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class="vector-toc-numb">2</span> <span>Oblique pictorial</span> </div> </a> <ul id="toc-Oblique_pictorial-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cavalier_projection" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cavalier_projection"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Cavalier projection</span> </div> </a> <ul id="toc-Cavalier_projection-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cabinet_projection" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cabinet_projection"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Cabinet projection</span> </div> </a> <button aria-controls="toc-Cabinet_projection-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 Cabinet projection subsection</span> </button> <ul id="toc-Cabinet_projection-sublist" class="vector-toc-list"> <li id="toc-Mathematical_formula" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mathematical_formula"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Mathematical formula</span> </div> </a> <ul id="toc-Mathematical_formula-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Military_projection" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Military_projection"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Military projection</span> </div> </a> <ul id="toc-Military_projection-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Examples" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Examples"> <div 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href="https://cs.wikipedia.org/wiki/Koso%C3%BAhl%C3%A9_prom%C3%ADt%C3%A1n%C3%AD" title="Kosoúhlé promítání – Czech" lang="cs" hreflang="cs" data-title="Kosoúhlé promítání" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Perspektivisk_forkortning" title="Perspektivisk forkortning – Danish" lang="da" hreflang="da" data-title="Perspektivisk forkortning" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Schr%C3%A4griss" title="Schrägriss – German" lang="de" hreflang="de" data-title="Schrägriss" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li 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of all important aspects of the article.</span> <span class="date-container"><i>(<span class="date">February 2015</span>)</i></span></div></td></tr></tbody></table> <p class="mw-empty-elt"> </p> <div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Type of technical drawing</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the imaging of 3D objects. For an abstract mathematical discussion, see <a href="/wiki/Projection_(linear_algebra)" title="Projection (linear algebra)">Projection (linear algebra)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist 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.sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .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 sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Graphical_projection" class="mw-redirect" title="Graphical projection">Graphical projection</a></th></tr><tr><td class="sidebar-image"><span typeof="mw:File"><a href="/wiki/File:Axonometric_projection.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Axonometric_projection.svg/150px-Axonometric_projection.svg.png" decoding="async" width="150" height="128" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Axonometric_projection.svg/225px-Axonometric_projection.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/48/Axonometric_projection.svg/300px-Axonometric_projection.svg.png 2x" data-file-width="467" data-file-height="397" /></a></span></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Planar_projection" title="Planar projection">Planar</a></div><div class="sidebar-list-content mw-collapsible-content" style="text-align: left"> <ul><li><a href="/wiki/Parallel_projection" title="Parallel projection">Parallel projection</a> <ul><li><a href="/wiki/Orthographic_projection" title="Orthographic projection">Orthographic projection</a> <ul><li><a href="/wiki/Isometric_projection" title="Isometric projection">Isometric projection</a></li></ul></li> <li><a class="mw-selflink selflink">Oblique projection</a></li></ul></li> <li><a href="/wiki/Perspective_(graphical)" title="Perspective (graphical)">Perspective projection</a> <ul><li><a href="/wiki/Curvilinear_perspective" title="Curvilinear perspective">Curvilinear perspective</a></li> <li><a href="/wiki/Reverse_perspective" title="Reverse perspective">Reverse perspective</a></li></ul></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Views</div><div class="sidebar-list-content mw-collapsible-content" style="text-align: left"> <ul><li><a href="/wiki/Bird%27s-eye_view" title="Bird's-eye view">Bird's-eye view</a></li> <li><a href="/wiki/Cross_section_(geometry)" title="Cross section (geometry)">Cross section</a></li> <li><a href="/wiki/Cutaway_drawing" title="Cutaway drawing">Cutaway drawing</a></li> <li><a href="/wiki/Exploded_view_drawing" class="mw-redirect" title="Exploded view drawing">Exploded view drawing</a></li> <li><a href="/wiki/Fisheye_lens" title="Fisheye lens">Fisheye lens</a></li> <li><a href="/wiki/Multiview_projection" class="mw-redirect" title="Multiview projection">Multiviews</a></li> <li><a href="/wiki/Panorama" title="Panorama">Panorama</a></li> <li><a href="/wiki/Worm%27s-eye_view" title="Worm's-eye view">Worm's-eye view</a></li> <li><a href="/wiki/Zoom_lens" title="Zoom lens">Zoom lens</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Topics</div><div class="sidebar-list-content mw-collapsible-content" style="text-align: left"> <ul><li><a href="/wiki/3D_projection" title="3D projection">3D projection</a></li> <li><a href="/wiki/Anamorphosis" title="Anamorphosis">Anamorphosis</a></li> <li><a href="/wiki/Axonometry" title="Axonometry">Axonometry</a></li> <li><a href="/wiki/Computer_graphics" title="Computer graphics">Computer graphics</a></li> <li><a href="/wiki/Computer-aided_design" title="Computer-aided design">Computer-aided design</a></li> <li><a href="/wiki/Descriptive_geometry" title="Descriptive geometry">Descriptive geometry</a></li> <li><a href="/wiki/Engineering_drawing" title="Engineering drawing">Engineering drawing</a></li> <li><a href="/wiki/Map_projection" title="Map