{"id":8676,"date":"2024-03-24T23:33:13","date_gmt":"2024-03-24T23:33:13","guid":{"rendered":"https:\/\/williamcromar.com\/newmediawiki\/?p=8676"},"modified":"2024-03-24T23:33:19","modified_gmt":"2024-03-24T23:33:19","slug":"chapter-13-metaphors-to-drawing","status":"publish","type":"post","link":"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/","title":{"rendered":"CHAPTER 13 \u2014 Metaphors to Drawing"},"content":{"rendered":"\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title\" style=\"cursor:inherit\">Contents<\/div>\n<label for=\"ez-toc-cssicon-toggle-item-69f52d7a7d316\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"ez-toc-cssicon\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-69f52d7a7d316\"  aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Perspective_in_perspective\" >Perspective in perspective<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Why_bother\" >Why bother?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#The_structure_of_the_visible_world\" >The structure of the visible world<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Projection_rival_geometries\" >Projection: rival geometries<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#More-than-three_dimensions\" >More-than-three dimensions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Dimensions_by_analogy\" >Dimensions by analogy<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Rivals_%E2%80%94_or_allies\" >Rivals \u2014 or allies?<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Projection_the_origin_of_art\" >Projection: the origin of art<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Projection_drawing_systems\" >Projection: drawing systems<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Perspective_projection\" >Perspective projection<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Mirrors_and_windows\" >Mirrors and windows<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#A_picture_plane\" >A picture plane<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Three-point_perspective\" >Three-point perspective<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Two-point_perspective\" >Two-point perspective<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#One-point_perspective\" >One-point perspective<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Parallel_projection\" >Parallel projection<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Zero-point_%E2%80%9Cperspective%E2%80%9D\" >Zero-point \u201cperspective\u201d<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Axonometric_projection\" >Axonometric projection<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#%E2%80%9CImpossible%E2%80%9D_shapes\" >&#8220;Impossible&#8221; shapes<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Oblique_and_orthographic_projection\" >Oblique and orthographic projection<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/#Reference_planes_in_3D_modeling\" >Reference planes in 3D modeling<\/a><\/li><\/ul><\/nav><\/div>\n\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-right has-small-font-size\"><em>18-minute read<\/em><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"694\" height=\"694\" data-attachment-id=\"30\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/nmw\/paralleluniverses_01\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/07\/parallelUniverses_01.png\" data-orig-size=\"694,694\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"parallelUniverses_01\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/07\/parallelUniverses_01.png\" src=\"https:\/\/i0.wp.com\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/07\/parallelUniverses_01.png?resize=694%2C694&amp;ssl=1\" alt=\"\" class=\"wp-image-30\" style=\"width:416px;height:auto\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/07\/parallelUniverses_01.png 694w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/07\/parallelUniverses_01-300x300.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/07\/parallelUniverses_01-150x150.png 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/07\/parallelUniverses_01-100x100.png 100w\" sizes=\"auto, (max-width: 694px) 100vw, 694px\" \/><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Perspective_in_perspective\"><\/span>Perspective in perspective<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2000\" height=\"739\" data-attachment-id=\"8701\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/dp816489\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/DP816489.jpg\" data-orig-size=\"2000,739\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"DP816489\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/DP816489-1024x378.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/DP816489.jpg\" alt=\"\" class=\"wp-image-8701\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/DP816489.jpg 2000w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/DP816489-300x111.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/DP816489-1024x378.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/DP816489-768x284.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/DP816489-1536x568.jpg 1536w\" sizes=\"auto, (max-width: 2000px) 100vw, 2000px\" \/><figcaption class=\"wp-element-caption\"><em>Albrecht D\u00fcrer,&nbsp;<strong><a href=\"https:\/\/www.metmuseum.org\/art\/collection\/search\/366555\" target=\"_blank\" rel=\"noreferrer noopener\">Artist and Nude<\/a><\/strong>,&nbsp;circa&nbsp;1525<\/em><\/figcaption><\/figure>\n<\/div>\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p>Albrecht&nbsp;D\u00fcrer was known as the &#8220;da Vinci of the North&#8221; because he was fascinated with, and contributed to, the relationship between art and science. Like da Vinci, he was not only a skilled draughtsman but an inventor as well. He applied his energy to elaborate drawing &#8220;machines&#8221; that could capture perspective, the way of seeing that defined Renaissance image-making. We can still make and use these machines today.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"742\" height=\"379\" data-attachment-id=\"8705\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/ch13_004\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch13_004.jpg\" data-orig-size=\"742,379\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"ch13_004\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch13_004.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch13_004.jpg\" alt=\"\" class=\"wp-image-8705\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch13_004.jpg 742w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch13_004-300x153.jpg 300w\" sizes=\"auto, (max-width: 742px) 100vw, 742px\" \/><figcaption class=\"wp-element-caption\"><em>We see a modern version of the&nbsp;D\u00fcrer device here on&nbsp;the <strong>left<\/strong>. A drawing produced with it is seen at&nbsp;the <strong>center<\/strong>. At <strong>right<\/strong>, after using the tool, it becomes easy to visualize perspective vanishing points and lines. It even allows the artist to indulge in fantasy (note the levitating chair in one sketch!)  \u2014 student work from a studio by the author.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p>Mechanical drawing devices, like the <strong>T-square<\/strong> and <strong>triangle<\/strong>, the <strong>parallel bar<\/strong>, and the <strong>drafting machine<\/strong> all depended upon a <strong>drafting board<\/strong>. They allowed us to create the complex mechanics of one-, two-, and three-point perspective systems. Technology solved many of the limitations of the drafting board. The <strong>centrolinead<\/strong>, for example, was developed to orient remote vanishing points requiring an improbably large surface. The knowledge gained about perspective as a system by using these elaborate mechanical tools is easily transferable to sketching.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"829\" height=\"1024\" data-attachment-id=\"8703\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/829px-architect\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/829px-Architect.png\" data-orig-size=\"829,1024\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"829px-Architect\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/829px-Architect.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/829px-Architect.png\" alt=\"\" class=\"wp-image-8703\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/829px-Architect.png 829w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/829px-Architect-243x300.png 243w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/829px-Architect-768x949.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/829px-Architect-300x371.png 300w\" sizes=\"auto, (max-width: 829px) 100vw, 829px\" \/><figcaption class=\"wp-element-caption\"><em>Unknown,&nbsp;<strong><a href=\"https:\/\/en.wikipedia.org\/wiki\/Architect\" target=\"_blank\" rel=\"noreferrer noopener\">Architect at his Drafting Board<\/a><\/strong>,&nbsp;circa 1895<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"700\" height=\"638\" data-attachment-id=\"8704\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/centrolinead\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Centrolinead.jpg\" data-orig-size=\"700,638\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"Centrolinead\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Centrolinead.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Centrolinead.jpg\" alt=\"\" class=\"wp-image-8704\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Centrolinead.jpg 700w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Centrolinead-300x273.jpg 300w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><figcaption class=\"wp-element-caption\"><em>E. G. Lutz, illustration of a <strong><a href=\"https:\/\/gurneyjourney.blogspot.com\/2010\/06\/centrolinead.html\" target=\"_blank\" rel=\"noreferrer noopener\">centrolinead<\/a><\/strong><\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Why_bother\"><\/span>Why bother?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>But why would we want to even bother with any of that? These systems and tools may seem quaint when discussing a digital interface and its use. After all, the machine is processing so much of the mechanics of projection <em>for<\/em> us. This relieves us of the dirty work of constructing a perspective matrix or a set of orthographic drawings. Yet, the illustration below demonstrates precisely <em>why<\/em> it&#8217;s a necessary topic!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"831\" height=\"1024\" data-attachment-id=\"8707\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/william_hogarth_-_absurd_perspectives\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/William_Hogarth_-_Absurd_perspectives.png\" data-orig-size=\"831,1024\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"William_Hogarth_-_Absurd_perspectives\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/William_Hogarth_-_Absurd_perspectives.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/William_Hogarth_-_Absurd_perspectives.png\" alt=\"\" class=\"wp-image-8707\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/William_Hogarth_-_Absurd_perspectives.png 831w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/William_Hogarth_-_Absurd_perspectives-243x300.png 243w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/William_Hogarth_-_Absurd_perspectives-768x946.