft.au=Johnson%2C+Pamela+T.&rft_id=https%3A%2F%2Fdoi.org%2F10.1148%252Frg.263055186&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVolume+rendering" class="Z3988"></span></span> </li> <li id="cite_note-SilversteinParsad2008-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-SilversteinParsad2008_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSilversteinParsadTsirline2008" class="citation journal cs1">Silverstein, Jonathan C.; Parsad, Nigel M.; Tsirline, Victor (2008). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2651027">"Automatic perceptual color map generation for realistic volume visualization"</a>. <i>Journal of Biomedical Informatics</i>. <b>41</b> (6): 927–935. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.jbi.2008.02.008">10.1016/j.jbi.2008.02.008</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1532-0464">1532-0464</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2651027">2651027</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/18430609">18430609</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Biomedical+Informatics&rft.atitle=Automatic+perceptual+color+map+generation+for+realistic+volume+visualization&rft.volume=41&rft.issue=6&rft.pages=927-935&rft.date=2008&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC2651027%23id-name%3DPMC&rft.issn=1532-0464&rft_id=info%3Apmid%2F18430609&rft_id=info%3Adoi%2F10.1016%2Fj.jbi.2008.02.008&rft.aulast=Silverstein&rft.aufirst=Jonathan+C.&rft.au=Parsad%2C+Nigel+M.&rft.au=Tsirline%2C+Victor&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC2651027&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVolume+rendering" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=zndnSzkfkXwC&pg=PA185">Page 185</a> in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLeif_Kobbelt2006" class="citation book cs1">Leif Kobbelt (2006). <i>Vision, Modeling, and Visualization 2006: Proceedings, November 22-24</i>. IOS Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783898380812" title="Special:BookSources/9783898380812"><bdi>9783898380812</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Vision%2C+Modeling%2C+and+Visualization+2006%3A+Proceedings%2C+November+22-24&rft.pub=IOS+Press&rft.date=2006&rft.isbn=9783898380812&rft.au=Leif+Kobbelt&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVolume+rendering" class="Z3988"></span></span> </li> <li id="cite_note-_188-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-_188_4-0">^</a></b></span> <span class="reference-text">Marc Levoy, "Display of Surfaces from Volume Data", <a href="/wiki/IEEE" class="mw-redirect" title="IEEE">IEEE</a> CG&A, May 1988. <a rel="nofollow" class="external text" href="http://graphics.stanford.edu/papers/volume-cga88/">Archive of Paper</a></span> </li> <li id="cite_note-dch88-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-dch88_5-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDrebinCarpenterHanrahan1988" class="citation journal cs1">Drebin, Robert A.; Carpenter, Loren; Hanrahan, Pat (1988). 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Retrieved <span class="nowrap">28 June</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=SPLATTING%3A+A+Parallel%2C+Feed-Forward+Volume+Rendering+Algorithm&rft.date=1991-07&rft.aulast=Westover&rft.aufirst=Lee+Alan&rft_id=http%3A%2F%2Fwww.cs.unc.edu%2Ftechreports%2F91-029.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVolume+rendering" class="Z3988"></span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged September 2023">dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup></span> </li> <li id="cite_note-fastsplat-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-fastsplat_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHuang2002" class="citation web cs1">Huang, Jian (Spring 2002). <a rel="nofollow" class="external text" href="http://web.eecs.utk.edu/~huangj/CS594S02/splatting.ppt">"Splatting"</a> <span class="cs1-format">(PPT)</span><span class="reference-accessdate">. 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"Fast volume rendering using a shear-warp factorization of the viewing transformation". <a rel="nofollow" class="external text" href="http://graphics.stanford.edu/papers/shear/"><i>Proceedings of the 21st annual conference on Computer graphics and interactive techniques - SIGGRAPH '94</i></a>. SIGGRAPH '94. New York, NY, USA: ACM. pp. 451–458. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.75.7117">10.1.1.75.7117</a></span>. <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%2F192161.192283">10.1145/192161.192283</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0897916677" title="Special:BookSources/978-0897916677"><bdi>978-0897916677</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:1266012">1266012</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Fast+volume+rendering+using+a+shear-warp+factorization+of+the+viewing+transformation&rft.btitle=Proceedings+of+the+21st+annual+conference+on+Computer+graphics+and+interactive+techniques+-+SIGGRAPH+%2794&rft.place=New+York%2C+NY%2C+USA&rft.series=SIGGRAPH+%2794&rft.pages=451-458&rft.pub=ACM&rft.date=1994-01-01&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.75.7117%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A1266012%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1145%2F192161.192283&rft.isbn=978-0897916677&rft.aulast=Lacroute&rft.aufirst=Philippe&rft.au=Levoy%2C+Marc&rft_id=http%3A%2F%2Fgraphics.stanford.edu%2Fpapers%2Fshear%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVolume+rendering" class="Z3988"></span></span> </li> <li id="cite_note-HS89-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-HS89_9-0">^</a></b></span> <span class="reference-text">Hibbard W., Santek D., <a rel="nofollow" class="external text" href="http://www.ssec.wisc.edu/~billh/p39-hibbard.pdf">"Interactivity is the key"</a>, <i>Chapel Hill Workshop on Volume Visualization</i>, University of North Carolina, Chapel Hill, 1989, pp. 39–43.