projection">Map projection</a></li> <li><a href="/wiki/Picture_plane" title="Picture plane">Picture plane</a></li> <li><a href="/wiki/Plans_(drawings)" class="mw-redirect" title="Plans (drawings)">Plans (drawings)</a></li> <li><a href="/wiki/Projection_(linear_algebra)" title="Projection (linear algebra)">Projection (linear algebra)</a></li> <li><a href="/wiki/Projection_plane" title="Projection plane">Projection plane</a></li> <li><a href="/wiki/Projective_geometry" title="Projective geometry">Projective geometry</a></li> <li><a href="/wiki/Stereoscopy" title="Stereoscopy">Stereoscopy</a></li> <li><a href="/wiki/Technical_drawing" title="Technical drawing">Technical drawing</a></li> <li><a href="/wiki/True_length" title="True length">True length</a></li> <li><a href="/wiki/Vanishing_point" title="Vanishing point">Vanishing point</a></li> <li><a href="/wiki/Video_game_graphics" title="Video game graphics">Video game graphics</a></li> <li><a href="/wiki/Viewing_frustum" title="Viewing frustum">Viewing frustum</a></li></ul></div></div></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:Views" title="Template:Views"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Views" title="Template talk:Views"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Views" title="Special:EditPage/Template:Views"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Comparison_of_graphical_projections.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Comparison_of_graphical_projections.svg/220px-Comparison_of_graphical_projections.svg.png" decoding="async" width="220" height="251" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Comparison_of_graphical_projections.svg/330px-Comparison_of_graphical_projections.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/93/Comparison_of_graphical_projections.svg/440px-Comparison_of_graphical_projections.svg.png 2x" data-file-width="512" data-file-height="585" /></a><figcaption>Classification of <span class="nocaps" style="text-transform:lowercase;">Oblique projection</span> and some 3D projections</figcaption></figure> <p><b>Oblique projection</b> is a simple type of technical drawing of <a href="/wiki/Graphical_projection" class="mw-redirect" title="Graphical projection">graphical projection</a> used for producing two-dimensional (2D) <a href="/wiki/Image" title="Image">images</a> of three-dimensional (3D) objects. </p><p>The objects are not in <a href="/wiki/Perspective_(graphical)" title="Perspective (graphical)">perspective</a> and so do not correspond to any view of an object that can be obtained in practice, but the technique yields somewhat convincing and useful results. </p><p>Oblique projection is commonly used in technical drawing. The cavalier projection was used by French military artists in the 18th century to depict fortifications. </p><p>Oblique projection was used almost universally by Chinese artists from the 1st or 2nd centuries to the 18th century, especially to depict rectilinear objects such as houses.<sup id="cite_ref-Cucker299_1-0" class="reference"><a href="#cite_note-Cucker299-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Various graphical projection techniques can be used in computer graphics, including in Computer Aided Design (CAD), computer games, computer generated animations, and special effects used in movies. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Oblique_projection&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Graphical_projection_comparison.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Graphical_projection_comparison.png/220px-Graphical_projection_comparison.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Graphical_projection_comparison.png/330px-Graphical_projection_comparison.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/Graphical_projection_comparison.png/440px-Graphical_projection_comparison.png 2x" data-file-width="4550" data-file-height="4550" /></a><figcaption>Comparison of several types of <a href="/wiki/Graphical_projection" class="mw-redirect" title="Graphical projection">graphical projection</a>. The presence of one or more 90° angles within a pictorial image is usually a good indication that the perspective is <i>oblique</i>.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Various_projections_of_cube_above_plane.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Various_projections_of_cube_above_plane.svg/220px-Various_projections_of_cube_above_plane.svg.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Various_projections_of_cube_above_plane.svg/330px-Various_projections_of_cube_above_plane.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Various_projections_of_cube_above_plane.svg/440px-Various_projections_of_cube_above_plane.svg.png 2x" data-file-width="640" data-file-height="480" /></a><figcaption>Various graphical projections and how they are produced</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Oblique_projection_yz.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Oblique_projection_yz.svg/220px-Oblique_projection_yz.svg.png" decoding="async" width="220" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Oblique_projection_yz.svg/330px-Oblique_projection_yz.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Oblique_projection_yz.svg/440px-Oblique_projection_yz.svg.png 2x" data-file-width="514" data-file-height="518" /></a><figcaption>Oblique projection of a cube with foreshortening by half, seen from the side</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Oblique_projection_comparison_top.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Oblique_projection_comparison_top.svg/220px-Oblique_projection_comparison_top.svg.png" decoding="async" width="220" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Oblique_projection_comparison_top.svg/330px-Oblique_projection_comparison_top.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Oblique_projection_comparison_top.svg/440px-Oblique_projection_comparison_top.svg.png 2x" data-file-width="1134" data-file-height="567" /></a><figcaption>Top view of a comparison of an oblique projection (left) and an orthographic projection (right) of a unit cube (cyan) onto the projection plane (red). The <a href="/wiki/Foreshortening" class="mw-redirect" title="Foreshortening">foreshortening</a> factor (1/2 in this example) is inversely proportional to the <a href="/wiki/Tangent" title="Tangent">tangent</a> of the angle (63.43° in this example) between the <a href="/wiki/Projection_plane" title="Projection plane">projection plane</a> (colored brown) and the projection lines (dotted).