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/William_Hogarth_-_Absurd_perspectives-300x370.png 300w\" sizes=\"auto, (max-width: 831px) 100vw, 831px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p><em>William Hogarth,&nbsp;<strong><a href=\"https:\/\/en.wikipedia.org\/wiki\/Satire_on_False_Perspective\" target=\"_blank\" rel=\"noreferrer noopener\">Satire on False Perspective<\/a><\/strong>, 1753. The caption in the engraving reads: &#8220;Whoever makes a Design without the knowledge of Perspective will be liable to such absurdities as are shewn in this Frontispiece.&#8221; This remains as true for computer modeling and rendering as it has always been for tactile media.<\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"The_structure_of_the_visible_world\"><\/span>The structure of the visible world<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The laborious methods required to create, for example, a two-point perspective image are no longer necessary. However, with their loss as a process, we risk a loss of understanding of what these systems physically encode in drawing. This includes visual principles of composition, strategies for visually structuring an object or an environment, and pragmatic&nbsp;mental tools for aiding digital workflow. As tedious as these processes might have been, they allowed us to see, in their construction, the structure of the visual world. <\/p>\n\n\n\n<p>These drawing &#8220;machines&#8221; \u2014 perspective drawing, drafting, sketching, and modeling \u2014 produced very specific output and yielded specific means of 3-D visualization. Software is simply an extension of these machines. Most 3D modeling software is capable of showing you views of your work in all of the projection modes we will discuss! Software is thus, at one level, a mash-up of all prior drawing tools. Despite that, the software behaves as a unique and new tool. Like those other drawing machines when they were introduced as new technologies, digital modeling tools are fundamentally changing the way we see the world.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Projection_rival_geometries\"><\/span><strong>Projection: rival geometries<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"More-than-three_dimensions\"><\/span>More-than-three dimensions<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><em>\u2026 physicists do not study just the 3-D space we live in. There are &#8230; spaces which have totally different geometrical properties from the physical space within which we live. Who is to say, then, that \u201cthe true geometry\u201d is defined by the space in which Uranus and Neptune orbit the sun? There is \u201cHilbert space,\u201d where quantum-mechanical wave functions undulate; there is \u201cmomentum space,\u201d where Fourier components dwell; there is \u201creciprocal space,\u201d where wave vectors cavort; there is \u201cphase space,\u201d where many-particle configurations swish; and so on. There is absolutely no reason that the geometries of all these spaces should be the same; in fact, they couldn\u2019t possibly be the same! So it is essential and vital for physicists that different and \u201crival\u201d geometries should exist.<\/em><\/p>\n<cite><em>\u2014<\/em>&nbsp;Douglas Hofstadter<\/cite><\/blockquote>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" data-attachment-id=\"8710\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/8-cell-1\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/8-cell-1.gif\" data-orig-size=\"256,256\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8-cell-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/8-cell-1.gif\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/8-cell-1.gif\" alt=\"\" class=\"wp-image-8710\"\/><figcaption class=\"wp-element-caption\"><em>Jason Hise,&nbsp;<a href=\"http:\/\/en.wikipedia.org\/wiki\/File:8-cell.gif\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Tesseract<\/strong><\/a>, 2007&nbsp;<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p>Humans don&#8217;t perceive the fourth dimension the way we perceive three-dimensional space. We can move freely up and down in height, for example, but we can only move in&nbsp;<em>one&nbsp;<\/em>direction \u2014 forward \u2014 in time. So when physicists and n-dimensional geometers discuss the full reality of the fourth dimension, they must resort to visual analogy. To see a tesseract (a four-dimensional cube) as we do in the illustration above, we can animate it. But even this does not get us to a complete understanding of what the tesseract is in dimensions&nbsp;<em>we ourselves<\/em>&nbsp;are not privileged to move freely in.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Dimensions_by_analogy\"><\/span>Dimensions by analogy<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p>An analogy: imagine the experience of seeing a shadow of a cube on the ground. If we can rotate the cube, we can see the shadow change shape. However, unless we can fully perceive the cube, the rotating shadow gives us only a limited understanding. The shadow on the ground is a <strong>Projection<\/strong> of a three-dimensional reality onto the two-dimensional surface of the ground. The best way to &#8220;read&#8221; the illustration, then, is to imagine the rotating tesseract as the projection of a four-dimensional reality onto the three-dimensional world we can perceive without restriction.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" data-attachment-id=\"8714\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/cube-shadow\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/cube-shadow.jpg\" data-orig-size=\"1836,1836\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"cube-shadow\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/cube-shadow-1024x1024.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/cube-shadow-1024x1024.jpg\" alt=\"\" class=\"wp-image-8714\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/cube-shadow-1024x1024.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/cube-shadow-300x300.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/cube-shadow-150x150.jpg 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/cube-shadow-768x768.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/cube-shadow-1536x1536.jpg 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/cube-shadow-100x100.jpg 100w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/cube-shadow.jpg 1836w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Rendering of an elevated cube casting a shadow. If we can&#8217;t see the cube, we only understand the cube shadow as a kind of irregular hexagon.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"796\" height=\"462\" data-attachment-id=\"8712\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/gravity_potential_5039037155_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gravity_potential_5039037155_o.jpg\" data-orig-size=\"796,462\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"gravity_potential_5039037155_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gravity_potential_5039037155_o.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gravity_potential_5039037155_o.jpg\" alt=\"\" class=\"wp-image-8712\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gravity_potential_5039037155_o.jpg 796w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gravity_potential_5039037155_o-300x174.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gravity_potential_5039037155_o-768x446.jpg 768w\" sizes=\"auto, (max-width: 796px) 100vw, 796px\" \/><figcaption class=\"wp-element-caption\"><em>Allen McCloud,&nbsp;<a href=\"http:\/\/en.wikipedia.org\/wiki\/File:GravityPotential.jpg\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Gravity Well<\/strong><\/a>, 2008<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p>Another example of projection helps us understand the higher-dimensional reality of gravity&#8217;s effect on the fabric of space-time. Physicists project an idea of four-dimensional space-time onto a plane, which deforms under gravity&#8217;s influence. It&#8217;s like a large, stretchy sheet of rubber would behave if we placed a bowling ball on it. Of course, it&#8217;s absurd to think of the Sun sitting on a large, deformed plane. But if we see the plane as a projection of a 4D world, the analogy makes sense.<\/p>\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Rivals_%E2%80%94_or_allies\"><\/span>Rivals \u2014 or allies?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The current state of the computing interface only allows a modeler a <em>projected<\/em> view of work. At minimum we find ourselves developing a 3D environment projected onto the 2D surface of the monitor. And, if animating, it becomes worse as we add the fourth dimension! We find ourselves in the shoes of the physicist who is trying to understand a projection of a rival dimension into one we can perceive. But we do have one advantage: we can use our experiences of space and time to help us understand the projected reality of the world we are modeling. That poor physicist will never get to experience a truly higher-dimensional world.<\/p>\n\n\n\n<p>We&#8217;ll explore two ways the concept of projection informs modeling. We&#8217;ll see how perception and representation have been informed by projection from the beginning of art. From this, we&#8217;ll understand how using projection drawing systems in 2D representation can be of fundamental pragmatic use in 3D modeling. It turns out these are not rival, but rather complementary, geometries.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Projection_the_origin_of_art\"><\/span>Projection: the origin of art<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>In his blog&nbsp;<strong><em><a href=\"http:\/\/projectionsystems.wordpress.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">projection systems<\/a><\/em><\/strong>, Pablo Garcia writes extensively on projection as<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><em>both a technique and a conceptual framework. As a representational method, it refers to the use of lines or vectors, usually straight, to translate between two- and three-dimensional information. Conceptually, it refers to a way of thinking about 3D space and its representation, relying on empirical methods; non-arithmetic and precisely articulated information that is graphically manifest. &#8230; Projection spans back to our earliest times, using shadows and celestial objects to assist humans in the depiction and manipulation of our environment. As such, the study of projection is the study of virtual reality. Since cave paintings and, later, celestial alignments of monolithic structures, and, later still, the early science of Ancient Greece, virtual reality \u2014 the ability to re-present real-world data graphically \u2014 has been a critical element of what made humans elevate beyond our ancestors.<\/em><\/p>\n<cite>\u2014 Pablo Garcia<\/cite><\/blockquote>\n\n\n\n<p>Could it be that projection is the origin of art? Consider this fable presented by Professor Garcia. <strong>Pliny the Elder<\/strong>, an officer of the Roman Empire and author, recounts in his <em><strong>Natural History<\/strong><\/em> the tale of an ancient Greek artist and the origin of painting:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><em>Butades, a potter of Sicyon, was the first who invented, at Corinth, the art of modelling portraits in the earth which he used in his trade. It was through his daughter that he made the discovery; who, being deeply in love with a young man about to depart on a long journey, traced the profile of his face, as thrown upon the wall by the light of the lamp. Upon seeing this, her father filled in the outline, by compressing clay upon the surface, and so made a face in relief, which he then hardened by fire along with other articles of pottery.