{"id":8245,"date":"2024-03-22T12:04:12","date_gmt":"2024-03-22T12:04:12","guid":{"rendered":"https:\/\/williamcromar.com\/newmediawiki\/?p=8245"},"modified":"2024-07-27T10:32:18","modified_gmt":"2024-07-27T10:32:18","slug":"chapter-4-visual-elements-i-point-line-plane","status":"publish","type":"post","link":"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/","title":{"rendered":"CHAPTER 4 \u2014 Visual Elements I: Point, Line, Plane"},"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-69f10d608df0b\" 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-69f10d608df0b\"  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-4-visual-elements-i-point-line-plane\/#Dimensional_elements\" >Dimensional elements<\/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-4-visual-elements-i-point-line-plane\/#Cartesian_coordinate_system\" >Cartesian coordinate system<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Point\" >Point<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Line\" >Line<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Plane\" >Plane<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Volume\" >Volume<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Kinematics\" >Kinematics<\/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-8\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Kandinskys_Basic_Plane\" >Kandinsky&#8217;s Basic Plane<\/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-4-visual-elements-i-point-line-plane\/#Kandinskys_dimensions\" >Kandinsky\u2019s dimensions<\/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-4-visual-elements-i-point-line-plane\/#Point%E2%80%A6\" >Point\u2026<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Examples\" >Examples<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#In_the_studio\" >In the studio<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#%E2%80%A6and_Line%E2%80%A6\" >\u2026and Line\u2026<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Examples-2\" >Examples<\/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-4-visual-elements-i-point-line-plane\/#In_the_studio-2\" >In the studio<\/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-4-visual-elements-i-point-line-plane\/#%E2%80%A6to_Plane\" >\u2026to Plane<\/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-4-visual-elements-i-point-line-plane\/#Related_terms_Figure-ground_Form_Shape\" >Related terms: Figure-ground | Form | Shape<\/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-4-visual-elements-i-point-line-plane\/#Examples-3\" >Examples<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#In_the_studio-3\" >In the studio<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Sectioning_and_serial_planes\" >Sectioning and serial planes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Surface_mesh\" >Surface mesh<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Implied_volume\" >Implied volume<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Graphic_shape\" >Graphic shape<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Nets\" >Nets<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Organic_form\" >Organic form<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Figure_and_ground\" >Figure and ground<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-27\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Reification\" >Reification<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-28\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Mulltistability\" >Mulltistability<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-29\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Figure-ground_relationships\" >Figure-ground relationships<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-30\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Stable\" >Stable<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-31\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Reversible\" >Reversible<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-32\" href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/#Ambiguous\" >Ambiguous<\/a><\/li><\/ul><\/li><\/ul><\/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>22-minute read<\/em><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><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\" 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<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>You, who are blessed with shade as well as light, you who are gifted with two eyes, endowed with a knowledge of perspective, and charmed with the enjoyment of various colours, you, who can actually<\/em> see <em>an angle, and contemplate the complete circumference of a Circle in the happy region of the Three Dimensions \u2014 how shall I make clear to you the extreme difficulty which we in Flatland experience in recognizing one another\u2019s configurations?<\/em><\/p>\n<cite>\u2014 Edwin Abbot, Flatland  <sup><a href=\"#footnote_1_8245\" id=\"identifier_1_8245\" class=\"footnote-link footnote-identifier-link\" title=\"Abbot, Edwin. Flatland: A Romance of Many Dimensions. Seeley &amp; Co., London. 1884. Re-published Prometheus Books, Amherst NY. 2005. p. 17.\">1<\/a><\/sup><\/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=\"772\" height=\"1018\" data-attachment-id=\"8316\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/flatland_4986306088_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/flatland_4986306088_o.jpg\" data-orig-size=\"772,1018\" 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=\"flatland_4986306088_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/flatland_4986306088_o.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/flatland_4986306088_o.jpg\" alt=\"\" class=\"wp-image-8316\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/flatland_4986306088_o.jpg 772w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/flatland_4986306088_o-228x300.jpg 228w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/flatland_4986306088_o-768x1013.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/flatland_4986306088_o-300x396.jpg 300w\" sizes=\"auto, (max-width: 772px) 100vw, 772px\" \/><figcaption class=\"wp-element-caption\"><em>Cover illustration for Edwin Abbot&#8217;s&nbsp;<a href=\"http:\/\/en.wikipedia.org\/wiki\/Flatland\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Flatland: a Romance of Many Dimensions<\/strong><\/a>, 1884. A satirical novel about Victorian social structure, it remains a relevant introduction to the concept of perceiving dimensions.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p>In&nbsp;<em>Flatland<\/em>, Edwin Abbot writes a story from the point of view of a two-dimensional being who encounters three dimensions. But it turns out that it\u2019s <em>our<\/em> story! By analogy, he demonstrates how to understand elements that lie beyond our ability to perceive.<\/p>\n\n\n\n<p>Even those with which we are familiar can be hard to grasp. However, understanding visual <strong>Elements <\/strong>will allow an artist to <em>see&nbsp;<\/em>and&nbsp;<em>use&nbsp;<\/em>them.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Dimensional_elements\"><\/span>Dimensional elements<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>This chapter concentrates on the phenomena of <strong>Point<\/strong>,<strong> Line, <\/strong>and<strong> Plane<\/strong>. But let\u2019s first, let&#8217;s contextualize them.  We&#8217;ll note&nbsp;<em>all&nbsp;<\/em>the elements below.<em> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">In this chapter, we cover those highlighted in red.<\/mark><\/em><\/p>\n\n\n\n<style>\n\t.demoele {\n\t\twidth:100%;\n\t\tborder:0px none;\n\t\tborder-collapse:collapse;\n\t\tpadding:5px;\n                text-align: center;\n\t}\n\t.demoele th {\n\t\tborder:0px none;\n\t\tpadding:5px;\n\t}\n\t.demoele td {\n\t\tborder:0px none;\n\t\tpadding:5px;\n\t}\n\n\t.cellback {\n\t\tbackground:#eeeeee;\n\t}\n\n<\/style>\n<table class=\"demoele\">\n\t<tbody>\n        <tr class=\"cellback\">\n\t\t<td><strong>Chapter<\/strong><\/td>\n                <td><strong>Element<\/strong><\/td>\n\t\t<td><strong>Subsets<\/strong><\/td>\n\t\t<td><strong>Dimension<\/strong><\/td>\n\t<\/tr>\t\t<tr>\n\t\t<td><strong style=\"color: red;\">4<\/strong><\/td>\n\t\t<td style=\"color: red;\">Point<\/td>\n\t\t<td>&nbsp;<\/td>\n\t\t<td style=\"color: red;\">0<\/td>\n\t<\/tr>\n\t<tr>\n\t\t<td>&nbsp;<\/td>\n\t\t<td style=\"color: red;\">Line<\/td>\n\t\t<td>&nbsp;<\/td>\n\t\t<td style=\"color: red;\">1<\/td>\n\t<\/tr>\n\t<tr>\n\t\t<td>&nbsp;<\/td>\n\t\t<td style=\"color: red;\">Plane<\/td>\n\t\t<td style=\"color: red;\">Figure\/Ground<\/td>\n\t\t<td style=\"color: red;\">2<\/td>\n\t<\/tr>\n\t<tr class=\"cellback\">\n\t\t<td><strong>5<\/strong><\/td>\n\t\t<td>Volume<\/td>\n\t\t<td>Mass<\/td>\n\t\t<td>3<\/td>\n\t<\/tr>\n\t<tr>\n\t\t<td><strong>6<\/strong><\/td>\n\t\t<td>Kinetics<\/td>\n\t\t<td>Time\/Motion<\/td>\n\t\t<td>4<\/td>\n\t<\/tr>\n\t<tr class=\"cellback\">\n\t\t<td><strong>7<\/strong><\/td>\n\t\t<td>Light<\/td>\n\t\t<td>Value<\/td>\n\t\t<td>Optical<\/td>\n\t<\/tr>\n\t<tr class=\"cellback\">\n\t\t<td>&nbsp;<\/td>\n\t\t<td>Color<\/td>\n\t\t<td>Hue, Saturation, Brightness<\/td>\n\t\t<td>&nbsp;<\/td>\n\t<\/tr>\n\t<tr class=\"cellback\">\n\t\t<td>&nbsp;<\/td>\n\t\t<td>Texture<\/td>\n\t\t<td>&nbsp;<\/td>\n\t\t<td>&nbsp;<\/td>\n\t<\/tr>\n\t<tbody>\n<\/table>\n\n\n\n<p>Example: a <strong>Line<\/strong>, having length as a property, is a <strong>one-Dimensional<\/strong> entity. <strong>Color<\/strong> is <strong>Optical<\/strong>,&nbsp;meaning it is an innate property of material and therefore something we see regardless of a thing\u2019s dimension. In other words, a line of a given length can be either blue, yellow, or red. This sounds simple, but this property will change our perception of the line.<\/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=\"974\" height=\"1024\" data-attachment-id=\"8253\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/piet_mondriaan_1942_-_new_york_city_i\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I.jpg\" data-orig-size=\"1836,1931\" 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=\"Piet_Mondriaan_1942_-_New_York_City_I\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-974x1024.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-974x1024.jpg\" alt=\"\" class=\"wp-image-8253\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-974x1024.jpg 974w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-285x300.jpg 285w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-768x808.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-1460x1536.jpg 1460w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-300x316.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I.jpg 1836w\" sizes=\"auto, (max-width: 974px) 100vw, 974px\" \/><figcaption class=\"wp-element-caption\"><em>Piet Mondrian, <strong>New York City 1<\/strong>, 1942. The original with color, and the author\u2019s digital modification without color. How does the presence or absence of color change your perception of the artist\u2019s line and composition?<\/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=\"974\" height=\"1024\" data-attachment-id=\"8254\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/piet_mondriaan_1942_-_new_york_city_i-copy\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-copy.jpg\" data-orig-size=\"1836,1931\" 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=\"Piet_Mondriaan_1942_-_New_York_City_I-copy\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-copy-974x1024.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-copy-974x1024.jpg\" alt=\"\" class=\"wp-image-8254\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-copy-974x1024.jpg 974w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-copy-285x300.jpg 285w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-copy-768x808.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-copy-1460x1536.jpg 1460w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-copy-300x316.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Piet_Mondriaan_1942_-_New_York_City_I-copy.jpg 1836w\" sizes=\"auto, (max-width: 974px) 100vw, 974px\" \/><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p>To some, it seems paradoxical to speak of a 1-D&nbsp;<strong>Line<\/strong><em>&nbsp;<\/em>in a 3-D context. To others,&nbsp;it\u2019s tempting to neglect the use of&nbsp;<strong>Color<\/strong>, on the belief the power of&nbsp;<strong>Volume<\/strong><em>&nbsp;<\/em>alone will do all the heavy lifting for 3-D. In this chapter, we\u2019ll demonstrate that, just as they have a place in 2-D visual design, <em>all<\/em> visual elements are relevant to 3D visual design for modelers.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cartesian_coordinate_system\"><\/span>Cartesian coordinate system<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\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"994\" height=\"1024\" data-attachment-id=\"8255\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_003\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_003.png\" data-orig-size=\"994,1024\" 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=\"ch04_003\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_003.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_003.png\" alt=\"\" class=\"wp-image-8255\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_003.png 994w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_003-291x300.png 291w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_003-768x791.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_003-300x309.png 300w\" sizes=\"auto, (max-width: 994px) 100vw, 994px\" \/><\/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\">\n<p><em>The Cartesian coordinate system. The X-axis<\/em> typically describes width, Y depth,<em> and Z height. The XY plane is usually horizontal like the ground (but in the modeling program Maya, it\u2019s the XZ). Where all three axes intersect is the Origin, where all values are zero.<\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n<p>As we focus on <em>Dimensional <\/em>visual elements, we\u2019ll do so through definitions, metaphors, and examples from tactile 3D courses. Using a mathematical vocabulary of point, line, and plane, the <strong>Cartesian coordinate system<\/strong>, discussed in greater depth in Chapter 13, creates a parallel universe wherein one develops masses and voids (<strong>Volume<\/strong>). But there\u2019s more. Many so-called 3D programs can create <em>Kinematics&nbsp;<\/em>to put these volumes into motion using a timeline. Thus, in reality, these function as 4D modelers for animation. These dimensional entities can remain stubbornly abstract until we can find their tangible expression in our universe, so let\u2019s review what we encounter in various dimensions, illustrated 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\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"704\" height=\"704\" data-attachment-id=\"8256\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/0d_4901992302_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/0d_4901992302_o.jpg\" data-orig-size=\"704,704\" 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=\"0d_4901992302_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/0d_4901992302_o.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/0d_4901992302_o.jpg\" alt=\"\" class=\"wp-image-8256\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/0d_4901992302_o.jpg 704w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/0d_4901992302_o-300x300.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/0d_4901992302_o-150x150.jpg 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/0d_4901992302_o-100x100.jpg 100w\" sizes=\"auto, (max-width: 704px) 100vw, 704px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Point\"><\/span>Point<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p><em>An entity with no dimension. Mathematically, the only property a point can have is location. In digital modeling programs, we describe a point by one Cartesian coordinate (X, Y, Z). A particularly privileged point is the Origin: 0,0,0 in Cartesian space, located at the mutual point of intersection of the reference axes and planes.