</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Oblique_projection_comparison_front.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Oblique_projection_comparison_front.svg/220px-Oblique_projection_comparison_front.svg.png" decoding="async" width="220" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Oblique_projection_comparison_front.svg/330px-Oblique_projection_comparison_front.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Oblique_projection_comparison_front.svg/440px-Oblique_projection_comparison_front.svg.png 2x" data-file-width="1134" data-file-height="567" /></a><figcaption>Front view of the same.</figcaption></figure> <p>Oblique projection is a type of <a href="/wiki/Parallel_projection" title="Parallel projection">parallel projection</a>: </p> <ul><li>it projects an image by intersecting parallel rays (projectors)</li> <li>from the three-dimensional source object with the drawing surface (projection plane).</li></ul> <p>In both oblique projection and <a href="/wiki/Orthographic_projection" title="Orthographic projection">orthographic projection</a>, parallel lines of the source object produce parallel lines in the projected image. The projectors in oblique projection intersect the projection plane at an oblique angle to produce the projected image, as opposed to the perpendicular angle used in orthographic projection. </p><p>Mathematically, the parallel projection of the point <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x,y,z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x,y,z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22a8c93372e8f8b6e24d523bd5545aed3430baf4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.45ex; height:2.843ex;" alt="{\displaystyle (x,y,z)}" /></span> on the <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle xy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle xy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c72eb345e496513fb8b2fa4aa8c4d89b855f9a01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.485ex; height:2.009ex;" alt="{\displaystyle xy}" /></span>-plane gives <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x+az,y+bz,0)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mi>a</mi> <mi>z</mi> <mo>,</mo> <mi>y</mi> <mo>+</mo> <mi>b</mi> <mi>z</mi> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x+az,y+bz,0)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c3706363efc66b2abb07cd02e2938aa6c00cc0b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.609ex; height:2.843ex;" alt="{\displaystyle (x+az,y+bz,0)}" /></span>. The constants <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}" /></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}" /></span> uniquely specify a parallel projection. When <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a=b=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mi>b</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a=b=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9c78ffbb4fc115e8e2a630de5f90fa625effc69" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.587ex; height:2.176ex;" alt="{\displaystyle a=b=0}" /></span>, the projection is said to be "orthographic" or "orthogonal". Otherwise, it is "oblique". The constants <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}" /></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}" /></span> are not necessarily less than 1, and as a consequence lengths measured on an oblique projection may be either larger or shorter than they were in space. In a general oblique projection, spheres of the space are projected as ellipses on the drawing plane, and not as circles as they would appear from an orthogonal projection. </p><p>Oblique drawing is also the crudest "3D" drawing method but the easiest to master. One way to draw using an oblique view is to draw the side of the object in two dimensions, i.e. flat, and then draw the other sides at an angle of 45°, but instead of drawing the sides full size they are only drawn with half the depth creating 'forced depth' – adding an element of realism to the object. Even with this 'forced depth', oblique drawings look very unconvincing to the eye. For this reason oblique is rarely used by professional designers or engineers. </p> <div class="mw-heading mw-heading2"><h2 id="Oblique_pictorial">Oblique pictorial</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Oblique_projection&action=edit&section=2" title="Edit section: Oblique pictorial"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In an <i><a href="/w/index.php?title=Oblique_pictorial&action=edit&redlink=1" class="new" title="Oblique pictorial (page does not exist)">oblique pictorial</a></i> drawing, the angles displayed among the axis, as well as the <a href="/wiki/Foreshortening" class="mw-redirect" title="Foreshortening">foreshortening</a> factors (scale) are arbitrary. More precisely, any given set of three coplanar segments originating from the same point may be construed as forming some oblique perspective of three sides of a cube. This result is known as <a href="/wiki/Pohlke%27s_theorem" title="Pohlke's theorem">Pohlke's theorem</a>, from the German mathematician Pohlke, who published it in the early 19th century.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>The resulting distortions make the <a href="https://en.wiktionary.org/wiki/technique" class="extiw" title="wikt:technique">technique</a> unsuitable for formal, working drawings. Nevertheless, the distortions are partially overcome by aligning one plane of the image parallel to the plane of projection. Doing so creates a true shape image of the chosen plane. This specific category of oblique projections, whereby lengths along the directions <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" /></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}" /></span> are preserved, but lengths along direction <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}" /></span> are drawn at angle using a reduction factor is very much in use for industrial drawings. </p> <ul><li><i>Cavalier projection</i> is the name of such a projection, where the length along the <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}" /></span> axis remains unscaled.