<\/em><\/p>\n<cite>\u2014 Pliny the Elder<\/cite><\/blockquote>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"642\" height=\"800\" data-attachment-id=\"8718\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/allan-david-1744-1796-the-origin-of-painting\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/David_Allan_1744-1796_-_The_Origin_of_Painting_The_Maid_of_Corinth_-_NG_612_-_National_Galleries_of_Scotland.jpg\" data-orig-size=\"642,800\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;Photo Credit: National Galleries&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;Allan, David; The Origin of Painting; National Galleries of Scotland; http:\/\/www.artuk.org\/artworks\/the-origin-of-painting-209750&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;Copyright information and licence terms for this image can be found on the Art UK website at http:\/\/www.artuk.org\/artworks\/20975&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;Allan, David, 1744-1796; The Origin of Painting&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Allan, David, 1744-1796; The Origin of Painting\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Allan, David; The Origin of Painting; National Galleries of Scotland; http:\/\/www.artuk.org\/artworks\/the-origin-of-painting-209750&lt;\/p&gt;\n\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/David_Allan_1744-1796_-_The_Origin_of_Painting_The_Maid_of_Corinth_-_NG_612_-_National_Galleries_of_Scotland.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/David_Allan_1744-1796_-_The_Origin_of_Painting_The_Maid_of_Corinth_-_NG_612_-_National_Galleries_of_Scotland.jpg\" alt=\"\" class=\"wp-image-8718\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/David_Allan_1744-1796_-_The_Origin_of_Painting_The_Maid_of_Corinth_-_NG_612_-_National_Galleries_of_Scotland.jpg 642w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/David_Allan_1744-1796_-_The_Origin_of_Painting_The_Maid_of_Corinth_-_NG_612_-_National_Galleries_of_Scotland-241x300.jpg 241w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/David_Allan_1744-1796_-_The_Origin_of_Painting_The_Maid_of_Corinth_-_NG_612_-_National_Galleries_of_Scotland-300x374.jpg 300w\" sizes=\"auto, (max-width: 642px) 100vw, 642px\" \/><figcaption class=\"wp-element-caption\"><em>David Allan,&nbsp;<strong><a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:David_Allan_(1744-1796)_-_The_Origin_of_Painting_(The_Maid_of_Corinth)_-_NG_612_-_National_Galleries_of_Scotland.jpg\" target=\"_blank\" rel=\"noreferrer noopener\">Origin of Painting<\/a><\/strong>, 1775&nbsp;<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" data-attachment-id=\"8717\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/schinkel_origin_of_painting_4986329844\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/schinkel_origin_of_painting_4986329844.jpg\" data-orig-size=\"\" data-comments-opened=\"1\" data-image-meta=\"[]\" data-image-title=\"schinkel_origin_of_painting_4986329844\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/schinkel_origin_of_painting_4986329844.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/schinkel_origin_of_painting_4986329844.jpg\" alt=\"\" class=\"wp-image-8717\"\/><figcaption class=\"wp-element-caption\"><em>Karl Schinkel,&nbsp;<strong><a href=\"https:\/\/arthur.io\/art\/karl-friedrich-schinkel\/origin-of-painting\">Origin of Painting<\/a><\/strong>, 1830<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p>Discussing Butades, Professor Garcia references architectural historian Robert Evans, who<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><em>&#8230; in his essay \u201cTranslations from Drawing to Building\u201d makes an astute observation regarding the Schinkel version shown above. In comparing it to David Allen\u2019s rendition, he notes that Schinkel, an architect, is the only of his contemporaries to depict the shadow as cast by the sun. Allen and others use the point source of a lamp. Evans uses this discrepancy to explain the two major paradigms of projection: parallel (orthography) and centric&nbsp;<\/em>[perspective]<em>&nbsp;projection. The artist uses the converging lines to make enlargements and reductions in the scale of the image, by changing the physical relationships between light, subject, and wall. The architect requires precision in scale for transmission of information. The sun provides this control, so it doesn\u2019t matter where the subject is; the sun\u2019s rays are parallel, guaranteeing a precise same-scale reproduction when the shadow reaches its screen.<\/em><\/p>\n<cite>\u2014 Pablo Garcia<\/cite><\/blockquote>\n\n\n\n<p>As we&#8217;ll discuss below, you will use <a href=\"http:\/\/en.wikipedia.org\/wiki\/Parallel_projection\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>parallel projection<\/strong><\/a> drawing strategies to create&nbsp;<strong><a href=\"http:\/\/en.wikipedia.org\/wiki\/Multiview_orthographic_projection\" target=\"_blank\" rel=\"noreferrer noopener\">orthographic<\/a> image<em> <\/em>planes<\/strong>&nbsp;for 3D model creation. You will also use concepts from&nbsp;<a href=\"http:\/\/en.wikipedia.org\/wiki\/Perspective_%28graphical%29\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>perspective projection<\/strong><\/a>&nbsp;to create <strong>camera views<\/strong>&nbsp;for representing the finished model. In 3D modeling, understanding both becomes a critical skill.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"520\" height=\"312\" data-attachment-id=\"8722\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/perspective_foreshortening_5040788521_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/perspective_foreshortening_5040788521_o.jpg\" data-orig-size=\"520,312\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"perspective_foreshortening_5040788521_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/perspective_foreshortening_5040788521_o.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/perspective_foreshortening_5040788521_o.jpg\" alt=\"\" class=\"wp-image-8722\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/perspective_foreshortening_5040788521_o.jpg 520w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/perspective_foreshortening_5040788521_o-300x180.jpg 300w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p><em>The parallel projection of a cube on&nbsp;the left&nbsp;displays no perspective foreshortening, while on&nbsp;the <strong>right<\/strong>&nbsp;it is seen with&nbsp;<a href=\"http:\/\/en.wikipedia.org\/wiki\/File:Perspective-foreshortening.svg\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>perspective foreshortening<\/strong><\/a>.<\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"320\" height=\"320\" data-attachment-id=\"8723\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/orthographic_camera_distance_focal_length\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Orthographic_camera_distance_focal_length.gif\" data-orig-size=\"320,320\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Orthographic_camera_distance_focal_length\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Orthographic_camera_distance_focal_length.gif\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/5\/5e\/Orthographic_camera_distance_focal_length.gif\" alt=\"\" class=\"wp-image-8723\"\/><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p><em>We can see the <a href=\"http:\/\/en.wikipedia.org\/wiki\/File:Orthographic_camera_distance_focal_length.gif\" target=\"_blank\" rel=\"noreferrer noopener\">relationship<\/a> between parallel and perspective views in this animation. A parallel projection corresponds to a hypothetical perspective projection where the camera lies an infinite distance away from the object and has an infinite focal length. The modeling viewport can manipulate views such as this. The animation cycle starts with a <strong>three-point perspective<\/strong> and ends with the type of parallel projection known as an <strong>isometric<\/strong>.<\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Projection_drawing_systems\"><\/span>Projection: drawing systems<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"292\" data-attachment-id=\"8725\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/erica_gohdes_reading_between_the_outlines_5041720944_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/erica_gohdes_reading_between_the_outlines_5041720944_o.jpg\" data-orig-size=\"800,292\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;3&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;KODAK Z7590 ZOOM DIGITAL CAMERA&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1178462181&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;8.5&quot;,&quot;iso&quot;:&quot;140&quot;,&quot;shutter_speed&quot;:&quot;0.04&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"erica_gohdes_reading_between_the_outlines_5041720944_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/erica_gohdes_reading_between_the_outlines_5041720944_o.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/erica_gohdes_reading_between_the_outlines_5041720944_o.jpg\" alt=\"\" class=\"wp-image-8725\" style=\"width:1000px\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/erica_gohdes_reading_between_the_outlines_5041720944_o.jpg 800w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/erica_gohdes_reading_between_the_outlines_5041720944_o-300x110.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/erica_gohdes_reading_between_the_outlines_5041720944_o-768x280.jpg 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption class=\"wp-element-caption\"><em><a href=\"http:\/\/www.free-range.org.uk\/cgi-bin\/portfolio.pl?yearID=12&amp;exhibitionID=410&amp;memberID=10239\">Erica Gohdes<\/a>,<\/em> <em><strong>Reading Between the (Out)Lines<\/strong>, 2007. In the artist&#8217;s words: &#8220;3D Interpretations of Cup Drawings using Scientific Projection Systems such as Perspective Drawing, Isometric Drawing, Orthographic Projection, Oblique Projection and Combinations of the above.&#8221;<\/em>&nbsp;<\/figcaption><\/figure>\n<\/div>\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p>A traditional discussion of projection systems leads from simple line drawings to highly complex perspectives. But mechanical drawings are deceptively abstract. Because perspective very closely approximates the way we naturally see the world, it makes more sense to approach the topic of projection systems from the more familiar, less abstract position. We can then work our way &#8220;backward&#8221; to pure orthographic drawing. We&#8217;ll first look at why it&#8217;s even necessary to know about these systems in a post-drawing world. Then we&#8217;ll follow by looking at perspective and parallel projection methodologies and how they express themselves in the 3D modeling user interface. Like Erica Gohdes&#8217; teacups, these projections constitute many ways of looking at one thing, each useful in their turn.