{"id":1170,"date":"2021-09-19T15:18:38","date_gmt":"2021-09-19T15:18:38","guid":{"rendered":"https:\/\/www.parametriczoo.com\/?p=1170"},"modified":"2021-09-19T15:35:40","modified_gmt":"2021-09-19T15:35:40","slug":"dome-with-planar-quads","status":"publish","type":"post","link":"https:\/\/www.parametriczoo.com\/index.php\/2021\/09\/19\/dome-with-planar-quads\/","title":{"rendered":"Dome with Planar Quads"},"content":{"rendered":"<p>[et_pb_section fb_built=&#8221;1&#8243; _builder_version=&#8221;3.22.7&#8243; custom_padding=&#8221;34px||35px|||&#8221;][et_pb_row custom_padding=&#8221;20px|||||&#8221; _builder_version=&#8221;3.22.7&#8243;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;3.22.7&#8243;][et_pb_text _builder_version=&#8221;3.22.7&#8243; min_height=&#8221;53.3px&#8221;]<\/p>\n<p>Recently I was working on a project that involved using meshes with planar faces. In most cases we use normal meshes and the employ different techniques of mesh planarization. These techniques often use different optimization techniques such as forced base algorithm for relaxation or gradient based minimizations to move the vertices of the mesh slightly from the initial position and reduce the non-planarity of the mesh cells. The success of these techniques are heavily depending on the size and topology of the input mesh as well as the magnitude of mesh non-planarity.<\/p>\n<p><span><\/span><\/p>\n<p>[\/et_pb_text][et_pb_image src=&#8221;https:\/\/www.parametriczoo.com\/wp-content\/uploads\/2021\/09\/screen-shot.jpg&#8221; _builder_version=&#8221;3.22.7&#8243;][\/et_pb_image][et_pb_text _builder_version=&#8221;3.22.7&#8243; min_height=&#8221;53.3px&#8221;]<\/p>\n<p><span style=\"font-size: 14px;\">Another approach to planar meshes is to create the meshes with planar faces at the first place. An example is the <\/span><a href=\"https:\/\/www.parametriczoo.com\/index.php\/download\/quad-mesh-dome-v1-0\/\" style=\"font-size: 14px;\">Quad Mesh Dome<\/a><span style=\"font-size: 14px;\"> which contains the Planar Quad faces. This object is created using dynamic programming technique. <\/span><span style=\"font-size: 14px;\"> It starts with an initial pattern on the top which contains arbitrary&nbsp;number of planar quads. Then in the next row, two faces are created in the space between the upper faces. In creation of the new faces the position of the shared vertex is calculated as such that both quad faces stay planar. This process repeats for all two consecutive faces in the current row until 2*n faces are created in the next row. Then the problem is redefined as the faces of the new row become the input for the faces for the next row.&nbsp;<\/span><\/p>\n<p><span style=\"font-size: 14px;\">The result is a mesh (dome) which contains always planar faces. A mesh with planar quads is very useful in architectural design.<\/span><\/p>\n<p><span><\/span><\/p>\n<p>[\/et_pb_text][et_pb_video src=&#8221;https:\/\/youtu.be\/daLSTKyCT00&#8243; _builder_version=&#8221;3.22.7&#8243;][\/et_pb_video][\/et_pb_column][\/et_pb_row][et_pb_row custom_padding=&#8221;8px|||||&#8221; _builder_version=&#8221;3.22.7&#8243;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;3.22.7&#8243;][et_pb_button button_url=&#8221;https:\/\/www.parametriczoo.com\/index.php\/download\/quad-mesh-dome-v1-0\/&#8221; button_text=&#8221;Download &#8221; button_alignment=&#8221;center&#8221; _builder_version=&#8221;3.22.7&#8243; custom_button=&#8221;on&#8221; button_text_size=&#8221;27px&#8221; button_bg_color=&#8221;#f2f2f2&#8243; button_font=&#8221;||||||||&#8221;][\/et_pb_button][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Recently I was working on a project that involved using meshes with planar faces. In most cases we use normal meshes and the employ different techniques of mesh planarization. These techniques often use different optimization techniques such as forced base algorithm for relaxation or gradient based minimizations to move the vertices of the mesh slightly [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1183,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":""},"categories":[64],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v19.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Dome with Planar Quads - Parametric Zoo<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.parametriczoo.com\/index.php\/2021\/09\/19\/dome-with-planar-quads\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Dome with Planar Quads - Parametric Zoo\" \/>\n<meta property=\"og:description\" content=\"Recently I was working on a project that involved using meshes with planar faces. In most cases we use normal meshes and the employ different techniques of mesh planarization. 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