<sup id="cite_ref-pp_3-0" class="reference"><a href="#cite_note-pp-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li> <li><i>Cabinet projection</i>, popular in furniture illustrations, is an example of such a technique, where in the receding axis is scaled to half-size<sup id="cite_ref-pp_3-1" class="reference"><a href="#cite_note-pp-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> (sometimes instead two-thirds the original).<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Cavalier_projection">Cavalier projection</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Oblique_projection&action=edit&section=3" title="Edit section: Cavalier projection"><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">Further information: <a href="/wiki/Mathematics_and_art" title="Mathematics and art">Mathematics and art</a></div> <p>In <b>cavalier projection</b> (sometimes <b>cavalier perspective</b> or <b>high view point</b>) a point of the object is represented by three coordinates, <i>x</i>, <i>y</i> and <i>z</i>. On the drawing, it is represented by only two coordinates, <i>x″</i> and <i>y″</i>. On the flat drawing, two axes, <i>x</i> and <i>z</i> on the figure, are <a href="/wiki/Perpendicular" title="Perpendicular">perpendicular</a> and the length on these axes are drawn with a 1:1 scale; it is thus similar to the <a href="/wiki/Dimetric_projection" class="mw-redirect" title="Dimetric projection">dimetric projections</a>, although it is not an <a href="/wiki/Axonometric_projection" title="Axonometric projection">axonometric projection</a>, as the third axis, here <i>y</i>, is drawn in diagonal, making an arbitrary angle with the <i>x″</i> axis, usually 30 or 45°. The length of the third axis is not scaled.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>It is very easy to draw, especially with pen and paper. It is thus often used when a figure must be drawn by hand, e.g. on a black board (lesson, oral examination). </p><p>The representation was initially used for military <a href="/wiki/Fortification" title="Fortification">fortifications</a>. In French, the "cavalier" (literally <i>rider, horseman</i>, see <i><a href="/wiki/Cavalry" title="Cavalry">Cavalry</a></i>) is an artificial hill behind the walls that allows sighting of the enemy above the walls.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The cavalier perspective was the way the things were seen from this high point. Some also explain the name by the fact that it was the way a rider could see a small object on the ground from his horseback.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Cabinet_projection">Cabinet projection</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Oblique_projection&action=edit&section=4" title="Edit section: Cabinet projection"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The term <i>cabinet projection</i> stems from its use in illustrations by the furniture industry.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Like cavalier perspective, one face of the projected object is parallel to the viewing plane, and the third axis is projected as going off at an angle (typically <style data-mw-deduplicate="TemplateStyles:r886049734">.mw-parser-output .monospaced{font-family:monospace,monospace}</style><span class="monospaced">atan(2)</span> or about ~63.4°). Unlike cavalier projection, where the third axis keeps its length, with cabinet projection the length of the receding lines is cut in half. </p> <div class="mw-heading mw-heading3"><h3 id="Mathematical_formula">Mathematical formula</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Oblique_projection&action=edit&section=5" title="Edit section: Mathematical formula"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As a formula, if the plane facing the viewer is <i>xy</i>, and the receding axis is <i>z</i>, then a point <i>P</i> is projected like this: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P{\begin{pmatrix}x\\y\\z\end{pmatrix}}={\begin{pmatrix}x+{\frac {1}{2}}z\cos \alpha \\y+{\frac {1}{2}}z\sin \alpha \\0\end{pmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>x</mi> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>x</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>z</mi> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>z</mi> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P{\begin{pmatrix}x\\y\\z\end{pmatrix}}={\begin{pmatrix}x+{\frac {1}{2}}z\cos \alpha \\y+{\frac {1}{2}}z\sin \alpha \\0\end{pmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a379c187d7dcd4c7f6494aeb10ba4006f218248c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.838ex; width:28.099ex; height:10.843ex;" alt="{\displaystyle P{\begin{pmatrix}x\\y\\z\end{pmatrix}}={\begin{pmatrix}x+{\frac {1}{2}}z\cos \alpha \\y+{\frac {1}{2}}z\sin \alpha \\0\end{pmatrix}}}" /></span></dd></dl> <p>Where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span> is the mentioned angle. </p><p>The <a href="/wiki/Transformation_matrix" title="Transformation matrix">transformation matrix</a> is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P={\begin{bmatrix}1&0&{\frac {1}{2}}\cos \alpha \\0&1&{\frac {1}{2}}\sin \alpha \\0&0&0\end{bmatrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={\begin{bmatrix}1&0&{\frac {1}{2}}\cos \alpha \\0&1&{\frac {1}{2}}\sin \alpha \\0&0&0\end{bmatrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45927f16936c724de8cda0452075511f0de33e24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.838ex; width:22.697ex; height:10.843ex;" alt="{\displaystyle P={\begin{bmatrix}1&0&{\frac {1}{2}}\cos \alpha \\0&1&{\frac {1}{2}}\sin \alpha \\0&0&0\end{bmatrix}}}" /></span></dd></dl> <p>Alternatively one could remove one third from the leading arm projected off the starting face, thus giving the same result. </p> <div class="mw-heading mw-heading2"><h2 id="Military_projection">Military projection</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Oblique_projection&action=edit&section=6" title="Edit section: Military projection"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the <i>military projection</i>, the angles of the <i>x</i> and <i>z</i>-axis and <i>y</i> and <i>z</i> -axis are at 45°, meaning that the angle between the <i>x</i>-axis and the <i>y</i>-axis is 90°. That is, the <i>xy</i>-plane is not skewed. It is rotated over 45°, though.