&nbsp;&nbsp;&nbsp;<\/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:33.33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"704\" height=\"704\" data-attachment-id=\"8257\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/1d_4901405597_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/1d_4901405597_o.jpg\" data-orig-size=\"704,704\" 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=\"1d_4901405597_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/1d_4901405597_o.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/1d_4901405597_o.jpg\" alt=\"\" class=\"wp-image-8257\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/1d_4901405597_o.jpg 704w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/1d_4901405597_o-300x300.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/1d_4901405597_o-150x150.jpg 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/1d_4901405597_o-100x100.jpg 100w\" sizes=\"auto, (max-width: 704px) 100vw, 704px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Line\"><\/span>Line<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p><em>An entity with one dimension. A line is a point we push along a vector of some length. Any line of any length contains an infinite number of points and subdivided lines. Digital modeling programs associate length with the direction of the X-axis<\/em>. <em>However a line can be created in any direction, can be associated with straight or curved vectors, and can be created by many forces, such as translation (movement along a line), rotation (movement about a center), or scaling (changing relative size).&nbsp;<\/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:33.33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"704\" height=\"704\" data-attachment-id=\"8258\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/2d_4901405737_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/2d_4901405737_o.jpg\" data-orig-size=\"704,704\" 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=\"2d_4901405737_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/2d_4901405737_o.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/2d_4901405737_o.jpg\" alt=\"\" class=\"wp-image-8258\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/2d_4901405737_o.jpg 704w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/2d_4901405737_o-300x300.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/2d_4901405737_o-150x150.jpg 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/2d_4901405737_o-100x100.jpg 100w\" sizes=\"auto, (max-width: 704px) 100vw, 704px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Plane\"><\/span>Plane<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p><em>An entity with two dimensions. A plane is a line we push along a vector of some length. Any plane of any size contains an infinite number of points, lines, and other subdivided planes. Programs associate an XY plane with width and depth. However, a plane can be created in any direction and can be associated with many shapes, not simply rectangles or regular polygons. A plane can be curved and closed to imply volume.&nbsp;&nbsp;<\/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:33.33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"704\" height=\"704\" data-attachment-id=\"8259\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/3d_4901992602_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/3d_4901992602_o.jpg\" data-orig-size=\"704,704\" 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=\"3d_4901992602_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/3d_4901992602_o.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/3d_4901992602_o.jpg\" alt=\"\" class=\"wp-image-8259\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/3d_4901992602_o.jpg 704w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/3d_4901992602_o-300x300.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/3d_4901992602_o-150x150.jpg 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/3d_4901992602_o-100x100.jpg 100w\" sizes=\"auto, (max-width: 704px) 100vw, 704px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Volume\"><\/span>Volume<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p><em>An entity with three dimensions. A volume is a plane w<\/em>e <em>push along a vector of some length. Any volume of any size contains an infinite number of points, lines, planes, and other subdivided volumes. Programs associate the development of depth with the extrusion of an XY plane through the Z direction<\/em>. <em>However, a volume can be created in any orientation, using virtually any kind of vector and any kind of force.<\/em>&nbsp;&nbsp;<\/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:33.33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"704\" height=\"704\" data-attachment-id=\"8260\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/4d_4901405943_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/4d_4901405943_o.jpg\" data-orig-size=\"704,704\" 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=\"4d_4901405943_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/4d_4901405943_o.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/4d_4901405943_o.jpg\" alt=\"\" class=\"wp-image-8260\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/4d_4901405943_o.jpg 704w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/4d_4901405943_o-300x300.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/4d_4901405943_o-150x150.jpg 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/4d_4901405943_o-100x100.jpg 100w\" sizes=\"auto, (max-width: 704px) 100vw, 704px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Kinematics\"><\/span>Kinematics<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p><em>Entities with four dimensions. A kinematic element is a volume we push along a vector of some length and <strong>duration<\/strong>. However, we should also understand that an object at rest <strong>also<\/strong> exists in time. An entity existing for any duration contains an infinite number of points, lines, planes, subdivided volumes, and potential locations while it exists. Programs often associate motion (T) with units called frames in a timeline. Frames are not referenced with spatial coordinates, although events resulting from frame manipulation are seen as spatial manipulation in the viewport.<\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Kandinskys_Basic_Plane\"><\/span>Kandinsky&#8217;s Basic Plane<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>It is fairly easy to see the systematic development of Dimension in a mathematical setting. The way artists deal with dimension also follows a system, albeit a more intuitive kind. In the very title of his book <em><strong>Point and Line to Plane<\/strong><\/em>, abstract painter and Bauhaus Basic Course instructor Wassily Kandinksy suggests emotional and spiritual relationships in the geometrical elements which underpin every visual work \u2014 point and line \u2014 in relationship to the plane of infinite potential he calls the <strong>basic plane<\/strong>. <sup><a href=\"#footnote_2_8245\" id=\"identifier_2_8245\" class=\"footnote-link footnote-identifier-link\" title=\"Kandinsky, Wassily (trans. Rebay, Hilla). Point and Line to Plane. Dover Editions. 1979. p.115.\">2<\/a><\/sup><\/p>\n\n\n\n<p>For Kandinksy, the basic plane, or <strong>BP<\/strong>, is the painter\u2019s canvas. By analogy, for the digital modeler, it is a Cartesian reference plane like the horizontal XY plane seen in the viewport. The most obvious difference between these two BPs is that Kandinksy\u2019s is a material surface, while the digital one is an untouchable, pure state of geometry.&nbsp;<\/p>\n\n\n\n<p>The problem for the digital artist is how to bridge the conceptual gap. We can\u2019t make the digital BP into an object (at least not right now). However, we can \u201csee\u201d manifestations of dimension in artifacts and objects that possess their character. With some help from his fellow painter and Bauhaus instructor Paul Klee, we can extend Kandinsky\u2019s logic and make the metaphorical leap of association between the mathematical and the physical, the digital and the tactile.<em>&nbsp;<\/em><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Kandinskys_dimensions\"><\/span>Kandinsky\u2019s dimensions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Point%E2%80%A6\"><\/span><em>Point\u2026<\/em><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>\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>Here, find an illustration of a point. Well, actually, an infinite number of points. Yes, they&#8217;re there, but you can\u2019t see them: they have no dimension!&nbsp;<\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n<p>As a practical matter, when Kandinsky discusses a point, he\u2019s not discussing the mathematical abstraction we \u201csee\u201d above.<\/p>\n\n\n\n<p>He rather talks about a dab or stain of pigment placed on the canvas, a physical event that at a certain scale extends the point to a form with color or even texture or thickness, and this physicality can give the point an emotional charge.&nbsp;As Ellen Lupton and Jennifer Cole Phillips describe it, \u201cGraphically, \u2026 a point takes form as a dot, a visible mark. A point can be an insignificant fleck of matter or a concentrated locus of power. It can penetrate like a bullet, pierce like a nail, or pucker like a kiss.\u201d <sup><a href=\"#footnote_3_8245\" id=\"identifier_3_8245\" class=\"footnote-link footnote-identifier-link\" title=\"Lupton, Ellen and Phillips, Jennifer Cole. Graphic Design: The New Basics. Princeton Architectural Press. 2008. p.14.\">3<\/a><\/sup><\/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<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Examples\"><\/span>Examples<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p>So if you try to model a single Cartesian point and render it, prepare for an exercise in futility. However, using the point locus to create an entity that has attributes of material, color, and texture applied to a volume, and placing it in a context where its scale and ability to focus is manifest, the point will acquire character and meaning. A few examples:<\/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 data-wp-context=\"{&quot;imageId&quot;:&quot;69f10d5fd3a58&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69f10d5fd3a58\" class=\"aligncenter size-large wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"709\" data-attachment-id=\"2399\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/geometry-color-meaning\/kandinsky\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/08\/kandinsky.jpg\" data-orig-size=\"1090,755\" 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=\"kandinsky\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/08\/kandinsky-1024x709.jpg\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/08\/kandinsky-1024x709.jpg\" alt=\"\" class=\"wp-image-2399\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/08\/kandinsky-1024x709.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/08\/kandinsky-300x208.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/08\/kandinsky-768x532.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/08\/kandinsky.jpg 1090w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Enlarge\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>&nbsp;Wassily Kandinsky,&nbsp;<strong>Composition VIII<\/strong>, 1923. Kandinsky evokes points by stains of color, dots, and intersections of line. He follows up with the most lucid theory describing the strategy of non-objective painting: to create \u201can exact replica of some inner emotion.\u201d<\/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\"><div class=\"wp-block-image\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69f10d5fd4bb7&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69f10d5fd4bb7\" class=\"aligncenter size-full wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"860\" height=\"566\" data-attachment-id=\"8266\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/jordan_cans_seurat_4902511614_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/jordan_cans_seurat_4902511614_o.jpg\" data-orig-size=\"860,566\" 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=\"jordan_cans_seurat_4902511614_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/jordan_cans_seurat_4902511614_o.jpg\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/jordan_cans_seurat_4902511614_o.jpg\" alt=\"\" class=\"wp-image-8266\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/jordan_cans_seurat_4902511614_o.jpg 860w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/jordan_cans_seurat_4902511614_o-300x197.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/jordan_cans_seurat_4902511614_o-768x505.jpg 768w\" sizes=\"auto, (max-width: 860px) 100vw, 860px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Enlarge\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>\u00a0Chris Jordan,\u00a0<strong>Cans Seurat<\/strong>, 2007. The original painting,\u00a0<strong>A Sunday Afternoon on the Island of La Grande Jatte<\/strong>\u00a0by Georges Seurat, used tiny \u201cpoints\u201d of color, achieving the illusion of form. Jordan&#8217;s ecological subtext depicts his park with 106,000 cans, the number used in the US every thirty seconds.<\/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 data-wp-context=\"{&quot;imageId&quot;:&quot;69f10d5fd5fad&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69f10d5fd5fad\" class=\"aligncenter size-large wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"614\" data-attachment-id=\"8267\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/200501_redrain_4412849999_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/200501_redrain_4412849999_o.jpg\" data-orig-size=\"1280,768\" 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=\"200501_redrain_4412849999_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/200501_redrain_4412849999_o-1024x614.jpg\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/200501_redrain_4412849999_o-1024x614.jpg\" alt=\"\" class=\"wp-image-8267\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/200501_redrain_4412849999_o-1024x614.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/200501_redrain_4412849999_o-300x180.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/200501_redrain_4412849999_o-768x461.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/200501_redrain_4412849999_o.jpg 1280w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Enlarge\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>&nbsp;William Cromar,&nbsp;<strong>redr\u0250in<\/strong>, 2005. The author used 3D modeling to generate intersecting geometries and organization of points for this installation in thread and wax.<\/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\"><div class=\"wp-block-image\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69f10d5fd7b4d&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69f10d5fd7b4d\" class=\"aligncenter size-large wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" data-attachment-id=\"8268\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/parc-de-la-villette-2018-c2a9-philippe-guignard-air-images-9\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/parc-de-la-villette-2018-c2a9-philippe-guignard-air-images-9.webp\" data-orig-size=\"1920,1080\" 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=\"parc-de-la-villette-2018-c2a9-philippe-guignard-air-images-9\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/parc-de-la-villette-2018-c2a9-philippe-guignard-air-images-9-1024x576.webp\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/parc-de-la-villette-2018-c2a9-philippe-guignard-air-images-9-1024x576.webp\" alt=\"\" class=\"wp-image-8268\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/parc-de-la-villette-2018-c2a9-philippe-guignard-air-images-9-1024x576.webp 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/parc-de-la-villette-2018-c2a9-philippe-guignard-air-images-9-300x169.webp 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/parc-de-la-villette-2018-c2a9-philippe-guignard-air-images-9-768x432.webp 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/parc-de-la-villette-2018-c2a9-philippe-guignard-air-images-9-1536x864.webp 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/parc-de-la-villette-2018-c2a9-philippe-guignard-air-images-9.webp 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Enlarge\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>Bernard Tschumi, <strong>Parc de la Villette<\/strong>, 1987. One can\u2019t help but notice the punctuated presence of the red <strong>follies<\/strong>&nbsp;(pavilions) in this Parisian park.