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"305\" height=\"202\" data-attachment-id=\"8728\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/teacup_5043974038_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/teacup_5043974038_o.jpg\" data-orig-size=\"305,202\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;2.8&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;KODAK Z7590 ZOOM DIGITAL CAMERA&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1178461360&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;6.3&quot;,&quot;iso&quot;:&quot;140&quot;,&quot;shutter_speed&quot;:&quot;0.033333333333333&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"teacup_5043974038_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/teacup_5043974038_o.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/teacup_5043974038_o.jpg\" alt=\"\" class=\"wp-image-8728\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/teacup_5043974038_o.jpg 305w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/teacup_5043974038_o-300x199.jpg 300w\" sizes=\"auto, (max-width: 305px) 100vw, 305px\" \/><figcaption class=\"wp-element-caption\"><em>Section drawing of a teacup<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Perspective_projection\"><\/span>Perspective projection<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"600\" data-attachment-id=\"8731\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/erica_gohdes_perspective_cup\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/erica_gohdes_perspective_cup.jpg\" data-orig-size=\"800,600\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;3.2&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;KODAK Z7590 ZOOM DIGITAL CAMERA&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1178461919&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;12.4&quot;,&quot;iso&quot;:&quot;140&quot;,&quot;shutter_speed&quot;:&quot;0.025&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"erica_gohdes_perspective_cup\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/erica_gohdes_perspective_cup.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/erica_gohdes_perspective_cup.jpg\" alt=\"\" class=\"wp-image-8731\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/erica_gohdes_perspective_cup.jpg 800w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/erica_gohdes_perspective_cup-300x225.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/erica_gohdes_perspective_cup-768x576.jpg 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p><em><a href=\"http:\/\/www.free-range.org.uk\/cgi-bin\/portfolio.pl?yearID=12&amp;exhibitionID=410&amp;memberID=10239\">Erica Gohdes<\/a>,\u00a0<strong>Reading Between the (Out)Lines<\/strong>, 2007.\u00a0<\/em><\/p>\n\n\n\n<p><em>Erica&#8217;s <strong>Perspective Cup<\/strong>\u00a0seems stretched because she&#8217;s placed a fixed perspective view back into &#8220;our&#8221; perspective matrix. We can use this technique to create a &#8220;forced&#8221; perspective seen in a stage set design and the optical illusion found in an\u00a0<a href=\"http:\/\/en.wikipedia.org\/wiki\/Ames_room\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Ames Room<\/strong><\/a>.<\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n<p>Perspective is a &#8220;natural&#8221; way to see the world. But it&#8217;s a very unnatural and difficult thing to construct! This possibly explains why it was not until the early Renaissance that the mechanics of human optics were systematized in drawing. Before the Renaissance, artists attempted intuitive suggestions of objects receding in space in a non-systematic way. Either that, or perspective was ignored altogether in favor of equally valid systems of hierarchic scale, symbolic, or abstract representation. <\/p>\n\n\n\n<p>The humanist worldview of the Renaissance \u2014 the human being is the center and measure of all \u2014 allowed artists such as Filippo Brunelleschi, Leon Battista Aberti, and Albrecht D\u00fcrer to conceive of the components of a perspective matrix. These include a station point where the viewer stands, a picture plane that captures images of objects as they travel along lines of sight to the viewer, and vanishing points along a horizon line coincidental with the height of the viewer&#8217;s eye. All of these refer back to the particular point of view of an individual spectator.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Mirrors_and_windows\"><\/span>Mirrors and windows<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The development of perspective was aided by the invention and use of several technologies that make these abstractions relatively tangible, as seen below:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"919\" data-attachment-id=\"8733\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/brunelleschi_mirror_device_5051243701_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/brunelleschi_mirror_device_5051243701_o.webp\" data-orig-size=\"1920,1723\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"brunelleschi_mirror_device_5051243701_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/brunelleschi_mirror_device_5051243701_o-1024x919.webp\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/brunelleschi_mirror_device_5051243701_o-1024x919.webp\" alt=\"\" class=\"wp-image-8733\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/brunelleschi_mirror_device_5051243701_o-1024x919.webp 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/brunelleschi_mirror_device_5051243701_o-300x269.webp 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/brunelleschi_mirror_device_5051243701_o-768x689.webp 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/brunelleschi_mirror_device_5051243701_o-1536x1378.webp 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/brunelleschi_mirror_device_5051243701_o.webp 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Brunelleschi&#8217;s <a href=\"https:\/\/aeon.co\/ideas\/perspective-is-a-lesson-in-how-science-collaborates-with-art\"><strong>double-mirror device<\/strong><\/a> for seeing perspective<\/em>,<em>\u00a0circa 1415. This device allowed him to understand relationships of the station point, picture plane, vanishing points, and horizon line in his study of Florence&#8217;s <strong>Baptistry<\/strong>.<\/em><\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2000\" height=\"1454\" data-attachment-id=\"8767\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/the-draughtsman-of-the-lute-the-met-museum-of-art\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/The-Draughtsman-of-the-Lute-The-Met-Museum-of-Art.jpg\" data-orig-size=\"2000,1454\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1711303727&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"The-Draughtsman-of-the-Lute-The-Met-Museum-of-Art\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/The-Draughtsman-of-the-Lute-The-Met-Museum-of-Art-1024x744.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/The-Draughtsman-of-the-Lute-The-Met-Museum-of-Art.jpg\" alt=\"\" class=\"wp-image-8767\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/The-Draughtsman-of-the-Lute-The-Met-Museum-of-Art.jpg 2000w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/The-Draughtsman-of-the-Lute-The-Met-Museum-of-Art-300x218.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/The-Draughtsman-of-the-Lute-The-Met-Museum-of-Art-1024x744.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/The-Draughtsman-of-the-Lute-The-Met-Museum-of-Art-768x558.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/The-Draughtsman-of-the-Lute-The-Met-Museum-of-Art-1536x1117.jpg 1536w\" sizes=\"auto, (max-width: 2000px) 100vw, 2000px\" \/><figcaption class=\"wp-element-caption\"><em>Albrecht D\u00fcrer, <strong><a href=\"https:\/\/artsandculture.google.com\/asset\/the-draughtsman-of-the-lute\/CQHQAZiHEhh0dQ?hl=en\" target=\"_blank\" rel=\"noreferrer noopener\">The Draughtsman of the Lute<\/a><\/strong>, circa 1520. Another of several devices created by D\u00fcrer using an elaborate system to make lines of sight tangible with a weighted string. Recording the coordinates of the string&#8217;s intersection with the picture plane, the artist could transfer that information to paper and &#8220;connect the dots&#8221; to complete the drawing.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"586\" height=\"1000\" data-attachment-id=\"8734\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/alberti_velo_5051886066\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/alberti_velo_5051886066.jpg\" data-orig-size=\"586,1000\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"alberti_velo_5051886066\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/alberti_velo_5051886066.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/alberti_velo_5051886066.jpg\" alt=\"\" class=\"wp-image-8734\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/alberti_velo_5051886066.jpg 586w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/alberti_velo_5051886066-176x300.jpg 176w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/alberti_velo_5051886066-300x512.jpg 300w\" sizes=\"auto, (max-width: 586px) 100vw, 586px\" \/><figcaption class=\"wp-element-caption\"><em>Alberti&#8217;s <strong><a href=\"http:\/\/www.essentialvermeer.com\/technique\/perspective\/vermeer-and-perspective.html\">perspective window<\/a><\/strong>. Adding a grid to the picture plane and a stylus to the station point permitted a rational structure. This allowed one to transcribe, unit by unit, visual information to paper<\/em>.<em> This crudely presaged the concept of a grid of pixels in the computer monitor.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"A_picture_plane\"><\/span>A picture plane<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>These devices made a tangible, screen-like expression out of the picture plane, not unlike the viewport on your monitor. But the simplest way to think of the picture plane is as a window onto a view. As Leonardo da Vinci described the new system,&nbsp;<em>&#8220;Perspective is nothing else than the seeing of an object through a sheet of glass, on the surface of which may be marked all the things that are behind the glass.&#8221;<\/em><\/p>\n\n\n\n<p>An easy way to experience the expression of a picture plane is to use an actual window. Using a grease pencil, draw a border approximately 9\u201d by 12\u201d on the window. Stand in one spot, close one eye, and without moving your position, draw the outlines of what you see inside the border. When you step away from your station point, you will see you&#8217;ve created exactly what you would on your paper or canvas by using an abstract picture plane. Once you&#8217;ve tried a few different windows and views, you will understand the term \u201cpicture plane\u201d.<\/p>\n\n\n\n<p>In addition to your computer monitor, some modern expressions of the picture plane on mobile platforms:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube-nocookie.com\/embed\/cNu4CluFOcw?si=lso40TARuqumO_xL\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n\n<p><em>Georgia Tech Augmented Environments Lab and Savannah College of Art and Design,\u00a0<\/em><strong><em>ARhrrrr<\/em><\/strong><em>, 2009. A prototype augmented reality first-person shooter game using a mobile camera phone. Pro: gets you off the couch. Con: encourages you to play with your food.