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Oblique_projection&action=edit&section=7" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Besides technical drawing and illustrations, <a href="/wiki/Video_game" title="Video game">video games</a> (especially those preceding the advent of 3D games) also often use a form of oblique projection. Examples include <i><a href="/wiki/SimCity_(1989_video_game)" title="SimCity (1989 video game)">SimCity</a></i>, <i><a href="/wiki/Ultima_VII" class="mw-redirect" title="Ultima VII">Ultima VII</a></i>, <i><a href="/wiki/Ultima_Online" title="Ultima Online">Ultima Online</a></i>, <i><a href="/wiki/EarthBound" title="EarthBound">EarthBound</a></i>, <i><a href="/wiki/Paperboy_(video_game)" title="Paperboy (video game)">Paperboy</a></i> and, more recently, <i><a href="/wiki/Tibia_(video_game)" title="Tibia (video game)">Tibia</a></i>. </p> <ul class="gallery mw-gallery-traditional" style="padding:0px;"> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Perspective_cavaliere_exemple_piece_revolution.svg" class="mw-file-description" title="The figures to the left are orthographic projections. The figure to the right is an oblique projection with an angle of 30° and a ratio of 1⁄2."><img alt="The figures to the left are orthographic projections. The figure to the right is an oblique projection with an angle of 30° and a ratio of 1⁄2." src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Perspective_cavaliere_exemple_piece_revolution.svg/109px-Perspective_cavaliere_exemple_piece_revolution.svg.png" decoding="async" width="109" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Perspective_cavaliere_exemple_piece_revolution.svg/164px-Perspective_cavaliere_exemple_piece_revolution.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Perspective_cavaliere_exemple_piece_revolution.svg/218px-Perspective_cavaliere_exemple_piece_revolution.svg.png 2x" data-file-width="505" data-file-height="555" /></a></span></div> <div class="gallerytext">The figures to the left are <a href="/wiki/Orthographic_projection" title="Orthographic projection">orthographic projections</a>. The figure to the right is an <b>oblique projection</b> with an angle of 30° and a ratio of <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span>.</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Potting-bench-cabinet-view.png" class="mw-file-description" title="Potting bench drawn in cabinet projection with an angle of 45° and a ratio of 2/3."><img alt="Potting bench drawn in cabinet projection with an angle of 45° and a ratio of 2/3." src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Potting-bench-cabinet-view.png/120px-Potting-bench-cabinet-view.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Potting-bench-cabinet-view.png/180px-Potting-bench-cabinet-view.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Potting-bench-cabinet-view.png/240px-Potting-bench-cabinet-view.png 2x" data-file-width="1224" data-file-height="1224" /></a></span></div> <div class="gallerytext"><a href="/wiki/Potting_bench" title="Potting bench">Potting bench</a> drawn in <b>cabinet projection</b> with an angle of 45° and a ratio of 2/3.</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Perspective_cavaliere_fortification.jpg" class="mw-file-description" title="Pieces of fortification in cavalier perspective (Cyclopaedia vol. 1, 1728)."><img alt="Pieces of fortification in cavalier perspective (Cyclopaedia vol. 1, 1728)." src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Perspective_cavaliere_fortification.jpg/200px-Perspective_cavaliere_fortification.jpg" decoding="async" width="200" height="97" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Perspective_cavaliere_fortification.jpg/300px-Perspective_cavaliere_fortification.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Perspective_cavaliere_fortification.jpg/400px-Perspective_cavaliere_fortification.jpg 2x" data-file-width="742" data-file-height="361" /></a></span></div> <div class="gallerytext">Pieces of fortification in <b>cavalier perspective</b> (<i><a href="/wiki/Cyclopaedia,_or_an_Universal_Dictionary_of_Arts_and_Sciences" class="mw-redirect" title="Cyclopaedia, or an Universal Dictionary of Arts and Sciences">Cyclopaedia</a></i> vol. 1, 1728).</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Perspective_cavaliere_report_coordonnees_90deg.svg" class="mw-file-description" title="How the coordinates are used to place a point on a cavalier perspective."><img alt="How the coordinates are used to place a point on a cavalier perspective." src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Perspective_cavaliere_report_coordonnees_90deg.svg/181px-Perspective_cavaliere_report_coordonnees_90deg.svg.png" decoding="async" width="181" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Perspective_cavaliere_report_coordonnees_90deg.svg/271px-Perspective_cavaliere_report_coordonnees_90deg.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Perspective_cavaliere_report_coordonnees_90deg.svg/361px-Perspective_cavaliere_report_coordonnees_90deg.svg.png 2x" data-file-width="556" data-file-height="370" /></a></span></div> <div class="gallerytext">How the coordinates are used to place a point on a <b>cavalier perspective</b>.</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Milit%C3%A4rperspektive.PNG" class="mw-file-description" title="Stone arch drawn in military perspective."><img alt="Stone arch drawn in military perspective." src="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Milit%C3%A4rperspektive.PNG/80px-Milit%C3%A4rperspektive.PNG" decoding="async" width="80" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Milit%C3%A4rperspektive.PNG/121px-Milit%C3%A4rperspektive.