&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 data-wp-context=\"{&quot;imageId&quot;:&quot;69f10d5fd86f7&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69f10d5fd86f7\" class=\"aligncenter size-full wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"781\" height=\"1024\" data-attachment-id=\"8269\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/tschumi_parc_de_la_villette_drawing_4902511378_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/tschumi_parc_de_la_villette_drawing_4902511378_o.jpg\" data-orig-size=\"781,1024\" 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=\"tschumi_parc_de_la_villette_drawing_4902511378_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/tschumi_parc_de_la_villette_drawing_4902511378_o.jpg\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/tschumi_parc_de_la_villette_drawing_4902511378_o.jpg\" alt=\"\" class=\"wp-image-8269\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/tschumi_parc_de_la_villette_drawing_4902511378_o.jpg 781w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/tschumi_parc_de_la_villette_drawing_4902511378_o-229x300.jpg 229w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/tschumi_parc_de_la_villette_drawing_4902511378_o-768x1007.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/tschumi_parc_de_la_villette_drawing_4902511378_o-300x393.jpg 300w\" sizes=\"auto, (max-width: 781px) 100vw, 781px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Enlarge\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>Tschumi\u2019s exploded view of the&nbsp;Parc, illustrates elements of <strong>point<\/strong> (follies), <strong>line<\/strong> (paths, tree lines), and <strong>plane<\/strong> (ground surfaces).<\/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 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 is-layout-flow wp-block-column-is-layout-flow\">\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"In_the_studio\"><\/span>In the studio<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p><em>Point examples from traditional tactile 3D design studios:<\/em><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69f10d5fd984b&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69f10d5fd984b\" class=\"aligncenter size-large wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"371\" data-attachment-id=\"8279\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_011\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_011.jpg\" data-orig-size=\"2400,870\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;2.67&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;hp photosmart 735&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1099218395&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;5.95&quot;,&quot;iso&quot;:&quot;100&quot;,&quot;shutter_speed&quot;:&quot;0.016667&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"ch04_011\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_011-1024x371.jpg\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_011-1024x371.jpg\" alt=\"\" class=\"wp-image-8279\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_011-1024x371.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_011-300x109.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_011-768x278.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_011-1536x557.jpg 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_011-2048x742.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Enlarge\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>All sand is not created equal: this student project creates an illusion of receding points. From a studio by the author.<\/em><\/figcaption><\/figure>\n<\/div>\n\n\n<div style=\"padding:56.25% 0 0 0;position:relative;\"><iframe src=\"https:\/\/player.vimeo.com\/video\/42896836?h=20214ece96&#038;title=0&#038;byline=0&#038;portrait=0\" style=\"position:absolute;top:0;left:0;width:100%;height:100%;\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture\" allowfullscreen><\/iframe><\/div>\n\n\n\n<p><em>James Leng, &nbsp;<strong>Point Cloud<\/strong>, 2012, marries weather data and the concept of a <strong>point cloud<\/strong> with a microprocessor to create an undulating, kinetic dot matrix that <strong>responds to weather<\/strong>.<\/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 data-wp-context=\"{&quot;imageId&quot;:&quot;69f10d5fdb0b1&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69f10d5fdb0b1\" class=\"aligncenter size-large wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"537\" height=\"1024\" data-attachment-id=\"8280\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_012\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_012.png\" data-orig-size=\"546,1041\" 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=\"ch04_012\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_012-537x1024.png\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_012-537x1024.png\" alt=\"\" class=\"wp-image-8280\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_012-537x1024.png 537w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_012-157x300.png 157w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_012-300x572.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_012.png 546w\" sizes=\"auto, (max-width: 537px) 100vw, 537px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Enlarge\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>Sand again, this time wed to acrylic plastic by a heat gun, providing dramatic foci of melting points frozen in a clear plane. Student work from a studio by the author.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E2%80%A6and_Line%E2%80%A6\"><\/span><em>\u2026and Line\u2026<\/em><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"717\" data-attachment-id=\"1282\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/line-art\/302_paul-klee-pedagogical-sketchbook_page_09-2\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/07\/302_Paul-Klee-Pedagogical-Sketchbook_Page_09-2.jpg\" data-orig-size=\"1170,819\" 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=\"302_Paul-Klee-Pedagogical-Sketchbook_Page_09-2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/07\/302_Paul-Klee-Pedagogical-Sketchbook_Page_09-2-1024x717.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/07\/302_Paul-Klee-Pedagogical-Sketchbook_Page_09-2-1024x717.jpg\" alt=\"\" class=\"wp-image-1282\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/07\/302_Paul-Klee-Pedagogical-Sketchbook_Page_09-2-1024x717.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/07\/302_Paul-Klee-Pedagogical-Sketchbook_Page_09-2-300x210.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/07\/302_Paul-Klee-Pedagogical-Sketchbook_Page_09-2-768x538.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/07\/302_Paul-Klee-Pedagogical-Sketchbook_Page_09-2.jpg 1170w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Paul Klee, illustrations of a \u201cline out for a walk,\u201d from the&nbsp;<strong>Pedagogical Sketchbook<\/strong>, 1925<\/em>  <sup><a href=\"#footnote_4_8245\" id=\"identifier_4_8245\" class=\"footnote-link footnote-identifier-link\" title=\"Klee, Paul. Pedagogical Sketchbook. Praeger. 7th ed. 1972. pp. 16-17.\">4<\/a><\/sup><\/figcaption><\/figure>\n<\/div>\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><em>A line is an infinite series of points. Understood geometrically, a line has length, but no breadth. A line is the connection between two points, or it is the path of a moving point. A line can be a positive mark or a negative gap. Lines appear at the edges of objects and where two planes meet. Graphically, lines exist in many weights; the thickness and texture as well as the path of the mark determine its visual presence. Lines are drawn with a pen, pencil, brush, mouse, or digital code. They can be straight or curved, continuous or broken. When a line reaches a certain thickness, it becomes a plane. Lines multiply to describe volumes, planes, and textures.<\/em><\/p>\n<cite>\u2014 Lupton and Phillips  <sup><a href=\"#footnote_5_8245\" id=\"identifier_5_8245\" class=\"footnote-link footnote-identifier-link\" title=\"Lupton, Ellen. Graphic Design: The New Basics. Princeton Architectural Press. 2008. p. 16.\">5<\/a><\/sup><\/cite><\/blockquote>\n\n\n\n<p>For Kandinsky, the line suggested the presence of directional force acting on a point.&nbsp;Paul Klee, another Bauhaus Basic instructor and painter, speaks poetically about that force, in the development of a moving dot as a &#8220;line out for a walk.&#8221;  <sup><a href=\"#footnote_6_8245\" id=\"identifier_6_8245\" class=\"footnote-link footnote-identifier-link\" title=\"Klee, Paul. Pedagogical Sketchbook. Praeger. 7th ed. 1972. p. 16.\">6<\/a><\/sup>&nbsp;We can see in the illustration from his <em><strong>Pedagogical Sketchbook<\/strong><\/em> that the character of the drawn line suggests the nature of the journey: a random meander, a deliberate goal-oriented stride, a welcome encounter interrupting the path.<\/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<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Examples-2\"><\/span>Examples<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p>In our first example, observe the \u201cinventor\u201d of wire sculpture, Alexander Calder, creating a drawing in space with his full-body portrait of the dancer and entertainer Josephine Baker.<\/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=\"645\" height=\"1024\" data-attachment-id=\"8285\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/calder_josephine_baker_4914104277_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/calder_josephine_baker_4914104277_o.jpg\" data-orig-size=\"1260,2000\" 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=\"calder_josephine_baker_4914104277_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/calder_josephine_baker_4914104277_o-645x1024.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/calder_josephine_baker_4914104277_o-645x1024.jpg\" alt=\"\" class=\"wp-image-8285\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/calder_josephine_baker_4914104277_o-645x1024.jpg 645w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/calder_josephine_baker_4914104277_o-189x300.jpg 189w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/calder_josephine_baker_4914104277_o-768x1219.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/calder_josephine_baker_4914104277_o-968x1536.jpg 968w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/calder_josephine_baker_4914104277_o-300x476.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/calder_josephine_baker_4914104277_o.jpg 1260w\" sizes=\"auto, (max-width: 645px) 100vw, 645px\" \/><figcaption class=\"wp-element-caption\"><em>Alexander Calder,&nbsp;<strong>Josephine Baker (III)<\/strong>, circa 1927&nbsp;<\/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\">\n<p>In another visualization of digital wireframing, we note sculptor Benedict Radcliffe\u2019s surreal Nike Air. It\u2019s not Photoshop: instead, he carefully crafts wireframe physical models from observation of digital media in a culturally significant role reversal.<\/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=\"1024\" height=\"683\" data-attachment-id=\"8286\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/modern-sculpture-benedict-radcliffe-1-1200x800-1\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/modern-sculpture-benedict-radcliffe-1-1200x800-1.jpg\" data-orig-size=\"1200,800\" 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=\"modern-sculpture-benedict-radcliffe-1-1200&amp;#215;800-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/modern-sculpture-benedict-radcliffe-1-1200x800-1-1024x683.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/modern-sculpture-benedict-radcliffe-1-1200x800-1-1024x683.jpg\" alt=\"\" class=\"wp-image-8286\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/modern-sculpture-benedict-radcliffe-1-1200x800-1-1024x683.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/modern-sculpture-benedict-radcliffe-1-1200x800-1-300x200.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/modern-sculpture-benedict-radcliffe-1-1200x800-1-768x512.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/modern-sculpture-benedict-radcliffe-1-1200x800-1.jpg 1200w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Benedict Radcliffe,&nbsp;<strong>Nike Air Max<\/strong>,&nbsp;2009&nbsp;<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p>Despite its contemporary cachet, the wireframe debuted over 500 years ago! We see it first in the chalice study attributed to Paolo Uccello. His drawing is a pen and ink study of Renaissance perspectival geometry. This drawing so precisely foresaw the convention of digital wireframe modeling that Angela Eames was able to create a contemporary digital homage. In response, this author created a physical sculpture, no mean feat for a wireframe!<\/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=\"708\" height=\"1024\" data-attachment-id=\"8288\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/paolo_uccello_studio_di_vaso_in_prospettiva_02-2\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Paolo_uccello_studio_di_vaso_in_prospettiva_02.webp\" data-orig-size=\"1175,1700\" 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=\"Paolo_uccello_studio_di_vaso_in_prospettiva_02\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Paolo_uccello_studio_di_vaso_in_prospettiva_02-708x1024.webp\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Paolo_uccello_studio_di_vaso_in_prospettiva_02-708x1024.webp\" alt=\"\" class=\"wp-image-8288\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Paolo_uccello_studio_di_vaso_in_prospettiva_02-708x1024.webp 708w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Paolo_uccello_studio_di_vaso_in_prospettiva_02-207x300.webp 207w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Paolo_uccello_studio_di_vaso_in_prospettiva_02-768x1111.webp 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Paolo_uccello_studio_di_vaso_in_prospettiva_02-1062x1536.webp 1062w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Paolo_uccello_studio_di_vaso_in_prospettiva_02-300x434.webp 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Paolo_uccello_studio_di_vaso_in_prospettiva_02.webp 1175w\" sizes=\"auto, (max-width: 708px) 100vw, 708px\" \/><figcaption class=\"wp-element-caption\"><em>Attributed to Paolo Uccello,&nbsp;<strong>Perspective Study of a Chalice<\/strong>, circa 1430-40<\/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=\"281\" height=\"400\" data-attachment-id=\"8289\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/eames_ucello_chalice_homage_4916304768_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/eames_ucello_chalice_homage_4916304768_o.jpg\" data-orig-size=\"281,400\" 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=\"eames_ucello_chalice_homage_4916304768_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/eames_ucello_chalice_homage_4916304768_o.