<\/em><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"598\" data-attachment-id=\"8738\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/choose-columns-rows-grid\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/choose-columns-rows-grid.webp\" data-orig-size=\"780,598\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"choose-columns-rows-grid\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/choose-columns-rows-grid.webp\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/choose-columns-rows-grid.webp\" alt=\"\" class=\"wp-image-8738\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/choose-columns-rows-grid.webp 780w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/choose-columns-rows-grid-300x230.webp 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/choose-columns-rows-grid-768x589.webp 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\"><em><strong><a href=\"https:\/\/www.gridraw.net\/\" target=\"_blank\" rel=\"noreferrer noopener\">GriDraw<\/a><\/strong> application creates a D\u00fcrer reference grid over a photograph.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Three-point_perspective\"><\/span>Three-point perspective<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"background-color:#eeeeee\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"626\" data-attachment-id=\"8739\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/00_maya_aerial_perspective_5048852244_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_aerial_perspective_5048852244_o.jpg\" data-orig-size=\"1920,1174\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"00_maya_aerial_perspective_5048852244_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_aerial_perspective_5048852244_o-1024x626.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_aerial_perspective_5048852244_o-1024x626.jpg\" alt=\"\" class=\"wp-image-8739\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_aerial_perspective_5048852244_o-1024x626.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_aerial_perspective_5048852244_o-300x183.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_aerial_perspective_5048852244_o-768x470.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_aerial_perspective_5048852244_o-1536x939.jpg 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_aerial_perspective_5048852244_o.jpg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Maya interface. The standard view opens a file in an aerial, three-point perspective projection.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"777\" data-attachment-id=\"8740\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/manhattan_three_point_perspective_5052058640_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/manhattan_three_point_perspective_5052058640_o.jpg\" data-orig-size=\"960,777\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"manhattan_three_point_perspective_5052058640_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/manhattan_three_point_perspective_5052058640_o.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/manhattan_three_point_perspective_5052058640_o.jpg\" alt=\"\" class=\"wp-image-8740\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/manhattan_three_point_perspective_5052058640_o.jpg 960w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/manhattan_three_point_perspective_5052058640_o-300x243.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/manhattan_three_point_perspective_5052058640_o-768x622.jpg 768w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><figcaption class=\"wp-element-caption\"><em>Classic aerial (three-point perspective) view\u00a0of Manhattan, 1935<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image wp-duotone-000000-eeeeee-1\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"928\" data-attachment-id=\"8741\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/3_point_perspective_matrix_5051437967\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/3_point_perspective_matrix_5051437967.png\" data-orig-size=\"1280,1160\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"3_point_perspective_matrix_5051437967\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/3_point_perspective_matrix_5051437967-1024x928.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/3_point_perspective_matrix_5051437967-1024x928.png\" alt=\"\" class=\"wp-image-8741\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/3_point_perspective_matrix_5051437967-1024x928.png 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/3_point_perspective_matrix_5051437967-300x272.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/3_point_perspective_matrix_5051437967-768x696.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/3_point_perspective_matrix_5051437967.png 1280w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Perspective matrix demonstrating the use of three vanishing points<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>When you first open a 3D program, you may encounter a view from a camera oriented toward a <strong>Three-Point Perspective<\/strong> view. You can recognize a three-point projection any time you see the verticals in your modeled volumes sloping in or out, skewed against the orthogonal edges of the viewport. Whenever the direction of your point of view (in the modeling UI, the camera) is not parallel to the ground plane, the resulting view is three-point. Aerial (a.k.a. bird&#8217;s-eye) or ground (a.k.a. worm&#8217;s-eye) views result from tipping the head up or down to view. <\/p>\n\n\n\n<p>But this kind of view is more common than the unusual view from an airplane down to skyscrapers. Even looking down at objects on a tabletop is a common manifestation of three-point. The relatively rigid, perfectly level viewing orientation needed to achieve two-point projection makes it less common in day-to-day experience than you might think.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Two-point_perspective\"><\/span>Two-point perspective<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"background-color:#eeeeee\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"626\" data-attachment-id=\"8745\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/03_perspective_2pt_viewport_5048234537_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/03_perspective_2pt_viewport_5048234537_o.jpg\" data-orig-size=\"1920,1174\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"03_perspective_2pt_viewport_5048234537_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/03_perspective_2pt_viewport_5048234537_o-1024x626.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/03_perspective_2pt_viewport_5048234537_o-1024x626.jpg\" alt=\"\" class=\"wp-image-8745\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/03_perspective_2pt_viewport_5048234537_o-1024x626.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/03_perspective_2pt_viewport_5048234537_o-300x183.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/03_perspective_2pt_viewport_5048234537_o-768x470.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/03_perspective_2pt_viewport_5048234537_o-1536x939.jpg 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/03_perspective_2pt_viewport_5048234537_o.jpg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Maya interface. The standard view is now seen in a two-point perspective projection. Note the verticals on the modeled objects are parallel with the upright edges of the viewport.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"background-color:#eeeeee\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"730\" data-attachment-id=\"8746\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/03_perspective_2pt_analysis_5048855486_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/03_perspective_2pt_analysis_5048855486_o.jpg\" data-orig-size=\"1268,904\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"03_perspective_2pt_analysis_5048855486_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/03_perspective_2pt_analysis_5048855486_o-1024x730.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/03_perspective_2pt_analysis_5048855486_o-1024x730.jpg\" alt=\"\" class=\"wp-image-8746\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/03_perspective_2pt_analysis_5048855486_o-1024x730.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/03_perspective_2pt_analysis_5048855486_o-300x214.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/03_perspective_2pt_analysis_5048855486_o-768x548.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/03_perspective_2pt_analysis_5048855486_o.jpg 1268w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Analysis of the view. The <strong>lines of sight<\/strong> projecting from the masses converge on a <strong>point of view<\/strong> at the lower left. The large gray rectangle indicates the <strong>picture plane<\/strong>, equivalent to the virtual location of the viewport.\u00a0Included in this view are <strong>vanishing points<\/strong> and a <strong>horizon line<\/strong> on the picture plane, indicating this is a true two-point view.\u00a0 <\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>Compare the view in the illustrations. In the first, we see the same camera lowered to a position about 5 feet off the XZ reference plane \u2014 eye level for a standing human \u2014 and rotated to be perfectly parallel with that ground plane. These are the conditions necessary to achieve a <strong>Two-Point Perspective<\/strong>. Even though this way of looking at the world is highly structured, it sometimes feels more &#8220;natural&#8221; to us than the more common three-point experience. We are upright creatures used to looking at the world with our eyes,\u00a0on average, gazing at the horizon. This is why we regard photographs with pictorial verticals parallel to the upright edges of the composition as aesthetically pleasing.\u00a0Again: a proper two-point perspective is created ONLY when the camera line of sight is parallel to the ground plane.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"One-point_perspective\"><\/span>One-point perspective<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"background-color:#eeeeee\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"626\" data-attachment-id=\"8748\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/02_maya_rightview_persp_5048232961_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/02_maya_rightview_persp_5048232961_o.jpg\" data-orig-size=\"1920,1174\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"02_maya_rightview_persp_5048232961_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/02_maya_rightview_persp_5048232961_o-1024x626.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/02_maya_rightview_persp_5048232961_o-1024x626.jpg\" alt=\"\" class=\"wp-image-8748\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/02_maya_rightview_persp_5048232961_o-1024x626.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/02_maya_rightview_persp_5048232961_o-300x183.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/02_maya_rightview_persp_5048232961_o-768x470.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/02_maya_rightview_persp_5048232961_o-1536x939.jpg 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/02_maya_rightview_persp_5048232961_o.jpg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em><em>Maya interface. The\u00a0view is now in a one-point perspective projection.\u00a0Note there is no proportional or angular distortion of the faces of the masses directly perpendicular to the line of sight and parallel to the picture plane.