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/97/Milit%C3%A4rperspektive.PNG/161px-Milit%C3%A4rperspektive.PNG 2x" data-file-width="300" data-file-height="447" /></a></span></div> <div class="gallerytext">Stone arch drawn in <b>military perspective</b>.</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Cabinet_perspective_45.svg" class="mw-file-description" title="Stone arch drawn in cabinet perspective."><img alt="Stone arch drawn in cabinet perspective." src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Cabinet_perspective_45.svg/143px-Cabinet_perspective_45.svg.png" decoding="async" width="143" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Cabinet_perspective_45.svg/214px-Cabinet_perspective_45.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/Cabinet_perspective_45.svg/286px-Cabinet_perspective_45.svg.png 2x" data-file-width="480" data-file-height="403" /></a></span></div> <div class="gallerytext">Stone arch drawn in <b>cabinet perspective</b>.</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Korean_art-Donggwoldo-Changdeokgung_and_Changgyeonggung-Dong-A_University-01.jpg" class="mw-file-description" title="A representative Korean painting depicting the two royal palaces, Changdeokgung and Changgyeonggung located in the east of the main palace, Gyeongbokgung."><img alt="A representative Korean painting depicting the two royal palaces, Changdeokgung and Changgyeonggung located in the east of the main palace, Gyeongbokgung." src="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Korean_art-Donggwoldo-Changdeokgung_and_Changgyeonggung-Dong-A_University-01.jpg/200px-Korean_art-Donggwoldo-Changdeokgung_and_Changgyeonggung-Dong-A_University-01.jpg" decoding="async" width="200" height="95" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Korean_art-Donggwoldo-Changdeokgung_and_Changgyeonggung-Dong-A_University-01.jpg/300px-Korean_art-Donggwoldo-Changdeokgung_and_Changgyeonggung-Dong-A_University-01.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/11/Korean_art-Donggwoldo-Changdeokgung_and_Changgyeonggung-Dong-A_University-01.jpg/400px-Korean_art-Donggwoldo-Changdeokgung_and_Changgyeonggung-Dong-A_University-01.jpg 2x" data-file-width="9823" data-file-height="4652" /></a></span></div> <div class="gallerytext">A representative <a href="/wiki/Korea" title="Korea">Korean</a> painting depicting the two royal palaces, <a href="/wiki/Changdeokgung" title="Changdeokgung">Changdeokgung</a> and <a href="/wiki/Changgyeonggung" title="Changgyeonggung">Changgyeonggung</a> located in the east of the main palace, <a href="/wiki/Gyeongbokgung" title="Gyeongbokgung">Gyeongbokgung</a>.</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Xu_Yang_-_Entrance_and_yard_of_a_yamen.jpg" class="mw-file-description" title="Entrance and yard of a yamen. Detail of scroll about Suzhou by Xu Yang, ordered by the Qianlong Emperor. 18th century"><img alt="Entrance and yard of a yamen. Detail of scroll about Suzhou by Xu Yang, ordered by the Qianlong Emperor. 18th century" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Xu_Yang_-_Entrance_and_yard_of_a_yamen.jpg/169px-Xu_Yang_-_Entrance_and_yard_of_a_yamen.jpg" decoding="async" width="169" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Xu_Yang_-_Entrance_and_yard_of_a_yamen.jpg/254px-Xu_Yang_-_Entrance_and_yard_of_a_yamen.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/53/Xu_Yang_-_Entrance_and_yard_of_a_yamen.jpg/338px-Xu_Yang_-_Entrance_and_yard_of_a_yamen.jpg 2x" data-file-width="3519" data-file-height="2498" /></a></span></div> <div class="gallerytext"><i>Entrance and yard of a yamen</i>. Detail of scroll about <a href="/wiki/Suzhou" title="Suzhou">Suzhou</a> by Xu Yang, ordered by the <a href="/wiki/Qianlong_Emperor" title="Qianlong Emperor">Qianlong Emperor</a>. 18th century</div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Plan_Port-Royal-des-Champs.jpg" class="mw-file-description" title="18th century plan of Port-Royal-des-Champs drawn in military projection"><img alt="18th century plan of Port-Royal-des-Champs drawn in military projection" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Plan_Port-Royal-des-Champs.jpg/78px-Plan_Port-Royal-des-Champs.jpg" decoding="async" width="78" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Plan_Port-Royal-des-Champs.jpg/117px-Plan_Port-Royal-des-Champs.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Plan_Port-Royal-des-Champs.jpg/156px-Plan_Port-Royal-des-Champs.jpg 2x" data-file-width="783" data-file-height="1201" /></a></span></div> <div class="gallerytext">18th century plan of <a href="/wiki/Port-Royal-des-Champs" title="Port-Royal-des-Champs">Port-Royal-des-Champs</a> drawn in <b>military projection</b></div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:SimCity-Indigo.gif" class="mw-file-description" title="A variation of military projection is used in the video game SimCity"><img alt="A variation of military projection is used in the video game SimCity" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/SimCity-Indigo.gif/160px-SimCity-Indigo.gif" decoding="async" width="160" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/SimCity-Indigo.gif/240px-SimCity-Indigo.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/SimCity-Indigo.gif/320px-SimCity-Indigo.gif 2x" data-file-width="1024" data-file-height="768" /></a></span></div> <div class="gallerytext">A variation of <b>military projection</b> is used in the video game <i>SimCity</i></div> </li> <li class="gallerybox" style="width: 235px"> <div class="thumb" style="width: 230px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Arteria_lusoria_MRA_MIP-03_-_Annotated.jpg" class="mw-file-description" title="A 3D rendered magnetic resonance angiography, shown in an oblique projection in order to distinguish the aberrant subclavian artery"><img alt="A 3D rendered magnetic resonance angiography, shown in an oblique projection in order to distinguish the aberrant subclavian artery" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Arteria_lusoria_MRA_MIP-03_-_Annotated.jpg/164px-Arteria_lusoria_MRA_MIP-03_-_Annotated.jpg" decoding="async" width="164" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Arteria_lusoria_MRA_MIP-03_-_Annotated.jpg/245px-Arteria_lusoria_MRA_MIP-03_-_Annotated.