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/eames_ucello_chalice_homage_4916304768_o.jpg\" alt=\"\" class=\"wp-image-8289\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/eames_ucello_chalice_homage_4916304768_o.jpg 281w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/eames_ucello_chalice_homage_4916304768_o-211x300.jpg 211w\" sizes=\"auto, (max-width: 281px) 100vw, 281px\" \/><figcaption class=\"wp-element-caption\"><em>Angela Eames, wireframe 3D model rendering, circa 2004<\/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\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"768\" height=\"1024\" data-attachment-id=\"8287\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/chalice01-2\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/chalice01.webp\" data-orig-size=\"1600,2133\" 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=\"chalice01\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/chalice01-768x1024.webp\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/chalice01-768x1024.webp\" alt=\"\" class=\"wp-image-8287\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/chalice01-768x1024.webp 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/chalice01-225x300.webp 225w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/chalice01-1152x1536.webp 1152w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/chalice01-1536x2048.webp 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/chalice01-300x400.webp 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/chalice01.webp 1600w\" sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><figcaption class=\"wp-element-caption\"><em>willliamCromar, <strong><a href=\"https:\/\/williamcromar.com\/uccello-chalice\/\">ucello chalice<\/a><\/strong>, 2022, resin stereolithography<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<iframe allowfullscreen width=\"100%\" height=\"480\" loading=\"lazy\" frameborder=\"0\" src=\"https:\/\/p3d.in\/e\/oXpsa+xray+spin+load\"><\/iframe>\n\n\n\n<p><em>Model for sculpture<\/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<p>A line can suggest the direction of a force. Innovative for its era, an architectural structure for <em><strong>La Sagrada Familia<\/strong><\/em> is determined by the funicular (rope and sandbag) model of the church by Antoni Gaud\u00ed, projected to be the tallest church in the world once it is completed sometime between 2026 and 2040.<\/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=\"1024\" height=\"1024\" data-attachment-id=\"8293\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/sagrada-familia-1024x1024-1\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Sagrada-Familia-1024x1024-1.webp\" data-orig-size=\"1024,1024\" 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=\"Sagrada-Familia-1024&amp;#215;1024-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Sagrada-Familia-1024x1024-1.webp\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Sagrada-Familia-1024x1024-1.webp\" alt=\"\" class=\"wp-image-8293\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Sagrada-Familia-1024x1024-1.webp 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Sagrada-Familia-1024x1024-1-300x300.webp 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Sagrada-Familia-1024x1024-1-150x150.webp 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Sagrada-Familia-1024x1024-1-768x768.webp 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Sagrada-Familia-1024x1024-1-100x100.webp 100w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>The <strong>Sagrada Familia<\/strong> in Barcelona is made complete by art collective DRIFT using <a href=\"https:\/\/news.artnet.com\/art-world\/see-how-the-dutch-collective-drift-uses-drones-and-lights-to-digitally-rebuild-the-colosseum-and-other-major-landmarks-2199804\" target=\"_blank\" rel=\"noreferrer noopener\">drone technology<\/a>, 2022<\/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\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"768\" height=\"1024\" data-attachment-id=\"8294\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/gaudi_sagrada_familia_model_4916285086_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_4916285086_o.jpg\" data-orig-size=\"1536,2048\" 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=\"gaudi_sagrada_familia_model_4916285086_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_4916285086_o-768x1024.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_4916285086_o-768x1024.jpg\" alt=\"\" class=\"wp-image-8294\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_4916285086_o-768x1024.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_4916285086_o-225x300.jpg 225w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_4916285086_o-1152x1536.jpg 1152w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_4916285086_o-300x400.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_4916285086_o.jpg 1536w\" sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><figcaption class=\"wp-element-caption\"><em>Antoni Gaud\u00ed, funicular model, <strong>La Sagrada Familia<\/strong>, which began in 1888 to study the structure.<\/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=\"768\" height=\"1024\" data-attachment-id=\"8295\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/gaudi_sagrada_familia_model_rotated_4916474552_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_rotated_4916474552_o.jpg\" data-orig-size=\"1536,2048\" 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=\"gaudi_sagrada_familia_model_rotated_4916474552_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_rotated_4916474552_o-768x1024.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_rotated_4916474552_o-768x1024.jpg\" alt=\"\" class=\"wp-image-8295\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_rotated_4916474552_o-768x1024.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_rotated_4916474552_o-225x300.jpg 225w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_rotated_4916474552_o-1152x1536.jpg 1152w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_rotated_4916474552_o-300x400.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gaudi_sagrada_familia_model_rotated_4916474552_o.jpg 1536w\" sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><figcaption class=\"wp-element-caption\"><em>The funicular model is rotated to see the structure predicted by linear ropes inside the cloud of sandbags.<\/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%\">\n<p>The sandbags are reminiscent of another kind of structure: quantum probability, suggested by the work of Antony Gormley. How does the human figure emerge from a density of lines bordering on texture?<\/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=\"781\" height=\"1024\" data-attachment-id=\"8296\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/gormley_quantum_cloud_4915682395_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gormley_quantum_cloud_4915682395_o.jpg\" data-orig-size=\"867,1137\" 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=\"gormley_quantum_cloud_4915682395_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gormley_quantum_cloud_4915682395_o-781x1024.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gormley_quantum_cloud_4915682395_o-781x1024.jpg\" alt=\"\" class=\"wp-image-8296\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gormley_quantum_cloud_4915682395_o-781x1024.jpg 781w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gormley_quantum_cloud_4915682395_o-229x300.jpg 229w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gormley_quantum_cloud_4915682395_o-768x1007.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gormley_quantum_cloud_4915682395_o-300x393.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gormley_quantum_cloud_4915682395_o.jpg 867w\" sizes=\"auto, (max-width: 781px) 100vw, 781px\" \/><figcaption class=\"wp-element-caption\"><em>Antony Gormley,&nbsp;<strong>Quantum Cloud<\/strong>, 2000<\/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 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\">\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"In_the_studio-2\"><\/span>In the studio<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p><em>Line examples from 3D design studios:<\/em><\/p>\n\n\n\n<p><em>A common exercise in tactile 3D design is the wire \u201cdrawing in space,\u201d often paired with figuration, to explore the use of lines. In this example, student used copper wire to create a life-size self-portrait. She was allowed to bend the wire over her features \u2014 not cheating, incidentally, as we\u2019ll see when we discuss concepts in the process of casting in Chapter 14. She still had to figure out how to relate wires to achieve a proportionally accurate result. The most important decisions included intuiting where topological lines should best be placed economically to achieve a phenomenon of implied mass.<\/em><\/p>\n<\/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=\"504\" height=\"758\" data-attachment-id=\"8302\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_022\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_022.jpg\" data-orig-size=\"504,758\" 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=\"ch04_022\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_022.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_022.jpg\" alt=\"\" class=\"wp-image-8302\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_022.jpg 504w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_022-199x300.jpg 199w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_022-300x451.jpg 300w\" sizes=\"auto, (max-width: 504px) 100vw, 504px\" \/><figcaption class=\"wp-element-caption\"><em>Student exercise, figure drawing with wire in space. From a studio by the author.<\/em>&nbsp;<\/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=\"338\" height=\"577\" data-attachment-id=\"8303\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_023\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_023.png\" data-orig-size=\"338,577\" 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=\"ch04_023\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_023.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_023.png\" alt=\"\" class=\"wp-image-8303\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_023.png 338w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_023-176x300.png 176w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_023-300x512.png 300w\" sizes=\"auto, (max-width: 338px) 100vw, 338px\" \/><figcaption class=\"wp-element-caption\"><em>Student exercise, now with wireframes in the viewport. From a studio by the author.<\/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\">\n<p><em>When you compare the tactile wire figure with the digital figure study here, you\u2019ll note many important points of reference are found in both. For example, a central axial line dividing left from right exists in both, alluding to the principle of symmetry discussed below. Note also how the ridges above the eye and at the cheeks are similarly modeled in tactile and digital modes. Another interesting similarity occurs in the density of data. Where significant events such as the eye or ear occur, the geometry gets denser. When digitally modeling from life, the artist will find it necessary to create tactile studies \u2014 sketching or physical modeling in clay \u2014 just as they do when modeling for a final product in plaster or stone.<\/em><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E2%80%A6to_Plane\"><\/span><em>\u2026to Plane<\/em><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Related_terms_Figure-ground_Form_Shape\"><\/span>Related terms: Figure-ground | Form | Shape<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=\"430\" height=\"786\" data-attachment-id=\"8308\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/paul_klee_line_and_plane_5025185361_o\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/paul_klee_line_and_plane_5025185361_o.jpg\" data-orig-size=\"430,786\" 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=\"paul_klee_line_and_plane_5025185361_o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/paul_klee_line_and_plane_5025185361_o.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/paul_klee_line_and_plane_5025185361_o.jpg\" alt=\"\" class=\"wp-image-8308\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/paul_klee_line_and_plane_5025185361_o.jpg 430w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/paul_klee_line_and_plane_5025185361_o-164x300.jpg 164w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/paul_klee_line_and_plane_5025185361_o-300x548.jpg 300w\" sizes=\"auto, (max-width: 430px) 100vw, 430px\" \/><\/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>Paul Klee, diagrams of line-to-plane relationships, 1925<\/em>.  <sup><a href=\"#footnote_7_8245\" id=\"identifier_7_8245\" class=\"footnote-link footnote-identifier-link\" title=\"Klee, Paul. Pedagogical Sketchbook. Praeger. 7th ed. 1972. pp. 18-19.\">7<\/a><\/sup><\/p>\n\n\n\n<p><em><strong>Top<\/strong> active and open-ended line \u2014 implied and passive plane.<\/em>&nbsp;<\/p>\n\n\n\n<p><em><strong>Middle<\/strong>&nbsp;active and closed line \u2014 linear character in the act of being created, planar character once completed.<\/em>&nbsp;<\/p>\n\n\n\n<p><em><strong>Bottom<\/strong>&nbsp;passive lines \u2014 angular or circular force applied to create active planes.<\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n<p>We may recall Kandinsky&#8217;s basic plane mentioned earlier. His pre-existing, autonomous world is defined by proportion \u2014 a square, vertical, or horizontal format to the canvas. Point and line also react to what Kandinsky calls the effective \u201ctonality\u201d determined by this proportion. For him, the horizontal suggests the kind of passive, restive state generated by cool tonality, while the vertical implies the active state of the warm.  <sup><a href=\"#footnote_8_8245\" id=\"identifier_8_8245\" class=\"footnote-link footnote-identifier-link\" title=\"Kandinsky, Wassily (trans. Rebay, Hilla). Point and Line to Plane. Dover Editions. 1979. p.115.\">8<\/a><\/sup>&nbsp;It\u2019s impossibly reductive to talk about Kandinksy\u2019s geometry without referencing tone and color, but we\u2019ll reserve a deeper discussion for that in Chapter 7.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"918\" height=\"328\" data-attachment-id=\"8309\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_026\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_026.jpg\" data-orig-size=\"918,328\" 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=\"ch04_026\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_026.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_026.jpg\" alt=\"\" class=\"wp-image-8309\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_026.jpg 918w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_026-300x107.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_026-768x274.jpg 768w\" sizes=\"auto, (max-width: 918px) 100vw, 918px\" \/><figcaption class=\"wp-element-caption\"><em>Kandinsky\u2019s \u201ctonality\u201d implies the vertical basic plane is warm and therefore active, the square neutral, and the horizontal cool and therefore passive.<\/em><\/figcaption><\/figure>\n<\/div>\n\n\n<p>In a set of illustrations we mentioned earlier from the <em><strong>Pedagogical Sketchbook<\/strong><\/em>  <sup><a href=\"#footnote_9_8245\" id=\"identifier_9_8245\" class=\"footnote-link footnote-identifier-link\" title=\"Klee, Paul. Pedagogical Sketchbook. Praeger. 7th ed. 1972. pp. 18-19.\">9<\/a><\/sup>, Paul Klee posits three states of line-to-plane relationships, which Lupton and Phillips describe:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><em>A plane is the path of a moving line; it is a line with breadth. A line closes to become a shape, a bounded plane. Shapes are planes with edges. In vector\u2013based software, every shape consists of line and fill. A plane can be parallel to the picture surface, or it can skew and recede into space. Ceilings, walls, floors, and windows are physical planes. A plane can be solid or perforated, opaque or transparent, textured or smooth.<\/em><\/p>\n<cite>\u2014 Lupton and Phillips  <sup><a href=\"#footnote_10_8245\" id=\"identifier_10_8245\" class=\"footnote-link footnote-identifier-link\" title=\"Lupton, Ellen and Phillips, Jennifer Cole. Graphic Design: The New Basics. Princeton Architectural Press. 2008. p. 18.\">10<\/a><\/sup><\/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\">\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Examples-3\"><\/span>Examples<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p>Constructivist Antoine Pevsner\u2019s exercises in translating lines yield overlapping 2D graphic planes, except the operations occur in multiple axial orientations, making transparent, spatially ambiguous objects.