<\/em><\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"background-color:#eeeeee\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"730\" data-attachment-id=\"8749\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/02_persective_projection_analysis_5048234031_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/02_persective_projection_analysis_5048234031_o.jpg\" data-orig-size=\"1268,904\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"02_persective_projection_analysis_5048234031_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/02_persective_projection_analysis_5048234031_o-1024x730.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/02_persective_projection_analysis_5048234031_o-1024x730.jpg\" alt=\"\" class=\"wp-image-8749\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/02_persective_projection_analysis_5048234031_o-1024x730.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/02_persective_projection_analysis_5048234031_o-300x214.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/02_persective_projection_analysis_5048234031_o-768x548.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/02_persective_projection_analysis_5048234031_o.jpg 1268w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em><em>Analysis of the view. The <strong>lines of sight<\/strong> projecting from the masses converge on a <strong>point of view<\/strong> at the lower right. The intersection of the lines of sight at the picture plane creates here a <strong>one-point perspective<\/strong> \u2014 always the case when the front planes of the objects are parallel with the picture plane.<\/em><\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>Compare the illustrations. The point of view has now been shifted so that the direction of the camera is perpendicular to the right sides of the masses. The resulting picture plane is parallel to them. This creates a  <strong>One-Point Perspective<\/strong> view. This kind of perspective is beloved by designers and painters of interior scenes, as it lends stability and comprehensibility to the masses and voids of defined spaces. A\u00a0<strong>Left<\/strong>,\u00a0<strong>Right<\/strong>,\u00a0<strong>Front<\/strong>,\u00a0or\u00a0<strong>Back<\/strong>\u00a0view in the UI will automatically create a one-point view. A\u00a0<strong>Top<\/strong>\u00a0or\u00a0<strong>Bottom<\/strong> view will also create a one-point, looking straight up or down instead of at the horizon.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Parallel_projection\"><\/span>Parallel projection<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"601\" data-attachment-id=\"8751\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/attachment\/32878\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32878.jpg\" data-orig-size=\"800,601\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;2.8&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;KODAK Z7590 ZOOM DIGITAL CAMERA&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1178461789&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;6.3&quot;,&quot;iso&quot;:&quot;80&quot;,&quot;shutter_speed&quot;:&quot;0.025&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"32878\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32878.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32878.jpg\" alt=\"\" class=\"wp-image-8751\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32878.jpg 800w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32878-300x225.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32878-768x577.jpg 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption class=\"wp-element-caption\"><em>Erica&#8217;s <strong>Isometric Cup<\/strong>\u00a0at\u00a0<strong>left<\/strong>\u00a0seems undistorted when viewed from above,\u00a0but the isometric distortion is revealed &#8230;<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"600\" data-attachment-id=\"8752\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/attachment\/32872\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32872.jpg\" data-orig-size=\"800,600\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;2.8&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;KODAK Z7590 ZOOM DIGITAL CAMERA&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1178461774&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;6.3&quot;,&quot;iso&quot;:&quot;80&quot;,&quot;shutter_speed&quot;:&quot;0.016666666666667&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"32872\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32872.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32872.jpg\" alt=\"\" class=\"wp-image-8752\" style=\"width:416px;height:auto\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32872.jpg 800w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32872-300x225.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32872-768x576.jpg 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption class=\"wp-element-caption\"><em>&#8230; in the front view shown here. This an example of <strong>re-projection<\/strong> \u2014 projecting the abstraction of a parallel projection back into &#8220;normal&#8221; space.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p>In perspective projection, as the illustrations demonstrate, the lines of sight from the objects pass through the picture plane and converge on a single point. As you might guess, in Parallel Projection, the lines of sight are parallel with each other as they project to the picture plane. By definition, they never converge. When we set a camera in a modeling program with&nbsp;Perspective&nbsp;off, it renders a parallel projection through that camera. Parallel projection is useful when a sense of dimension, proportion, or aspect ratio needs to be maintained as a model gets built.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Zero-point_%E2%80%9Cperspective%E2%80%9D\"><\/span>Zero-point \u201cperspective\u201d<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"background-color:#eeeeee\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"626\" data-attachment-id=\"8756\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/01_maya_rightview_parallel_5048854796_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/01_maya_rightview_parallel_5048854796_o.jpg\" data-orig-size=\"1920,1174\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"01_maya_rightview_parallel_5048854796_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/01_maya_rightview_parallel_5048854796_o-1024x626.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/01_maya_rightview_parallel_5048854796_o-1024x626.jpg\" alt=\"\" class=\"wp-image-8756\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/01_maya_rightview_parallel_5048854796_o-1024x626.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/01_maya_rightview_parallel_5048854796_o-300x183.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/01_maya_rightview_parallel_5048854796_o-768x470.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/01_maya_rightview_parallel_5048854796_o-1536x939.jpg 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/01_maya_rightview_parallel_5048854796_o.jpg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em><em><em>Maya interface, <strong>Right<\/strong> view in parallel projection by turning camera perspective &#8220;off.&#8221;<\/em><\/em><\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"background-color:#eeeeee\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"730\" data-attachment-id=\"8755\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/01_parallel_projection_analysis_5048855068_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/01_parallel_projection_analysis_5048855068_o.jpg\" data-orig-size=\"1268,904\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"01_parallel_projection_analysis_5048855068_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/01_parallel_projection_analysis_5048855068_o-1024x730.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/01_parallel_projection_analysis_5048855068_o-1024x730.jpg\" alt=\"\" class=\"wp-image-8755\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/01_parallel_projection_analysis_5048855068_o-1024x730.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/01_parallel_projection_analysis_5048855068_o-300x214.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/01_parallel_projection_analysis_5048855068_o-768x548.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/01_parallel_projection_analysis_5048855068_o.jpg 1268w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em><em><em>Analysis of the view. The <strong>lines of sight<\/strong> projecting from the masses do not converge, eliminating the <strong>point of view<\/strong>. The intersection of lines of sight at the picture plane creates a true-size and proportion projection of the mass faces (except for the upper plane on the far mass, which is seen in a projection parallel to the picture plane, but not to the plane being projected. We call this an <strong>oblique<\/strong> projection).<\/em><\/em><\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>If you&#8217;ve ever taken a photograph with a telephoto lens, you know this reduces the sense of depth in your shot, but it increases your ability to see very far. Turning <em>Perspective<\/em> off in a program&#8217;s virtual camera creates a strange, hyper-telephoto perspective projection with a theoretical viewpoint in which the camera stands at an infinite distance away from the object and has an infinite focal length or &#8220;zoom&#8217; (recall this is illustrated above). You&#8217;ve entered the strange world of <strong>Zero-Point \u201cPerspective<\/strong>,\u201d another name for parallel projection. It is a complete abstraction \u2014 no such hypothetically &#8220;infinite&#8221; camera exists \u2014 but as we will see, it is a highly useful one.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p>Parallel projections are used to create views known as <a href=\"http:\/\/en.wikipedia.org\/wiki\/Parallel_projection#Pictorials\" target=\"_blank\" rel=\"noreferrer noopener\">Pictorials<\/a>, which in the viewport are seen in <strong>Axonometric Projection<\/strong>. They are also used to create <strong>Orthographic Projections<\/strong> in drawing form, which the viewport can both emulate and use.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Axonometric_projection\"><\/span>Axonometric projection<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"background-color:#eeeeee\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"626\" data-attachment-id=\"8754\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/00_maya_parallel_oblique_isometric_5048853076_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_parallel_oblique_isometric_5048853076_o.jpg\" data-orig-size=\"1920,1174\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"00_maya_parallel_oblique_isometric_5048853076_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_parallel_oblique_isometric_5048853076_o-1024x626.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_parallel_oblique_isometric_5048853076_o-1024x626.jpg\" alt=\"\" class=\"wp-image-8754\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_parallel_oblique_isometric_5048853076_o-1024x626.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_parallel_oblique_isometric_5048853076_o-300x183.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_parallel_oblique_isometric_5048853076_o-768x470.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_parallel_oblique_isometric_5048853076_o-1536x939.jpg 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_parallel_oblique_isometric_5048853076_o.jpg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em><em>Maya interface. The standard view in an aerial parallel projection yields an <strong>isometric projection<\/strong>, a special case of axonometric.