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Arteria_lusoria_MRA_MIP-03_-_Annotated.jpg/327px-Arteria_lusoria_MRA_MIP-03_-_Annotated.jpg 2x" data-file-width="1268" data-file-height="931" /></a></span></div> <div class="gallerytext">A <a href="/wiki/3D_rendering" title="3D rendering">3D rendered</a> <a href="/wiki/Magnetic_resonance_angiography" title="Magnetic resonance angiography">magnetic resonance angiography</a>, shown in an oblique projection in order to distinguish the <a href="/wiki/Aberrant_subclavian_artery" title="Aberrant subclavian artery">aberrant subclavian artery</a></div> </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=Oblique_projection&action=edit&section=8" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Space-oblique_Mercator_projection" title="Space-oblique Mercator projection">Space-oblique Mercator projection</a></li> <li><a href="/wiki/Oblique_Mercator_projection" title="Oblique Mercator projection">Oblique Mercator projection</a></li> <li><a href="/wiki/Hatsusabur%C5%8D_Yoshida" title="Hatsusaburō Yoshida">Hatsusaburō Yoshida</a></li> <li><a href="/wiki/List_of_art_techniques" title="List of art techniques">List of art techniques</a></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=Oblique_projection&action=edit&section=9" 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"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Cucker299-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Cucker299_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="CITEREFCucker2013" class="citation book cs1"><a href="/wiki/Felipe_Cucker" title="Felipe Cucker">Cucker, Felipe</a> (2013). <i>Manifold Mirrors: The Crossing Paths of the Arts and Mathematics</i>. Cambridge University Press. pp. <span class="nowrap">269–</span>278. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-72876-8" title="Special:BookSources/978-0-521-72876-8"><bdi>978-0-521-72876-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Manifold+Mirrors%3A+The+Crossing+Paths+of+the+Arts+and+Mathematics&rft.pages=%3Cspan+class%3D%22nowrap%22%3E269-%3C%2Fspan%3E278&rft.pub=Cambridge+University+Press&rft.date=2013&rft.isbn=978-0-521-72876-8&rft.aulast=Cucker&rft.aufirst=Felipe&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOblique+projection" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/PohlkesTheorem.html">Weisstein, Eric W. "Pohlke's Theorem". From MathWorld—A Wolfram Web Resource.</a></span> </li> <li id="cite_note-pp-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-pp_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-pp_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.mtsu.edu/~csjudy/planeview3D/tutorial-parallel.html">Parallel Projections</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070423160654/http://www.mtsu.edu/~csjudy/planeview3D/tutorial-parallel.html">Archived</a> 23 April 2007 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> from <i>PlaneView3D Online</i></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBolton1995" class="citation cs2">Bolton, William (1995), <i>Basic Engineering</i>, Butterworth-Heinemann GNVQ Engineering Series, BH Newnes, p. 140, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780750625845" title="Special:BookSources/9780750625845"><bdi>9780750625845</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Basic+Engineering&rft.series=Butterworth-Heinemann+GNVQ+Engineering+Series&rft.pages=140&rft.pub=BH+Newnes&rft.date=1995&rft.isbn=9780750625845&rft.aulast=Bolton&rft.aufirst=William&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOblique+projection" class="Z3988"></span>.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100822152816/http://www.tpub.com/">"Repair and Maintenance Manuals - Integrated Publishing"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.tpub.com:80/">the original</a> on 22 August 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">22 August</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Repair+and+Maintenance+Manuals+-+Integrated+Publishing&rft_id=http%3A%2F%2Fwww.tpub.com%3A80%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOblique+projection" class="Z3988"></span> from <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100822152816/http://www.tpub.com/">"Repair and Maintenance Manuals - Integrated Publishing"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.tpub.com:80/">the original</a> on 22 August 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">22 August</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Repair+and+Maintenance+Manuals+-+Integrated+Publishing&rft_id=http%3A%2F%2Fwww.tpub.com%3A80%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOblique+projection" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Ingrid Carlbom, Joseph Paciorek, Planar Geometric Projections and Viewing Transformations, <a href="/wiki/ACM_Computing_Surveys" title="ACM Computing Surveys">ACM Computing Surveys</a>, v.10 n.4, pp. 465–502, Dec. 1978</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://trucsmaths.free.fr/etymologie.htm#C">Etymologie des maths, letter C</a> (French)</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://mapage.noos.fr/r.ferreol/langage/notations/notations.htm">DES QUESTIONS D'ORIGINES</a> (French)</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFChingJuroszek2011" class="citation cs2">Ching, Francis D. K.; Juroszek, Steven P. (2011), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=T7TJYHdhgw8C&pg=PA205"><i>Design Drawing</i></a> (2nd ed.), John Wiley & Sons, p. 205, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781118007372" title="Special:BookSources/9781118007372"><bdi>9781118007372</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Design+Drawing&rft.pages=205&rft.edition=2nd&rft.pub=John+Wiley+%26+Sons&rft.date=2011&rft.isbn=9781118007372&rft.aulast=Ching&rft.aufirst=Francis+D.+K.&rft.au=Juroszek%2C+Steven+P.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DT7TJYHdhgw8C%26pg%3DPA205&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOblique+projection" class="Z3988"></span>.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.compuphase.com/axometr.htm">"The Geometry of Perspective Drawing on the Computer"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">24 April</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Geometry+of+Perspective+Drawing+on+the+Computer&rft_id=http%3A%2F%2Fwww.compuphase.com%2Faxometr.