</span> </li> <li id="cite_note-phi99-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-phi99_10-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPfisterHardenberghKnittelLauer1999" class="citation book cs1">Pfister, Hanspeter; Hardenbergh, Jan; Knittel, Jim; Lauer, Hugh; Seiler, Larry (1999). "The VolumePro real-time ray-casting system". <i>Proceedings of the 26th annual conference on Computer graphics and interactive techniques - SIGGRAPH '99</i>. pp. 251–260. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.471.9205">10.1.1.471.9205</a></span>. <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%2F311535.311563">10.1145/311535.311563</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0201485608" title="Special:BookSources/978-0201485608"><bdi>978-0201485608</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:7673547">7673547</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+VolumePro+real-time+ray-casting+system&rft.btitle=Proceedings+of+the+26th+annual+conference+on+Computer+graphics+and+interactive+techniques+-+SIGGRAPH+%2799&rft.pages=251-260&rft.date=1999&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.471.9205%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A7673547%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1145%2F311535.311563&rft.isbn=978-0201485608&rft.aulast=Pfister&rft.aufirst=Hanspeter&rft.au=Hardenbergh%2C+Jan&rft.au=Knittel%2C+Jim&rft.au=Lauer%2C+Hugh&rft.au=Seiler%2C+Larry&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVolume+rendering" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: date and year (<a href="/wiki/Category:CS1_maint:_date_and_year" title="Category:CS1 maint: date and year">link</a>)</span></span> </li> <li id="cite_note-VP1000-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-VP1000_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWuBhatiaLauerSeiler2003" class="citation book cs1">Wu, Yin; Bhatia, Vishal; Lauer, Hugh; Seiler, Larry (2003). "Shear-image order ray casting volume rendering". <i>Proceedings of the 2003 symposium on Interactive 3D graphics</i>. p. 152. <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%2F641480.641510">10.1145/641480.641510</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1581136456" title="Special:BookSources/978-1581136456"><bdi>978-1581136456</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:14641432">14641432</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Shear-image+order+ray+casting+volume+rendering&rft.btitle=Proceedings+of+the+2003+symposium+on+Interactive+3D+graphics&rft.pages=152&rft.date=2003&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A14641432%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1145%2F641480.641510&rft.isbn=978-1581136456&rft.aulast=Wu&rft.aufirst=Yin&rft.au=Bhatia%2C+Vishal&rft.au=Lauer%2C+Hugh&rft.au=Seiler%2C+Larry&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVolume+rendering" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTeraRecon" class="citation web cs1">TeraRecon. <a rel="nofollow" class="external text" href="https://www.healthimaging.com/topics/diagnostic-imaging/terarecon-its-beginning-end-dedicated-diagnostic-advanced-visualization">"Product Announcement"</a>. <i>healthimaging.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">27 August</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=healthimaging.com&rft.atitle=Product+Announcement&rft.au=TeraRecon&rft_id=https%3A%2F%2Fwww.healthimaging.com%2Ftopics%2Fdiagnostic-imaging%2Fterarecon-its-beginning-end-dedicated-diagnostic-advanced-visualization&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVolume+rendering" class="Z3988"></span></span> </li> <li id="cite_note-shn03-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-shn03_13-0">^</a></b></span> <span class="reference-text">Sherbondy A., Houston M., Napel S.: <i>Fast volume segmentation with simultaneous visualization using programmable graphics hardware.</i> In Proceedings of <a href="/wiki/IEEE" class="mw-redirect" title="IEEE">IEEE</a> Visualization (2003), pp. 171–176.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">Tiede U., Schiemann T., Hoehne K.: <i>High quality rendering of attributed volume data</i> In Proceedings of <a href="/wiki/IEEE" class="mw-redirect" title="IEEE">IEEE</a> Visualization (1998), pp. 255-262.</span> </li> <li id="cite_note-mhc90-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-mhc90_15-0">^</a></b></span> <span class="reference-text">Max N., Hanrahan P., Crawfis R.: <i><a rel="nofollow" class="external text" href="http://www.sci.utah.edu/~jmk/papers/VolViz90-MAX.pdf">Area and volume coherence for efficient visualization of 3D scalar functions</a>.</i> In Computer Graphics (San Diego Workshop on Volume Visualization, 1990) vol. 24, pp. 27–33.