<\/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=\"1024\" height=\"864\" data-attachment-id=\"8311\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/maquette-of-a-monument-symbolising-the-liberation-of-the-spirit-1952-by-antoine-pevsner-1884-1962\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/pevsner_maquette_of_a_monument_symbolising_the_liberation_of_the_spirit_502608002.jpg\" data-orig-size=\"1200,1013\" 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;Maquette of a Monument Symbolising the Liberation of the Spirit 1952 Antoine Pevsner 1884-1962 Purchased 1953 http:\/\/www.tate.org.uk\/art\/work\/N06162&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;(c) ADAGP, Paris and DACS, London 2016 \/ Photo (c) Tate&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;Maquette of a Monument Symbolising the Liberation of the Spirit 1952 by Antoine Pevsner 1884-1962&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Maquette of a Monument Symbolising the Liberation of the Spirit 1952 by Antoine Pevsner 1884-1962\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Maquette of a Monument Symbolising the Liberation of the Spirit 1952 Antoine Pevsner 1884-1962 Purchased 1953 http:\/\/www.tate.org.uk\/art\/work\/N06162&lt;\/p&gt;\n\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/pevsner_maquette_of_a_monument_symbolising_the_liberation_of_the_spirit_502608002-1024x864.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/pevsner_maquette_of_a_monument_symbolising_the_liberation_of_the_spirit_502608002-1024x864.jpg\" alt=\"\" class=\"wp-image-8311\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/pevsner_maquette_of_a_monument_symbolising_the_liberation_of_the_spirit_502608002-1024x864.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/pevsner_maquette_of_a_monument_symbolising_the_liberation_of_the_spirit_502608002-300x253.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/pevsner_maquette_of_a_monument_symbolising_the_liberation_of_the_spirit_502608002-768x648.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/pevsner_maquette_of_a_monument_symbolising_the_liberation_of_the_spirit_502608002.jpg 1200w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Antoine Pevsner,&nbsp;<strong>Maquette of a Monument Symbolizing the Liberation of the Spirit<\/strong>, 1952<\/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\">\n<p>In another example, Pablo Picasso&#8217;s exploration of a guitar engages in a play of solid and void in which volume is ambiguous and implied: note how the sound hole, ordinarily perceived as receding, projects outward as a cylindrical plane. Picasso also completely redefined the terms of sculptural production away from traditional additive or subtractive modes and into a new technique of assembly, the 3D equivalent of collage.<\/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=\"354\" height=\"500\" data-attachment-id=\"6173\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-9-expression-form-content-and-narrative\/picasso_guitar\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/01\/picasso_guitar.jpg\" data-orig-size=\"354,500\" 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=\"picasso_guitar\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/01\/picasso_guitar.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/01\/picasso_guitar.jpg\" alt=\"\" class=\"wp-image-6173\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/01\/picasso_guitar.jpg 354w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/01\/picasso_guitar-212x300.jpg 212w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/01\/picasso_guitar-300x424.jpg 300w\" sizes=\"auto, (max-width: 354px) 100vw, 354px\" \/><figcaption class=\"wp-element-caption\"><em>Pablo Picasso,&nbsp;<strong>Guitar<\/strong>, 1914&nbsp;<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p>It&#8217;s surprising to note that furniture design sometimes outstrips sculpture as a laboratory for innovation. De Stijl designer Gerrit Rietveld concocted 3D planar relationships in furniture and as well as in architecture. At first glance, Frank Gehry\u2019s cardboard chair and ottoman seem made of planar&nbsp;slabs slipping past one another to accumulate mass, but we see those planes are in turn built up of smaller laminated planes, in turn built of the smallest plane: the thickness of cardboard.<\/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=\"864\" height=\"864\" data-attachment-id=\"1642\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/essentials\/rietveldchairrendered\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/08\/RietveldChairRendered.jpg\" data-orig-size=\"864,864\" 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=\"RietveldChairRendered\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/08\/RietveldChairRendered.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/08\/RietveldChairRendered.jpg\" alt=\"\" class=\"wp-image-1642\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/08\/RietveldChairRendered.jpg 864w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/08\/RietveldChairRendered-300x300.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/08\/RietveldChairRendered-150x150.jpg 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/08\/RietveldChairRendered-768x768.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2023\/08\/RietveldChairRendered-100x100.jpg 100w\" sizes=\"auto, (max-width: 864px) 100vw, 864px\" \/><figcaption class=\"wp-element-caption\"><em>Gerrit Rietveld,&nbsp;<strong>Red Blue Chair<\/strong>,&nbsp;1917<\/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=\"763\" height=\"1024\" data-attachment-id=\"8313\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/rietveldtable1_2048x2048\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/rietveldtable1_2048x2048.webp\" data-orig-size=\"1400,1880\" 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=\"rietveldtable1_2048x2048\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/rietveldtable1_2048x2048-763x1024.webp\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/rietveldtable1_2048x2048-763x1024.webp\" alt=\"\" class=\"wp-image-8313\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/rietveldtable1_2048x2048-763x1024.webp 763w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/rietveldtable1_2048x2048-223x300.webp 223w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/rietveldtable1_2048x2048-768x1031.webp 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/rietveldtable1_2048x2048-1144x1536.webp 1144w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/rietveldtable1_2048x2048-300x403.webp 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/rietveldtable1_2048x2048.webp 1400w\" sizes=\"auto, (max-width: 763px) 100vw, 763px\" \/><figcaption class=\"wp-element-caption\"><em>Gerrit Rietveld, <strong>Side Table<\/strong>,&nbsp;1922-3<\/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\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" data-attachment-id=\"8314\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/gehry_cardboard_chair_5026786663\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_5026786663.jpg\" data-orig-size=\"1290,1290\" 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=\"gehry_cardboard_chair_5026786663\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_5026786663-1024x1024.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_5026786663-1024x1024.jpg\" alt=\"\" class=\"wp-image-8314\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_5026786663-1024x1024.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_5026786663-300x300.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_5026786663-150x150.jpg 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_5026786663-768x768.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_5026786663-100x100.jpg 100w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_5026786663.jpg 1290w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Frank Gehry,&nbsp;<strong>Vitra Red Beaver Chair and Ottoman<\/strong>,&nbsp;1986<\/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=\"1024\" height=\"768\" data-attachment-id=\"8315\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/gehry_cardboard_chair_detail_5027403152\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_detail_5027403152.jpg\" data-orig-size=\"1440,1080\" 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=\"gehry_cardboard_chair_detail_5027403152\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_detail_5027403152-1024x768.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_detail_5027403152-1024x768.jpg\" alt=\"\" class=\"wp-image-8315\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_detail_5027403152-1024x768.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_detail_5027403152-300x225.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_detail_5027403152-768x576.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/gehry_cardboard_chair_detail_5027403152.jpg 1440w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Detail of construction<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p>Unlike the polygon plane created in digital modeling, these plane examples all contain thickness, and hence are technically volumes. When modeling situations where a planar element can be seen from multiple sides, be sure it is given a requisite mass. For ground planes, sky domes, or any other situation where you might create a \u201cstage-set\u201d surface, all of these can create the illusion of mass or space without actual thickness or depth. But if you are modeling Rietvelt\u2019s table and your camera would see the thickness of the table planes, they\u2019d better be modeled as masses.<\/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 is-layout-flow wp-block-column-is-layout-flow\">\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"In_the_studio-3\"><\/span>In the studio<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p><em>Plane examples from 3D design studios<\/em>:<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Sectioning_and_serial_planes\"><\/span>Sectioning and serial planes<span class=\"ez-toc-section-end\"><\/span><\/h5>\n\n\n\n<p><em>Like the one-dimensional line, it seems counter-intuitive to talk about the two-dimensional&nbsp;Shape&nbsp;in a 3D world. A common 3D design exercise reconciles it by analyzing a volumetric object through the use of Plane, specifically serial planes, a series of imaginary parallel planes that metaphorically put the object through a bread-slicing machine, ending up like the shoe seen here. Thus, these regular planes become a way of rationalizing organic <strong>Form<\/strong>, as seen in the orthographic projection drawings generating&nbsp;<strong>Figure-ground<\/strong> relationships. By studying the shoe in this way, this student was able to see topological relationships that could be rendered in a new material. His example also shows a clever material choice, weaving flat shoelaces. The pattern the weave creates is suggestive of a 3D modeling polygon mesh, one way of creating a form in a digital modeling program.<\/em><\/p>\n<\/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-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"783\" data-attachment-id=\"8318\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_033\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_033.jpg\" data-orig-size=\"1810,1384\" 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=\"ch04_033\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_033-1024x783.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_033-1024x783.jpg\" alt=\"\" class=\"wp-image-8318\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_033-1024x783.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_033-300x229.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_033-768x587.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_033-1536x1174.jpg 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_033.jpg 1810w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Student exercise, a planar study of a shoe. The top row includes superimposing parallel planes in two orientations and an \u201cegg-crate\u201d hybrid. The large image is a surface model of woven shoestrings. In the same exercise, black paper cutout \u201cdrawings\u201d suggest slicing planes revealing organic form and figure-ground relationships. From a studio by the author.&nbsp;<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column has-white-background-color has-background is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"468\" height=\"1024\" data-attachment-id=\"8319\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_034\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_034.jpg\" data-orig-size=\"649,1419\" 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=\"ch04_034\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_034-468x1024.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_034-468x1024.jpg\" alt=\"\" class=\"wp-image-8319\" style=\"width:300px\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_034-468x1024.jpg 468w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_034-137x300.jpg 137w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_034-300x656.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_034.jpg 649w\" sizes=\"auto, (max-width: 468px) 100vw, 468px\" \/><\/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-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"757\" data-attachment-id=\"7572\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-10-expressions-of-geometry\/2018_shoe_final_model\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/2018_shoe_final_model-scaled.jpg\" data-orig-size=\"2560,1892\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;2.2&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;iPhone 6&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1538290829&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;4.15&quot;,&quot;iso&quot;:&quot;320&quot;,&quot;shutter_speed&quot;:&quot;0.066666666666667&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"2018_shoe_final_model\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/2018_shoe_final_model-1024x757.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/2018_shoe_final_model-1024x757.jpg\" alt=\"\" class=\"wp-image-7572\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/2018_shoe_final_model-1024x757.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/2018_shoe_final_model-300x222.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/2018_shoe_final_model-768x568.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/2018_shoe_final_model-1536x1135.jpg 1536w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p><em>A similar student project, but this time using 3-D modeling and a laser cutter. From a studio by the author.<\/em><\/p>\n<\/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<h5 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Surface_mesh\"><\/span>Surface mesh<span class=\"ez-toc-section-end\"><\/span><\/h5>\n\n\n\n<p><em>In digital modeling, serial planes and structured right-angle grids like the egg-crate model are sometimes used to define shape, but the <strong>Polygon Mesh<\/strong> model is more often an unstructured grid of triangles or quadrilaterals: simple convex polygons. A combination of triangles and quads is seen in the digital shoe. Like the analysis in cardboard, a polygon mesh rationalizes complex form by simplifying it or changing its resolution (the amount of detail seen).&nbsp;&nbsp;<\/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-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" data-attachment-id=\"8320\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/maxresdefault\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/maxresdefault.jpg\" data-orig-size=\"1280,720\" 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=\"maxresdefault\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/maxresdefault-1024x576.