<\/em><\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"631\" data-attachment-id=\"8758\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/isometric-and-perspective-drawing-vector\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/istockphoto-804357534-1024x1024-1.jpg\" data-orig-size=\"1024,631\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;Getty Images\/iStockphoto&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;isometric and perspective drawing vector&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;isometric and perspective drawing vector&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"isometric and perspective drawing vector\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;isometric and perspective drawing vector&lt;\/p&gt;\n\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/istockphoto-804357534-1024x1024-1.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/istockphoto-804357534-1024x1024-1.jpg\" alt=\"\" class=\"wp-image-8758\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/istockphoto-804357534-1024x1024-1.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/istockphoto-804357534-1024x1024-1-300x185.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/istockphoto-804357534-1024x1024-1-768x473.jpg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Comparison of perspective and isometric<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image wp-duotone-000000-eeeeee-2\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"781\" height=\"1024\" data-attachment-id=\"8759\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/leonardo_cubes_5053222256\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/leonardo_cubes_5053222256.png\" data-orig-size=\"1138,1492\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"leonardo_cubes_5053222256\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/leonardo_cubes_5053222256-781x1024.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/leonardo_cubes_5053222256-781x1024.png\" alt=\"\" class=\"wp-image-8759\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/leonardo_cubes_5053222256-781x1024.png 781w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/leonardo_cubes_5053222256-229x300.png 229w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/leonardo_cubes_5053222256-768x1007.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/leonardo_cubes_5053222256-300x393.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/leonardo_cubes_5053222256.png 1138w\" sizes=\"auto, (max-width: 781px) 100vw, 781px\" \/><figcaption class=\"wp-element-caption\"><em><em>Leonardo da Vinci,\u00a0<\/em><strong><a href=\"https:\/\/personales.unican.es\/fioravam\/progsenior\/poliedrosarte.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Isometric Cubes<\/a><\/strong><em>, circa 1509. Spatial ambiguity occurs in isometric when the far lower corner of a cube aligns visually with the closer, upper corner.<\/em><\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>An <strong>Axonometric Projection <\/strong>is a pictorial view wherein the planes and axes of an object are not parallel to the picture plane so that more than one side of the object can be seen. A special case of axonometric typically seen in the viewport is known as an <strong>Isometric Projection<\/strong>, characterized by either a 60<sup>\u2218\u00a0<\/sup>or 120<sup>\u2218<\/sup>\u00a0angle to represent a 90<sup>\u2218<\/sup>\u00a0angle found in reality. This was systematized in the West around the <a href=\"http:\/\/en.wikipedia.org\/wiki\/William_Farish_%28chemist%29\" target=\"_blank\" rel=\"noreferrer noopener\">beginning of the 19th Century<\/a>, but according to <a href=\"http:\/\/www.iias.nl\/iiasn\/iiasn9\/eastasia\/krikke.html\" target=\"_blank\" rel=\"noreferrer noopener\">Jan Krikke<\/a>, its function as a spatial device originated in ancient China, where it was used as the equivalent of perspective in the West. It later found a home in the woodblock prints of Japan.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"748\" height=\"1024\" data-attachment-id=\"8760\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/girl_with_insect_cage_and_girl_reading_a_letter_5053301298_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/girl_with_insect_cage_and_girl_reading_a_letter_5053301298_o.png\" data-orig-size=\"1341,1836\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"girl_with_insect_cage_and_girl_reading_a_letter_5053301298_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/girl_with_insect_cage_and_girl_reading_a_letter_5053301298_o-748x1024.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/girl_with_insect_cage_and_girl_reading_a_letter_5053301298_o-748x1024.png\" alt=\"\" class=\"wp-image-8760\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/girl_with_insect_cage_and_girl_reading_a_letter_5053301298_o-748x1024.png 748w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/girl_with_insect_cage_and_girl_reading_a_letter_5053301298_o-219x300.png 219w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/girl_with_insect_cage_and_girl_reading_a_letter_5053301298_o-768x1051.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/girl_with_insect_cage_and_girl_reading_a_letter_5053301298_o-1122x1536.png 1122w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/girl_with_insect_cage_and_girl_reading_a_letter_5053301298_o-300x411.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/girl_with_insect_cage_and_girl_reading_a_letter_5053301298_o.png 1341w\" sizes=\"auto, (max-width: 748px) 100vw, 748px\" \/><figcaption class=\"wp-element-caption\"><em>Shigemasa Kitao,\u00a0<strong><a href=\"https:\/\/www.loc.gov\/item\/2002700006\/\" target=\"_blank\" rel=\"noreferrer noopener\">Girl With Insect Cage, and Girl Holding a Letter<\/a><\/strong>,\u00a0circa 1800<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<h5 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E2%80%9CImpossible%E2%80%9D_shapes\"><\/span>&#8220;Impossible&#8221; shapes<span class=\"ez-toc-section-end\"><\/span><\/h5>\n\n\n\n<p>One special property of axonometric projection is spatial ambiguity. This allowed artists to develop so-called &#8220;impossible&#8221; shapes in the early and middle 20th Century. Oscar Reutersvard, the father of the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Impossible_object\" target=\"_blank\" rel=\"noreferrer noopener\">impossible shape<\/a>, expressed them as pure geometric worlds, whereas M. C. Escher created plausibly habitable impossibilities like his <em><strong>Waterfall<\/strong><\/em>, though his drawings are distorted slightly out of isometry. Because it is easy to process algorithmically, isometry became very popular in games such as Will Wright&#8217;s\u00a0<em><a href=\"http:\/\/en.wikipedia.org\/wiki\/SimCity\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>SimCity<\/strong><\/a><\/em>. The elegant\u00a0<em><strong><a href=\"https:\/\/en.wikipedia.org\/wiki\/Echochrome\" target=\"_blank\" rel=\"noreferrer noopener\">Echochrome<\/a><\/strong><\/em> paid tribute both to Escher and the traditional use of isometric game space.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"886\" height=\"1024\" data-attachment-id=\"8762\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/oscar_reutersvard_impossible_triangle_505247628\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/oscar_reutersvard_impossible_triangle_505247628.jpg\" data-orig-size=\"1505,1740\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"oscar_reutersvard_impossible_triangle_505247628\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/oscar_reutersvard_impossible_triangle_505247628-886x1024.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/oscar_reutersvard_impossible_triangle_505247628-886x1024.jpg\" alt=\"\" class=\"wp-image-8762\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/oscar_reutersvard_impossible_triangle_505247628-886x1024.jpg 886w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/oscar_reutersvard_impossible_triangle_505247628-259x300.jpg 259w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/oscar_reutersvard_impossible_triangle_505247628-768x888.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/oscar_reutersvard_impossible_triangle_505247628-1329x1536.jpg 1329w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/oscar_reutersvard_impossible_triangle_505247628-300x347.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/oscar_reutersvard_impossible_triangle_505247628.jpg 1505w\" sizes=\"auto, (max-width: 886px) 100vw, 886px\" \/><figcaption class=\"wp-element-caption\"><em>Oscar Reutersvard,\u00a0<strong><a href=\"https:\/\/images.auctionet.com\/uploads\/item_3287232_dbf5ef7dce.jpg\" target=\"_blank\" rel=\"noreferrer noopener\">Impossible Triangle<\/a><\/strong>,\u00a01932<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"802\" height=\"1024\" data-attachment-id=\"8763\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/escher-waterfall-1961-1\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Escher-Waterfall-1961-1.jpg\" data-orig-size=\"1253,1600\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Escher-Waterfall-1961-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Escher-Waterfall-1961-1-802x1024.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Escher-Waterfall-1961-1-802x1024.jpg\" alt=\"\" class=\"wp-image-8763\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Escher-Waterfall-1961-1-802x1024.jpg 802w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Escher-Waterfall-1961-1-235x300.jpg 235w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Escher-Waterfall-1961-1-768x981.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Escher-Waterfall-1961-1-1203x1536.jpg 1203w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Escher-Waterfall-1961-1-300x383.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Escher-Waterfall-1961-1.jpg 1253w\" sizes=\"auto, (max-width: 802px) 100vw, 802px\" \/><figcaption class=\"wp-element-caption\"><em>M. C. Escher,\u00a0<strong><a href=\"https:\/\/en.wikipedia.org\/wiki\/Waterfall_(M._C._Escher)\" target=\"_blank\" rel=\"noreferrer noopener\">Waterfall<\/a><\/strong>, 1961. The geometry of the waterfall is based on the same principle as Reutersvard&#8217;s triangle.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube-nocookie.com\/embed\/GybxIwfU4rI?si=VFo6bVvAu_iekZrT\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n\n<p><em>Sony Entertainment, Trailer for\u00a0<strong>Echochrome<\/strong>, 2008<\/em><\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Oblique_and_orthographic_projection\"><\/span>Oblique and orthographic projection<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"400\" height=\"600\" data-attachment-id=\"8766\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/attachment\/32875\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32875.jpg\" data-orig-size=\"400,600\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;2.8&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;KODAK Z7590 ZOOM DIGITAL CAMERA&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1178461385&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;6.3&quot;,&quot;iso&quot;:&quot;140&quot;,&quot;shutter_speed&quot;:&quot;0.033333333333333&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"32875\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32875.