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOblique+projection" class="Z3988"></span></span> </li> </ol></div></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=Oblique_projection&action=edit&section=10" title="Edit section: Further reading"><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"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><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" /></a></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:Oblique_projection" class="extiw" title="commons:Category:Oblique projection">Oblique projection</a></span>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735" /><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409" /> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><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" /></a></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:Cabinet_projection" class="extiw" title="commons:Category:Cabinet projection">Cabinet projection</a></span>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735" /><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409" /> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><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" /></a></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:Cavalier_perspective" class="extiw" title="commons:Category:Cavalier perspective">Cavalier perspective</a></span>.</div></div> </div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFoley1997" class="citation book cs1">Foley, James (1997). <i>Computer Graphics</i>. Boston: Addison-Wesley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-201-84840-6" title="Special:BookSources/0-201-84840-6"><bdi>0-201-84840-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computer+Graphics&rft.place=Boston&rft.pub=Addison-Wesley&rft.date=1997&rft.isbn=0-201-84840-6&rft.aulast=Foley&rft.aufirst=James&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOblique+projection" class="Z3988"></span></li> <li>Ingrid Carlbom, Joseph Paciorek, Planar Geometric Projections and Viewing Transformations, <a href="/wiki/ACM_Computing_Surveys" title="ACM Computing Surveys">ACM Computing Surveys</a>, v.10 n.4, p. 465–502, Dec. 1978</li> <li>Alpha et al. 1988, <a rel="nofollow" class="external text" href="https://pubs.usgs.gov/imap/1799/report.pdf"><i>Atlas of Oblique Maps, A Collection of Landform Portrayals of Selected Areas of the World</i></a> (<a href="/wiki/US_Geological_Survey" class="mw-redirect" title="US Geological Survey">US Geological Survey</a>)</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Oblique_projection&action=edit&section=11" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100822152816/http://www.tpub.com//content/draftsman/14276/css/14276_308.htm">Illustrator Draftsman 3 & 2 – Volume 2 Standard Practices and Theory, page 68</a> from <a rel="nofollow" class="external free" href="https://web.archive.org/web/20100822152816/http://www.tpub.com:80/">https://web.archive.org/web/20100822152816/http://www.tpub.com:80/</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" 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class="mw-redirect" title="Data visualization">Data visualization</a></li> <li><a href="/wiki/Visualization_(graphics)" title="Visualization (graphics)">Educational visualization</a></li> <li><a href="/wiki/Flow_visualization" title="Flow visualization">Flow visualization</a></li> <li><a href="/wiki/Geovisualization" title="Geovisualization">Geovisualization</a></li> <li><a href="/wiki/Information_visualization" class="mw-redirect" title="Information visualization">Information visualization</a></li> <li><a href="/wiki/Mathematical_diagram" title="Mathematical diagram">Mathematical visualization</a></li> <li><a href="/wiki/Medical_imaging" title="Medical imaging">Medical imaging</a></li> <li><a href="/wiki/Molecular_graphics" title="Molecular graphics">Molecular graphics</a></li> <li><a href="/wiki/Visualization_(graphics)" title="Visualization (graphics)">Product visualization</a></li> <li><a href="/wiki/Scientific_visualization" title="Scientific visualization">Scientific visualization</a></li> <li><a href="/wiki/Social_visualization" title="Social visualization">Social visualization</a></li> <li><a href="/wiki/Software_visualization" title="Software visualization">Software visualization</a></li> <li><a href="/wiki/Technical_drawing" title="Technical drawing">Technical drawing</a></li> <li><a href="/wiki/User_interface_design" title="User interface design">User interface design</a></li> <li><a href="/wiki/Visual_culture" title="Visual culture">Visual culture</a></li> <li><a href="/wiki/Volume_rendering" title="Volume rendering">Volume visualization</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Image <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="/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="/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="/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="/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/Information_art" title="Information art">Information art</a></li> <li><a href="/wiki/Infographic" title="Infographic">Information graphics</a></li> <li><a href="/wiki/Information_science" title="Information science">Information science</a></li> <li><a href="/wiki/Misleading_graph" title="Misleading graph">Misleading graph</a></li> <li><a href="/wiki/Neuroimaging" title="Neuroimaging">Neuroimaging</a></li> <li><a href="/wiki/Patent_drawing" title="Patent drawing">Patent drawing</a></li> <li><a href="/wiki/Scientific_modelling" title="Scientific modelling">Scientific modelling</a></li> <li><a href="/wiki/Spatial_analysis" title="Spatial analysis">Spatial analysis</a></li> <li><a href="/wiki/Visual_analytics" title="Visual analytics">Visual analytics</a></li> <li><a href="/wiki/Visual_perception" title="Visual perception">Visual perception</a></li> <li><a href="/wiki/Volume_cartography" title="Volume cartography">Volume cartography</a></li> <li><a href="/wiki/Volume_rendering" title="Volume rendering">Volume rendering</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; 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