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/maxresdefault-1024x576.jpg\" alt=\"\" class=\"wp-image-8320\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/maxresdefault-1024x576.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/maxresdefault-300x169.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/maxresdefault-768x432.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/maxresdefault.jpg 1280w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Low-resolution polygon model of a shoe in SketchUp<\/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=\"770\" height=\"770\" data-attachment-id=\"7058\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-11-polys-and-subdivs-and-nurbs-oh-my\/lores-shoe\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/02\/lores-shoe.jpeg\" data-orig-size=\"770,770\" 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=\"lores-shoe\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/02\/lores-shoe.jpeg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/02\/lores-shoe.jpeg\" alt=\"\" class=\"wp-image-7058\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/02\/lores-shoe.jpeg 770w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/02\/lores-shoe-300x300.jpeg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/02\/lores-shoe-150x150.jpeg 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/02\/lores-shoe-768x768.jpeg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/02\/lores-shoe-100x100.jpeg 100w\" sizes=\"auto, (max-width: 770px) 100vw, 770px\" \/><figcaption class=\"wp-element-caption\"><em>United Nude,&nbsp;<strong>Lo Res Shoe<\/strong>, 2010. One of many designs found on the&nbsp;<strong><a href=\"http:\/\/www.loresproject.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">Lo Res Project<\/a>&nbsp;<\/strong>website.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p><em>The <strong>Lo Res Project<\/strong> by United Nude reverses the conventional relationship: instead of making a complex physical form by smoothing a simple polygon model, it literally builds the low-resolution polygon model of a shoe, for example, into an actual shoe you can buy. Retail, it goes for \u2014&nbsp;well, if you have to ask you can\u2019t afford it! This is high, fashion-forward fashion by architect Rem Koolhaas, slumming in product design.&nbsp;<\/em><\/p>\n<\/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<h5 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Implied_volume\"><\/span>Implied volume<span class=\"ez-toc-section-end\"><\/span><\/h5>\n\n\n\n<p><em>Another kind of shape study common to 3D design courses poses the problem of creating spatial relationships through a hierarchy of non-serial planes that imply the volume of an object. We can see this technique applied in origami or pop-up architectural sculptures like those created by Japanese architect <strong>Masahiro Chatani<\/strong>. One inspiration for these kinds of projects is the work of Russian Constructivist sculptor <strong>Naum Gabo<\/strong>. Gabo demonstrated it was possible to evoke volume without creating mass in works like the Constructed Head.&nbsp;<\/em><\/p>\n<\/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=\"1024\" data-attachment-id=\"8325\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/origami-pliage-origamic-architecture-1024x1024-1\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/origami-pliage-origamic-architecture-1024x1024-1.png\" data-orig-size=\"1024,1024\" 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=\"origami-pliage-origamic-architecture-1024&amp;#215;1024-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/origami-pliage-origamic-architecture-1024x1024-1.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/origami-pliage-origamic-architecture-1024x1024-1.png\" alt=\"\" class=\"wp-image-8325\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/origami-pliage-origamic-architecture-1024x1024-1.png 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/origami-pliage-origamic-architecture-1024x1024-1-300x300.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/origami-pliage-origamic-architecture-1024x1024-1-150x150.png 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/origami-pliage-origamic-architecture-1024x1024-1-768x768.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/origami-pliage-origamic-architecture-1024x1024-1-100x100.png 100w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Masahiro Chatani, <strong>Blocks<\/strong>,&nbsp;early 1980s<\/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=\"600\" height=\"719\" data-attachment-id=\"8326\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_038\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_038.jpg\" data-orig-size=\"600,719\" 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=\"ch04_038\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_038.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_038.jpg\" alt=\"\" class=\"wp-image-8326\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_038.jpg 600w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_038-250x300.jpg 250w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_038-300x360.jpg 300w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><figcaption class=\"wp-element-caption\"><em>Naum Gabo, <strong>Model for Constructed Head No.3 (Head in a Niche)<\/strong>,&nbsp;1917<\/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><em>A structure defined by an economy of means, the edges in Gabo\u2019s head are evocative of the stitching edges between surface patches in a <strong>NURBS<\/strong>-based 3D model. In the digital model we see here, color represents a different curving surface plane, and the edges between them define a curvilinear slicing plane that cuts the volume into these surface patches. In both the tactile and digital versions, divisions need to be carefully planned based on the features of the analyzed, implied volume.&nbsp;<\/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=\"400\" height=\"437\" data-attachment-id=\"8327\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/mag1art1fig29\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/mag1art1fig29.jpg\" data-orig-size=\"400,437\" 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=\"mag1art1fig29\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/mag1art1fig29.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/mag1art1fig29.jpg\" alt=\"\" class=\"wp-image-8327\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/mag1art1fig29.jpg 400w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/mag1art1fig29-275x300.jpg 275w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/mag1art1fig29-300x328.jpg 300w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><figcaption class=\"wp-element-caption\"><em>Head from a\u00a0<a href=\"https:\/\/web.archive.org\/web\/20050524072909\/http:\/\/www.chill3d.com\/tutorials\/headtut.htm\" target=\"_blank\" rel=\"noreferrer noopener\">NURBS tutorial<\/a>. The purple lines indicate the curves, which act as edges defining the surface planes.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Graphic_shape\"><\/span>Graphic shape<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>A point is given presence by expressing it with optical properties such as color and texture, while a line can be appreciated additionally by observing thickness or length, straightness or curviness. For a plane to achieve expressive character, the possibilities are mind-boggling by comparison. Even when color and texture are reduced to black and white, the shapes and forms possessed by expressive planes are infinite. In 2005, artist Allan McCollum began the <em>Shapes Project<\/em>, developing a simple system that yields enough unique shapes so everyone alive on earth can be given one. The shape elements are created and combined in Adobe Illustrator by an intuitive system, not a computed algorithm.<\/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=\"807\" data-attachment-id=\"8329\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/communitypost_4-20-2020_featuredimage_installation-view_-allan-mccollum-_the-shapes-project_-petzel-gallery-new-york-2006-500x394-1-1\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/CommunityPost_4.20.2020_FeaturedImage_Installation-view_-Allan-McCollum-_The-Shapes-Project_-Petzel-Gallery-New-York-2006-500x394-1-1.jpg\" data-orig-size=\"1140,898\" 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=\"CommunityPost_4.20.2020_FeaturedImage_Installation-view_-Allan-McCollum-_The-Shapes-Project_-Petzel-Gallery-New-York-2006-500&amp;#215;394-1-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/CommunityPost_4.20.2020_FeaturedImage_Installation-view_-Allan-McCollum-_The-Shapes-Project_-Petzel-Gallery-New-York-2006-500x394-1-1-1024x807.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/CommunityPost_4.20.2020_FeaturedImage_Installation-view_-Allan-McCollum-_The-Shapes-Project_-Petzel-Gallery-New-York-2006-500x394-1-1-1024x807.jpg\" alt=\"\" class=\"wp-image-8329\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/CommunityPost_4.20.2020_FeaturedImage_Installation-view_-Allan-McCollum-_The-Shapes-Project_-Petzel-Gallery-New-York-2006-500x394-1-1-1024x807.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/CommunityPost_4.20.2020_FeaturedImage_Installation-view_-Allan-McCollum-_The-Shapes-Project_-Petzel-Gallery-New-York-2006-500x394-1-1-300x236.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/CommunityPost_4.20.2020_FeaturedImage_Installation-view_-Allan-McCollum-_The-Shapes-Project_-Petzel-Gallery-New-York-2006-500x394-1-1-768x605.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/CommunityPost_4.20.2020_FeaturedImage_Installation-view_-Allan-McCollum-_The-Shapes-Project_-Petzel-Gallery-New-York-2006-500x394-1-1.jpg 1140w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Allan McCollum,&nbsp;<strong>The Shapes Project<\/strong>,&nbsp;2005-6. 7,056 unique monoprints, installed at Friedrich Petzel Gallery, New York, 2006.<\/em><\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"797\" height=\"800\" data-attachment-id=\"8331\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/mccollum_bkg_exhvw2008_pedestals_800_\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/mccollum_bkg_exhvw2008_pedestals_800_.jpg\" data-orig-size=\"797,800\" 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=\"mccollum_bkg_exhvw2008_pedestals_800_\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/mccollum_bkg_exhvw2008_pedestals_800_.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/mccollum_bkg_exhvw2008_pedestals_800_.jpg\" alt=\"\" class=\"wp-image-8331\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/mccollum_bkg_exhvw2008_pedestals_800_.jpg 797w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/mccollum_bkg_exhvw2008_pedestals_800_-300x301.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/mccollum_bkg_exhvw2008_pedestals_800_-150x150.jpg 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/mccollum_bkg_exhvw2008_pedestals_800_-768x771.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/mccollum_bkg_exhvw2008_pedestals_800_-100x100.jpg 100w\" sizes=\"auto, (max-width: 797px) 100vw, 797px\" \/><figcaption class=\"wp-element-caption\"><em>Shapes, created as vector objects in Adobe Illustrator, can be digitally fabricated in a variety of materials \u2014 here, shown in laminated birch plywood \u2014 adding color and texture to the already mind-boggling possibilities.<\/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=\"716\" height=\"1024\" data-attachment-id=\"8330\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/shapes-project-3\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/shapes-project-3.webp\" data-orig-size=\"1400,2001\" 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=\"shapes-project-3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/shapes-project-3-716x1024.webp\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/shapes-project-3-716x1024.webp\" alt=\"\" class=\"wp-image-8330\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/shapes-project-3-716x1024.webp 716w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/shapes-project-3-210x300.webp 210w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/shapes-project-3-768x1098.webp 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/shapes-project-3-1075x1536.webp 1075w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/shapes-project-3-300x429.webp 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/shapes-project-3.webp 1400w\" sizes=\"auto, (max-width: 716px) 100vw, 716px\" \/><figcaption class=\"wp-element-caption\"><em>Illustration of McCollum\u2019s process, a system combining quadrants with his standard set of shape elements.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p>Each of McCollum\u2019s <em>Shapes <\/em>is a <strong>Graphic <\/strong>or<strong>  Geometric Shape<\/strong>. Graphic shapes can be generators for symbols, logos, or icons, and are often created from a compound of simpler, geometrically defined 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\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"853\" data-attachment-id=\"8332\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_043\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_043.png\" data-orig-size=\"2400,2000\" 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=\"ch04_043\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_043-1024x853.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_043-1024x853.png\" alt=\"\" class=\"wp-image-8332\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_043-1024x853.png 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_043-300x250.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_043-768x640.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_043-1536x1280.png 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_043-2048x1707.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\">\n<p><em>Simple geometric planes are combined to create more complex graphic shapes. At the top, two circles superimpose. In the center, an ellipse is cut on the bias, and half is mirror-rotated. At the bottom, a hexagon\u2019s edges are extended, and the result is superimposed over a circle. All of these compounds generate a graphic shape that has a specific symbolic meaning. Do the results mean anything significant to you?<\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Nets\"><\/span>Nets<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Oddly, the world of polygon modeling is a world of graphic shapes. So how can that be? Take a simple cube, and imagine it as a cardboard box that we cut along the edges, unfolding and flattening. This is a process we call finding the <strong>net<\/strong> of a polyhedron. When flattened, the cube becomes six squares. German artist Albrecht D\u00fcrer was fascinated by nets. He produced many for his treatise on geometry, <em>Four Books on Measurement<\/em>, which among other topics discussed the <strong>Platonic Solids<\/strong> we\u2019ll explore in Chapter 5. A net can be generated out of more than <strong>regular polyhedra<\/strong>; a highly complex net results from unfolding an irregular polygon&nbsp;solid such as a torso.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"222\" data-attachment-id=\"8335\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_044\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_044.png\" data-orig-size=\"3000,650\" 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=\"ch04_044\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_044-1024x222.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_044-1024x222.png\" alt=\"\" class=\"wp-image-8335\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_044-1024x222.png 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_044-300x65.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_044-768x166.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_044-1536x333.png 1536w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_044-2048x444.