</span> </li> <li id="cite_note-eke01-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-eke01_16-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEngelKrausErtl2001" class="citation book cs1">Engel, Klaus; Kraus, Martin; Ertl, Thomas (2001). "High-quality pre-integrated volume rendering using hardware-accelerated pixel shading". <i>Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware</i>. pp. 9–16. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.458.1814">10.1.1.458.1814</a></span>. <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%2F383507.383515">10.1145/383507.383515</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1581134070" title="Special:BookSources/978-1581134070"><bdi>978-1581134070</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:14409951">14409951</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=High-quality+pre-integrated+volume+rendering+using+hardware-accelerated+pixel+shading&rft.btitle=Proceedings+of+the+ACM+SIGGRAPH%2FEUROGRAPHICS+workshop+on+Graphics+hardware&rft.pages=9-16&rft.date=2001&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.458.1814%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A14409951%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1145%2F383507.383515&rft.isbn=978-1581134070&rft.aulast=Engel&rft.aufirst=Klaus&rft.au=Kraus%2C+Martin&rft.au=Ertl%2C+Thomas&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVolume+rendering" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: date and year (<a href="/wiki/Category:CS1_maint:_date_and_year" title="Category:CS1 maint: date and year">link</a>)</span></span> </li> <li id="cite_note-lwm04-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-lwm04_17-0">^</a></b></span> <span class="reference-text">Lum E., Wilson B., Ma K.: <i><a rel="nofollow" class="external text" href="http://www.cg.tuwien.ac.at/courses/Seminar/WS2004/papers/%5BLum2004%5D%20High-Quality%20Lighting%20and%20Efficient%20Pre-Integration%20for%20Volume%20Rendering.pdf">High-Quality Lighting and Efficient Pre-Integration for Volume Rendering</a>.</i> In Eurographics/<a href="/wiki/IEEE" class="mw-redirect" title="IEEE">IEEE</a> Symposium on Visualization 2004.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Volume_rendering&action=edit&section=20" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>M. Ikits, J. Kniss, A. Lefohn and C. Hansen: <a rel="nofollow" class="external text" href="https://developer.nvidia.com/gpugems/gpugems/part-vi-beyond-triangles/chapter-39-volume-rendering-techniques"><i>Volume Rendering Techniques</i></a>. In: <i>GPU Gems</i>, Chapter 39 (online-version in the developer zone of Nvidia).</li> <li><a rel="nofollow" class="external text" href="http://www.byclb.com/TR/Tutorials/volume_rendering/Index.aspx">Volume Rendering</a>, Volume Rendering Basics Tutorial by Ph.D. Ömer Cengiz ÇELEBİ</li> <li>Barthold Lichtenbelt, Randy Crane, Shaz Naqvi, <i>Introduction to Volume Rendering</i> (Hewlett-Packard Professional Books), Hewlett-Packard Company 1998.</li> <li>Peng H., Ruan, Z, Long, F, Simpson, JH, Myers, EW: <i>V3D enables real-time 3D visualization and quantitative analysis of large-scale biological image data sets.</i> Nature Biotechnology, 2010 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnbt.1612">10.1038/nbt.1612</a> <a rel="nofollow" class="external text" href="http://www.nature.com/nbt/journal/vaop/ncurrent/full/nbt.1612.html">Volume Rendering of large high-dimensional image data</a>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDaniel_Weiskopf2006" class="citation book cs1">Daniel Weiskopf (2006). <i>GPU-Based Interactive Visualization Techniques</i>. Springer Science & Business Media. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-33263-3" title="Special:BookSources/978-3-540-33263-3"><bdi>978-3-540-33263-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=GPU-Based+Interactive+Visualization+Techniques&rft.pub=Springer+Science+%26+Business+Media&rft.date=2006&rft.isbn=978-3-540-33263-3&rft.au=Daniel+Weiskopf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AVolume+rendering" class="Z3988"></span></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox 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style="padding:3px"><table class="nowraplinks 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:Visualization" title="Template:Visualization"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Visualization" title="Template talk:Visualization"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Visualization" title="Special:EditPage/Template:Visualization"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Visualization_of_technical_information" style="font-size:114%;margin:0 4em"><a href="/wiki/Visualization_(graphics)" title="Visualization (graphics)">Visualization</a> of technical 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 class="mw-selflink selflink">Volume visualization</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Image <br />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 <br />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 class="mw-selflink selflink">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 href="/wiki/Rendering_(computer_graphics)" title="Rendering (computer graphics)">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 class="mw-selflink selflink">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><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Volume_rendering&oldid=1245253229">https://en.wikipedia.org/w/index.php?title=Volume_rendering&oldid=1245253229</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a 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