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32875.jpg\" alt=\"\" class=\"wp-image-8766\" style=\"aspect-ratio:1;object-fit:cover\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32875.jpg 400w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32875-200x300.jpg 200w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/32875-300x450.jpg 300w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p><em>Erica&#8217;s\u00a0<strong>Orthographic Cup<\/strong> appears to be the extrusion of the profile of the cup \u2014  and that&#8217;s precisely what it is!<\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n<p>Pictorial geometries have a peculiar property: while linear measurements are undistorted, angular measurements are. This occurs because either:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>the <em>picture plane<\/em> is not parallel to the faces of the object \u2014 the axonometric view \u2014 or &#8230; <\/li>\n\n\n\n<li>2) the <em>angle of projection<\/em> is not perpendicular to a picture plane parallel to the object, a parallel projection known as <strong><a href=\"http:\/\/en.wikipedia.org\/wiki\/Oblique_projection\" target=\"_blank\" rel=\"noreferrer noopener\">Oblique<\/a><\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>If, on the other hand, the picture plane is parallel to the faces of the object, and the angles of projection are perpendicular to the picture plane, this is known as <strong><a href=\"http:\/\/en.wikipedia.org\/wiki\/Multiview_orthographic_projection\" target=\"_blank\" rel=\"noreferrer noopener\">Orthographic<\/a><\/strong> projection.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"background-color:#eeeeee\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"626\" data-attachment-id=\"8770\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/00_maya_fourview_parallel_5048853688_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_fourview_parallel_5048853688_o.jpg\" data-orig-size=\"1920,1174\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"00_maya_fourview_parallel_5048853688_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_fourview_parallel_5048853688_o-1024x626.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_fourview_parallel_5048853688_o-1024x626.jpg\" alt=\"\" class=\"wp-image-8770\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_fourview_parallel_5048853688_o-1024x626.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_fourview_parallel_5048853688_o-300x183.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_fourview_parallel_5048853688_o-768x470.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_fourview_parallel_5048853688_o-1536x939.jpg 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/00_maya_fourview_parallel_5048853688_o.jpg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em><em>Maya interface. The standard 4-view presents in the organization of third angle projection.<\/em><\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube-nocookie.com\/embed\/ZtaPw7ZWmR4?si=Ic5sRvqDJwm3GmCK\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n\n<p><em>&#8220;Glass box&#8221; animation by\u00a0<a href=\"http:\/\/www.youtube.com\/user\/denlieu\" target=\"_blank\" rel=\"noreferrer noopener\">Dennis Lieu<\/a><\/em><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image wp-duotone-000000-eeeeee-3\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"356\" height=\"356\" data-attachment-id=\"8771\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/orthographic_projection_5055437177_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/orthographic_projection_5055437177_o.jpg\" data-orig-size=\"356,356\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"orthographic_projection_5055437177_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/orthographic_projection_5055437177_o.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/orthographic_projection_5055437177_o.jpg\" alt=\"\" class=\"wp-image-8771\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/orthographic_projection_5055437177_o.jpg 356w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/orthographic_projection_5055437177_o-300x300.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/orthographic_projection_5055437177_o-150x150.jpg 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/orthographic_projection_5055437177_o-100x100.jpg 100w\" sizes=\"auto, (max-width: 356px) 100vw, 356px\" \/><figcaption class=\"wp-element-caption\"><em><em>Third angle drawing diagram. Equivalent to the 3 upper right unfolded &#8220;glass box&#8221; panes in the video.<\/em><\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#eeeeee\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>Orthographic projection is the preferred choice for making technical drawings and architectural plans. That&#8217;s because it contains no angular or linear distortion. Measurement, and a certain way of perceiving Cartesian space, are facilitated by creating projection relationships in multiple orthographic views. In these, a plan or top view aligns vertically with an elevation or front view. This in turn aligns horizontally with another elevation or side view. The standard four-view viewport in Maya emulates this orthographic organization, known as &#8220;third-angle&#8221; projection. Third-angle drawings present an object as if several orthographic projections of an object were performed on the faces of a glass cube. This cube unfolds flat to facilitate a drawing view, seen conceptually in the video here.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Reference_planes_in_3D_modeling\"><\/span><strong>Reference planes in 3D modeling<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Orthographic drawings \u2014 top, side, front, back, or a combination \u2014 are imported into camera views in the modeling program to create <strong>Reference<\/strong> or<strong> Image Planes<\/strong>. These can be manipulated to a proper scale. Here we see an illustration of the process of organizing a series of architectural drawings into third-angle projection. This is an organization that can also be created for drawings of figures, vehicles, or other objects. In the example, key projection lines are created or highlighted in red. These can be used to size and align the drawings in image planes:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"791\" data-attachment-id=\"8773\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/lequeue2\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue2.png\" data-orig-size=\"3300,2550\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"lequeue2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue2-1024x791.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue2-1024x791.png\" alt=\"\" class=\"wp-image-8773\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue2-1024x791.png 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue2-300x232.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue2-768x593.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue2-1536x1187.png 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue2-2048x1583.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p><em>Orthographic third angle organization for an architectural object. The plan is at top left. The red lines are created to indicate alignments \u2014 of the plan with the section below, of the section with the front view, etc. This organization was created in Photoshop from images of original drawings by Jean Jacques Lequeu for\u00a0<strong>A Temple Dedicated to Equality, For the Garden of the Philosophy<\/strong>, circa 1850.<\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"626\" data-attachment-id=\"8775\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/lequeue_image_planes_4view_5055428021_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_4view_5055428021_o.jpg\" data-orig-size=\"1920,1174\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"lequeue_image_planes_4view_5055428021_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_4view_5055428021_o-1024x626.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_4view_5055428021_o-1024x626.jpg\" alt=\"\" class=\"wp-image-8775\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_4view_5055428021_o-1024x626.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_4view_5055428021_o-300x183.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_4view_5055428021_o-768x470.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_4view_5055428021_o-1536x939.jpg 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_4view_5055428021_o.jpg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p><em>The drawings are separated and imported into image planes, where they can be sized and organized to the grid. The standard 4-view viewport preset can be used to create the proper top-front-side projection alignments.<\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"626\" data-attachment-id=\"8776\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/lequeue_image_planes_persp_5055428471_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_persp_5055428471_o.jpg\" data-orig-size=\"1920,1174\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"lequeue_image_planes_persp_5055428471_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_persp_5055428471_o-1024x626.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_persp_5055428471_o-1024x626.jpg\" alt=\"\" class=\"wp-image-8776\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_persp_5055428471_o-1024x626.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_persp_5055428471_o-300x183.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_persp_5055428471_o-768x470.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_persp_5055428471_o-1536x939.jpg 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/lequeue_image_planes_persp_5055428471_o.jpg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p><em>View of the perspective viewport shows how the images are organized in order to model the building. Toggling back and forth between single and multiple parallel and perspective views is a common method to create an accurate model.<\/em><\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>18-minute read Perspective in perspective Albrecht&nbsp;D\u00fcrer was known as the &#8220;da Vinci of the North&#8221; because he was fascinated with, and contributed to, the relationship between art and science. Like da Vinci, he was not only a skilled draughtsman but an inventor as well. He applied his energy to elaborate drawing &#8220;machines&#8221; that could capture&#8230; <a href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/\">read more &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_eb_attr":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[8],"tags":[],"class_list":["post-8676","post","type-post","status-publish","format-standard","hentry","category-paralleluniverses"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>CHAPTER 13 \u2014 Metaphors to Drawing - newMediaWiki<\/title>\n<meta name=\"description\" content=\"Chapter 13 Metaphors to Drawing: Projection systems informing drawing from the origin of art through the Renaissance to today&#039;s modeling UI.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-13-metaphors-to-drawing\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"CHAPTER 13 \u2014 Metaphors to Drawing - 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