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Unfolding a cube creates its net: a graphic, cruciform shape<\/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\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"709\" height=\"798\" data-attachment-id=\"8336\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_045\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_045.jpg\" data-orig-size=\"709,798\" 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=\"ch04_045\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_045.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_045.jpg\" alt=\"\" class=\"wp-image-8336\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_045.jpg 709w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_045-267x300.jpg 267w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_045-300x338.jpg 300w\" sizes=\"auto, (max-width: 709px) 100vw, 709px\" \/><figcaption class=\"wp-element-caption\"><em>Albrecht D\u00fcrer\u2019s net illustration for a tetrahedron<\/em><\/figcaption><\/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\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"128\" height=\"160\" data-attachment-id=\"8337\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_046\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_046.gif\" data-orig-size=\"128,160\" 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=\"ch04_046\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_046.gif\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_046.gif\" alt=\"\" class=\"wp-image-8337\" style=\"width:180px\"\/><figcaption class=\"wp-element-caption\"><em>Unfolding a highly complex net created by a polygon model of a human torso<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Organic_form\"><\/span>Organic form<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>In the torso example above, the polygonal graphic shapes become increasingly complex and randomized. So, they are characterized less by their sense of geometric order. Instead of feeling human-made, they take on an aura of the natural: they approach a sense of <strong>organic form<\/strong>. Claiming that he and his fellow Dada artists \u201caimed to destroy the reasonable deceptions of man and recover the natural and unreasonable order,\u201d  <sup><a href=\"#footnote_11_8245\" id=\"identifier_11_8245\" class=\"footnote-link footnote-identifier-link\" title=\"Quoted in Moszynska, Anna, Abstract Art, Thames and Hudson, London, 1990, p. 66.\">11<\/a><\/sup>&nbsp;Jean Arp uses organic form to reinforce the non-mechanical origin of many of his compositions.<\/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=\"830\" data-attachment-id=\"8339\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_047\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_047.jpg\" data-orig-size=\"1264,1024\" 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=\"ch04_047\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_047-1024x830.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_047-1024x830.jpg\" alt=\"\" class=\"wp-image-8339\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_047-1024x830.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_047-300x243.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_047-768x622.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_047.jpg 1264w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Jean Arp, <strong>Constellation According to the Laws of Chance<\/strong>,&nbsp;circa 1930&nbsp;<\/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\">\n<p>It took architects about three generations to catch up to Arp: compare his forms Zaha Hadid\u2019s <em><strong>Pavilion for the Burnham Plan Centennial<\/strong><\/em> in Chicago. Supporting but in contrast to the organic form, Hadid uses digital modeling to develop a rational, geometric system of a structure akin to the ribs of a boat. The Pavilion is also comparable in section to the student drawing of the shoe, which shares the same strategy \u2014 parallel Cartesian planes \u2014 to rationalize an intuitively understood organic form.<\/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=\"900\" height=\"621\" data-attachment-id=\"8340\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/1498_090127-indd\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_048.jpg\" data-orig-size=\"900,621\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;Evan.E&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;1498_090127.indd&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"1498_090127.indd\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_048.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_048.jpg\" alt=\"\" class=\"wp-image-8340\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_048.jpg 900w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_048-300x207.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_048-768x530.jpg 768w\" sizes=\"auto, (max-width: 900px) 100vw, 900px\" \/><figcaption class=\"wp-element-caption\"><em>Zaha Hadid, plan of&nbsp;<strong>Pavilion for the Burnham Plan Centennial<\/strong>,&nbsp;2009&nbsp;<\/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\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" data-attachment-id=\"8341\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_049\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_049.jpg\" data-orig-size=\"1200,900\" 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=\"ch04_049\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_049-1024x768.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_049-1024x768.jpg\" alt=\"\" class=\"wp-image-8341\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_049-1024x768.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_049-300x225.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_049-768x576.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_049.jpg 1200w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Entry to Hadid\u2019s&nbsp;<strong>Pavilion<\/strong><\/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=\"864\" height=\"620\" data-attachment-id=\"8342\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/1498_090127-indd-2\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_050.jpg\" data-orig-size=\"864,620\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;Evan.E&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;1498_090127.indd&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"1498_090127.indd\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_050.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_050.jpg\" alt=\"\" class=\"wp-image-8342\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_050.jpg 864w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_050-300x215.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_050-768x551.jpg 768w\" sizes=\"auto, (max-width: 864px) 100vw, 864px\" \/><figcaption class=\"wp-element-caption\"><em>Sections through Hadid\u2019s&nbsp;<strong>Pavilion<\/strong>, modified by the author to emphasize the shape of the mass being sliced)<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Figure_and_ground\"><\/span>Figure and ground<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>In the shoe drawing and Hadid\u2019s section mentioned earlier, we observe a way of drawing that has a long history as a convention for architectural representation and is quite useful to 3D modelers. This is a drawing that seems to slice through an object. So, how does this work? We blacken in the mass shape and we allow white to represent open space. Architects in the academy of the \u00c9cole des Beaux-Arts called this technique <strong>poch\u00e9<\/strong>, from a French term meaning <strong>pocket<\/strong>, implying an enclosed space. Thus, graphically, it allows a viewer to understand the shape of space and structure in an architectural drawing. When we see a <em>poch\u00e9 <\/em>plan drawing of <em><strong>Sant\u2019Andrea al Quirinale<\/strong><\/em> by Gian Lorenzo Bernini, we appreciate how Baroque architects play eccentric, distorted forms off one another to create dramatic spaces.<\/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=\"990\" height=\"1024\" data-attachment-id=\"8344\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_051\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_051.png\" data-orig-size=\"1961,2029\" 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=\"ch04_051\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_051-990x1024.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_051-990x1024.png\" alt=\"\" class=\"wp-image-8344\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_051-990x1024.png 990w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_051-290x300.png 290w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_051-768x795.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_051-1485x1536.png 1485w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_051-300x310.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_051.png 1961w\" sizes=\"auto, (max-width: 990px) 100vw, 990px\" \/><figcaption class=\"wp-element-caption\"><em>Plan drawing of&nbsp;<strong>Sant\u2019Andrea al Quirinale<\/strong>&nbsp;demonstrating <strong>poch\u00e9<\/strong><\/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=\"683\" height=\"1024\" data-attachment-id=\"8345\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_052\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_052.jpg\" data-orig-size=\"1000,1500\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;3.5&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;Canon EOS 350D DIGITAL&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1144595339&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;10&quot;,&quot;iso&quot;:&quot;100&quot;,&quot;shutter_speed&quot;:&quot;0.16666666666667&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"ch04_052\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_052-683x1024.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_052-683x1024.jpg\" alt=\"\" class=\"wp-image-8345\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_052-683x1024.jpg 683w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_052-200x300.jpg 200w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_052-768x1152.jpg 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_052-300x450.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_052.jpg 1000w\" sizes=\"auto, (max-width: 683px) 100vw, 683px\" \/><figcaption class=\"wp-element-caption\"><em>Gian Lorenzo Bernini, <strong>Sant\u2019Andrea al Quirinale<\/strong>,&nbsp;1661. Interior view toward the front altar.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<p>The&nbsp;<strong>poch\u00e9<\/strong><em>&nbsp;<\/em>drawing is an example of a <strong>Figure-Ground<\/strong> drawing, which some artists call a <strong>Positive-Negative Shape<\/strong> drawing. When we speak of the <strong>Figure<\/strong> (or<em> <\/em><strong>Positive Shape<\/strong>) in a drawing, we usually refer to meaningful marks made on the <strong>Ground<\/strong> (or <strong>Negative Shape<\/strong>), what we\u2019ll recall Kandinsky calls the Basic Plane. We can say a positive shape represents a figure drawn inside the visual field of a ground, while a negative shape is everything the figure is <em>not<\/em>. But that can be a crude distinction. Here we see a simple drawing of a group of black figures on a white ground. But what else can you see?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Reification\"><\/span>Reification<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Here we see an example of a visual phenomenon known as <strong>Illusory Contours<\/strong>. In the <em><strong>Kanizsa Triangle<\/strong><\/em>, named after psychologist Gaetano Kanizsa, we see a white, downward-pointing triangle. Many even observe this white \u201cfigure\u201d as somehow whiter than the ground! This is an example of <strong>Reification<\/strong>, which in Gestalt theory identifies a perceptual experience that contains more information than the stimulus actually contains. We\u2019ll consider Gestalt (German for&nbsp;<em>shape<\/em>) more deeply in a future chapter.<\/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=\"960\" height=\"1024\" data-attachment-id=\"8347\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_053\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_053.png\" data-orig-size=\"1000,1067\" 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=\"ch04_053\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_053-960x1024.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_053-960x1024.png\" alt=\"\" class=\"wp-image-8347\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_053-960x1024.png 960w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_053-281x300.png 281w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_053-768x819.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_053-300x320.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_053.png 1000w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><figcaption class=\"wp-element-caption\"><em>The Kanizsa Triangle<\/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=\"861\" height=\"1024\" data-attachment-id=\"8348\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_054\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_054.png\" data-orig-size=\"1000,1189\" 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=\"ch04_054\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_054-861x1024.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_054-861x1024.png\" alt=\"\" class=\"wp-image-8348\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_054-861x1024.png 861w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_054-252x300.png 252w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_054-768x913.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_054-300x357.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_054.png 1000w\" sizes=\"auto, (max-width: 861px) 100vw, 861px\" \/><figcaption class=\"wp-element-caption\"><em>Attributed to one Mrs. Collins, a silhouette maker working in Bath, this silhouette of <strong>Jane Austin<\/strong> from the second edition of <strong>Mansfield Park<\/strong> inscribed \u201c<strong>L\u2019aimable Jane<\/strong>,\u201d circa 1810-15, predates Edgar Rubin\u2019s development of the Rubin Face-Vase illusion (seen below) by a century.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Mulltistability\"><\/span>Mulltistability<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=\"1024\" height=\"742\" data-attachment-id=\"8350\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/the-queens-speech\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/The-Queens-Speech.jpg\" data-orig-size=\"1024,742\" 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=\"The-Queens-Speech\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/The-Queens-Speech.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/The-Queens-Speech.jpg\" alt=\"\" class=\"wp-image-8350\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/The-Queens-Speech.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/The-Queens-Speech-300x217.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/The-Queens-Speech-768x557.jpg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em><strong>&nbsp;<\/strong>Judy Cousins for Kaiser Porcelains, <strong>Royal Silhouette Vase<\/strong>,&nbsp;1977<\/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>We can see another Gestalt concept, <strong>Multistability<\/strong>, in the Rubin Vase, named after Danish psychologist Edgar Rubin. In the illustration, notice how his illusion bounces between the perception of a vase and the profiles of two faces as our brains try to \u201cshape\u201d the ambiguous relationship between figure and ground. This is a mass-void analog in 3D, a vase created for the Silver Jubilee of Queen Elizabeth II in 1977. It generates the illusion through the spatial equivalent of figure and ground, which we call <strong>mass and void<\/strong>, as discussed in the next chapter.<\/p>\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Figure-ground_relationships\"><\/span>Figure-ground relationships<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>An artist working with positive and negative shapes can create impressive interactions generating various figure-ground relationships.<\/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 is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p>Starting with a nine-square grid, we&#8217;ll generate 3 states: <strong>stable<\/strong>, <strong>reversible<\/strong>, and <strong>ambiguous<\/strong>.<\/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\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" data-attachment-id=\"8351\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_056\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_056.png\" data-orig-size=\"1250,1250\" 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=\"ch04_056\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_056-1024x1024.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_056-1024x1024.png\" alt=\"\" class=\"wp-image-8351\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_056-1024x1024.png 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_056-300x300.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_056-150x150.png 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_056-768x768.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_056-100x100.png 100w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_056.png 1250w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-white-color has-alpha-channel-opacity has-white-background-color has-background\"\/>\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<h4 class=\"wp-block-heading has-text-align-center\"><span class=\"ez-toc-section\" id=\"Stable\"><\/span>Stable<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p><strong>STABLE&nbsp;<\/strong>figure-ground relationships derive from a singular figure disengaged from the edge of the ground, making the figure a clear, dominant focal point.<\/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=\"1024\" height=\"1024\" data-attachment-id=\"8352\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_057\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_057.png\" data-orig-size=\"1250,1250\" 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=\"ch04_057\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_057-1024x1024.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_057-1024x1024.png\" alt=\"\" class=\"wp-image-8352\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_057-1024x1024.png 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_057-300x300.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_057-150x150.png 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_057-768x768.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_057-100x100.png 100w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_057.png 1250w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/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><strong>2D Example<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"845\" height=\"561\" data-attachment-id=\"8353\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_058\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_058.jpg\" data-orig-size=\"845,561\" 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=\"ch04_058\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_058.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_058.jpg\" alt=\"\" class=\"wp-image-8353\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_058.jpg 845w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_058-300x199.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_058-768x510.jpg 768w\" sizes=\"auto, (max-width: 845px) 100vw, 845px\" \/><figcaption class=\"wp-element-caption\"><em>Ellsworth Kelly,&nbsp;<strong>Untitled<\/strong>,&nbsp;2009. The artwork itself is a figure, a powerful focal point on the wall.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p><strong>3D Example<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" data-attachment-id=\"8354\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_059\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_059-scaled.jpg\" data-orig-size=\"2560,1707\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;11&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;Canon EOS 350D DIGITAL&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1172499105&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;23&quot;,&quot;iso&quot;:&quot;100&quot;,&quot;shutter_speed&quot;:&quot;0.01&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"ch04_059\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_059-1024x683.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_059-1024x683.jpg\" alt=\"\" class=\"wp-image-8354\" style=\"width:373px;height:auto\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_059-1024x683.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_059-300x200.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_059-768x512.jpg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em><strong>The&nbsp;Pantheon<\/strong>&nbsp;in Rome, 126 CE, contains a single, open skylight, a dramatic visual anchor.<\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-white-color has-alpha-channel-opacity has-white-background-color has-background\"\/>\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<h4 class=\"wp-block-heading has-text-align-center\"><span class=\"ez-toc-section\" id=\"Reversible\"><\/span>Reversible<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p>Engaging the ground edge and alternating the squares yields a&nbsp;<strong>REVERSIBLE&nbsp;<\/strong>dominance \u2014 the eye may alternate between interpreting dark and light squares as figure.&nbsp;<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" data-attachment-id=\"8355\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_060\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_060.png\" data-orig-size=\"1250,1250\" 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=\"ch04_060\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_060-1024x1024.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_060-1024x1024.png\" alt=\"\" class=\"wp-image-8355\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_060-1024x1024.png 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_060-300x300.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_060-150x150.png 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_060-768x768.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_060-100x100.png 100w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_060.png 1250w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/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><strong>2D Example<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"950\" height=\"552\" data-attachment-id=\"8356\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_061\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_061.jpg\" data-orig-size=\"950,552\" 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=\"ch04_061\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_061.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_061.jpg\" alt=\"\" class=\"wp-image-8356\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_061.jpg 950w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_061-300x174.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_061-768x446.jpg 768w\" sizes=\"auto, (max-width: 950px) 100vw, 950px\" \/><figcaption class=\"wp-element-caption\"><em><em>M.C. Escher<\/em>,&nbsp;<strong>Day and Night<\/strong>,&nbsp;<em>1938, uses figure-ground reversal to reinforce its narrative.<\/em><\/em><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p><strong>3D Example<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"615\" height=\"346\" data-attachment-id=\"8357\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_062\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_062.jpg\" data-orig-size=\"615,346\" 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=\"ch04_062\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_062.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_062.jpg\" alt=\"\" class=\"wp-image-8357\" style=\"width:373px;height:auto\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_062.jpg 615w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_062-300x169.jpg 300w\" sizes=\"auto, (max-width: 615px) 100vw, 615px\" \/><figcaption class=\"wp-element-caption\"><em><em>Robert Smithson creates a water and land reversal in&nbsp;<\/em><strong>Broken Circle\/Spiral Hill<\/strong>,&nbsp;<em>1971-2011.<\/em><\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-white-color has-alpha-channel-opacity has-white-background-color has-background\"\/>\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<h4 class=\"wp-block-heading has-text-align-center\"><span class=\"ez-toc-section\" id=\"Ambiguous\"><\/span>Ambiguous<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p>We completely intertwine figure with ground in an&nbsp;<strong>AMBIGUOUS&nbsp;<\/strong>figure-ground relationship that contains the visual tension of no apparent focal point.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" data-attachment-id=\"8358\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_063\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_063.png\" data-orig-size=\"1250,1250\" 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=\"ch04_063\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_063-1024x1024.png\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_063-1024x1024.png\" alt=\"\" class=\"wp-image-8358\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_063-1024x1024.png 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_063-300x300.png 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_063-150x150.png 150w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_063-768x768.png 768w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_063-100x100.png 100w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_063.png 1250w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/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><strong>2D Example<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1408\" height=\"1000\" data-attachment-id=\"8359\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/ch04_064\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_064.jpg\" data-orig-size=\"1408,1000\" 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=\"ch04_064\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_064-1024x727.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_064.jpg\" alt=\"\" class=\"wp-image-8359\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_064.jpg 1408w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_064-300x213.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_064-1024x727.jpg 1024w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/ch04_064-768x545.jpg 768w\" sizes=\"auto, (max-width: 1408px) 100vw, 1408px\" \/><figcaption class=\"wp-element-caption\"><em><em><em>Pablo Picasso,&nbsp;<\/em><strong>Guitar<\/strong>,&nbsp;<em>1920, a Synthetic Cubist work with graphic edges &amp; ambiguous volume.<\/em><\/em><\/em><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p><strong>3D Example<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"854\" height=\"600\" data-attachment-id=\"8360\" data-permalink=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/storefront_restoration_10\/\" data-orig-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Storefront_Restoration_10.jpg\" data-orig-size=\"854,600\" 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=\"Storefront_Restoration_10\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Storefront_Restoration_10.jpg\" src=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Storefront_Restoration_10.jpg\" alt=\"\" class=\"wp-image-8360\" style=\"width:373px;height:auto\" srcset=\"https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Storefront_Restoration_10.jpg 854w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Storefront_Restoration_10-300x211.jpg 300w, https:\/\/williamcromar.com\/newmediawiki\/wp-content\/uploads\/2024\/03\/Storefront_Restoration_10-768x540.jpg 768w\" sizes=\"auto, (max-width: 854px) 100vw, 854px\" \/><figcaption class=\"wp-element-caption\"><em><em><em>Stephen Holl &amp; Vito Acconci<\/em>,&nbsp;<strong>Storefront for Art &amp; Architectur<\/strong>e,&nbsp;<em>1982, with ambiguous openings.<\/em><\/em><\/em><\/figcaption><\/figure>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<ol class=\"footnotes\"><li id=\"footnote_1_8245\" class=\"footnote\">Abbot, Edwin. Flatland: A Romance of Many Dimensions. Seeley &amp; Co., London. 1884. Re-published Prometheus Books, Amherst NY. 2005. p. 17.<span class=\"footnote-back-link-wrapper\">[<a href=\"#identifier_1_8245\" class=\"footnote-link footnote-back-link\">&#8617;<\/a>]<\/span><\/li><li id=\"footnote_2_8245\" class=\"footnote\">Kandinsky, Wassily (trans. Rebay, Hilla). Point and Line to Plane. Dover Editions. 1979. p.115.<span class=\"footnote-back-link-wrapper\">[<a href=\"#identifier_2_8245\" class=\"footnote-link footnote-back-link\">&#8617;<\/a>]<\/span><\/li><li id=\"footnote_3_8245\" class=\"footnote\">Lupton, Ellen and Phillips, Jennifer Cole. Graphic Design: The New Basics. Princeton Architectural Press. 2008. p.14.<span class=\"footnote-back-link-wrapper\">[<a href=\"#identifier_3_8245\" class=\"footnote-link footnote-back-link\">&#8617;<\/a>]<\/span><\/li><li id=\"footnote_4_8245\" class=\"footnote\">Klee, Paul. Pedagogical Sketchbook. Praeger. 7th ed. 1972. pp. 16-17.<span class=\"footnote-back-link-wrapper\">[<a href=\"#identifier_4_8245\" class=\"footnote-link footnote-back-link\">&#8617;<\/a>]<\/span><\/li><li id=\"footnote_5_8245\" class=\"footnote\">Lupton, Ellen. Graphic Design: The New Basics. Princeton Architectural Press. 2008. p. 16.<span class=\"footnote-back-link-wrapper\">[<a href=\"#identifier_5_8245\" class=\"footnote-link footnote-back-link\">&#8617;<\/a>]<\/span><\/li><li id=\"footnote_6_8245\" class=\"footnote\">Klee, Paul. Pedagogical Sketchbook. Praeger. 7th ed. 1972. p. 16.<span class=\"footnote-back-link-wrapper\">[<a href=\"#identifier_6_8245\" class=\"footnote-link footnote-back-link\">&#8617;<\/a>]<\/span><\/li><li id=\"footnote_7_8245\" class=\"footnote\">Klee, Paul. Pedagogical Sketchbook. Praeger. 7th ed. 1972. pp. 18-19.<span class=\"footnote-back-link-wrapper\">[<a href=\"#identifier_7_8245\" class=\"footnote-link footnote-back-link\">&#8617;<\/a>]<\/span><\/li><li id=\"footnote_8_8245\" class=\"footnote\">Kandinsky, Wassily (trans. Rebay, Hilla). Point and Line to Plane. Dover Editions. 1979. p.115.<span class=\"footnote-back-link-wrapper\">[<a href=\"#identifier_8_8245\" class=\"footnote-link footnote-back-link\">&#8617;<\/a>]<\/span><\/li><li id=\"footnote_9_8245\" class=\"footnote\">Klee, Paul. Pedagogical Sketchbook. Praeger. 7th ed. 1972. pp. 18-19.<span class=\"footnote-back-link-wrapper\">[<a href=\"#identifier_9_8245\" class=\"footnote-link footnote-back-link\">&#8617;<\/a>]<\/span><\/li><li id=\"footnote_10_8245\" class=\"footnote\">Lupton, Ellen and Phillips, Jennifer Cole. Graphic Design: The New Basics. Princeton Architectural Press. 2008. p. 18.<span class=\"footnote-back-link-wrapper\">[<a href=\"#identifier_10_8245\" class=\"footnote-link footnote-back-link\">&#8617;<\/a>]<\/span><\/li><li id=\"footnote_11_8245\" class=\"footnote\">Quoted in Moszynska, Anna, Abstract Art, Thames and Hudson, London, 1990, p. 66.<span class=\"footnote-back-link-wrapper\">[<a href=\"#identifier_11_8245\" class=\"footnote-link footnote-back-link\">&#8617;<\/a>]<\/span><\/li><\/ol>","protected":false},"excerpt":{"rendered":"<p>22-minute read You, who are blessed with shade as well as light, you who are gifted with two eyes, endowed with a knowledge of perspective, and charmed with the enjoyment of various colours, you, who can actually see an angle, and contemplate the complete circumference of a Circle in the happy region of the Three&#8230; <a href=\"https:\/\/williamcromar.com\/newmediawiki\/chapter-4-visual-elements-i-point-line-plane\/\">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-8245","post","type-post","status-publish","format-standard","hentry","category-paralleluniverses"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - 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