{"id":184,"date":"2016-10-10T16:19:54","date_gmt":"2016-10-10T14:19:54","guid":{"rendered":"http:\/\/robert-lindner.com\/blog\/?p=184"},"modified":"2016-10-10T16:19:54","modified_gmt":"2016-10-10T14:19:54","slug":"icosahedrons","status":"publish","type":"post","link":"https:\/\/leah-lindner.com\/blog\/2016\/10\/10\/icosahedrons\/","title":{"rendered":"Icosahedrons | How Blenders IcoSpheres work"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium ls_lazyimg\" src=\"https:\/\/leah-lindner.com\/blog\/wp-content\/plugins\/images-lazyload-and-slideshow\/blank_1x1.gif\" file=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/Process.gif\" alt=\"Icosahedron \/ Icosphere generation process Blender\" width=\"935\" height=\"740\" \/><noscript><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium\" src=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/Process.gif\" alt=\"Icosahedron \/ Icosphere generation process Blender\" width=\"935\" height=\"740\" \/><\/noscript><\/p>\n<p>For the research on my planet renderer I have been looking into how icospheres are constructed. The process is rather simple:<\/p>\n<p><!--more--><\/p>\n<ol>\n<li>Define the triangle edges with three intersecting planes that use the golden ratio (1+sqrt(5))\/2 : 1<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium ls_lazyimg\" src=\"https:\/\/leah-lindner.com\/blog\/wp-content\/plugins\/images-lazyload-and-slideshow\/blank_1x1.gif\" file=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/1-GoldenRatio.jpg\" alt=\"Golden ration icospher Blender\" width=\"1183\" height=\"977\" \/><noscript><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium\" src=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/1-GoldenRatio.jpg\" alt=\"Golden ration icospher Blender\" width=\"1183\" height=\"977\" \/><\/noscript><\/li>\n<li>Create 20 triangles between the vertices of those planes:\n<figure style=\"width: 1183px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"ls_lazyimg\" src=\"https:\/\/leah-lindner.com\/blog\/wp-content\/plugins\/images-lazyload-and-slideshow\/blank_1x1.gif\" file=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/2-Wire.jpg\" alt=\"Icosahedron triangles wireframe blender icosphere\" width=\"1183\" height=\"977\" \/><figcaption class=\"wp-caption-text\"><noscript><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/2-Wire.jpg\" alt=\"Icosahedron triangles wireframe blender icosphere\" width=\"1183\" height=\"977\" \/><\/noscript> 12 vertices<\/figcaption><\/figure>\n<p><figure style=\"width: 1183px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"ls_lazyimg\" src=\"https:\/\/leah-lindner.com\/blog\/wp-content\/plugins\/images-lazyload-and-slideshow\/blank_1x1.gif\" file=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/3-Icosahedron.jpg\" alt=\"icosahedron blender icosphere triangle wireframe\" width=\"1183\" height=\"977\" \/><figcaption class=\"wp-caption-text\"><noscript><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/3-Icosahedron.jpg\" alt=\"icosahedron blender icosphere triangle wireframe\" width=\"1183\" height=\"977\" \/><\/noscript> 20 triangles<\/figcaption><\/figure><\/li>\n<li>Subdivide those triangles and keep them in the shape of a sphere by making sure the distance from the center is the radius of the sphere:\n<figure style=\"width: 1183px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"ls_lazyimg\" src=\"https:\/\/leah-lindner.com\/blog\/wp-content\/plugins\/images-lazyload-and-slideshow\/blank_1x1.gif\" file=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/4-IcosphereSd1.jpg\" alt=\"Blender icosphere icosahedron subdivision 1\" width=\"1183\" height=\"977\" \/><figcaption class=\"wp-caption-text\"><noscript><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/4-IcosphereSd1.jpg\" alt=\"Blender icosphere icosahedron subdivision 1\" width=\"1183\" height=\"977\" \/><\/noscript> 80 triangles<\/figcaption><\/figure>\n<figure style=\"width: 1183px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium ls_lazyimg\" src=\"https:\/\/leah-lindner.com\/blog\/wp-content\/plugins\/images-lazyload-and-slideshow\/blank_1x1.gif\" file=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/5-IcosphereSd2.jpg\" alt=\"icosahedron blender icosphere subdivision\" width=\"1183\" height=\"977\" \/><figcaption class=\"wp-caption-text\"><noscript><img loading=\"lazy\" decoding=\"async\" class=\"size-medium\" src=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/5-IcosphereSd2.jpg\" alt=\"icosahedron blender icosphere subdivision\" width=\"1183\" height=\"977\" \/><\/noscript> 320 triangles<\/figcaption><\/figure>\n<figure style=\"width: 1183px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium ls_lazyimg\" src=\"https:\/\/leah-lindner.com\/blog\/wp-content\/plugins\/images-lazyload-and-slideshow\/blank_1x1.gif\" file=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/6-IcosphereSd3.jpg\" alt=\"Icosahedron Blender icosphere subdivision\" width=\"1183\" height=\"977\" \/><figcaption class=\"wp-caption-text\"><noscript><img loading=\"lazy\" decoding=\"async\" class=\"size-medium\" src=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/6-IcosphereSd3.jpg\" alt=\"Icosahedron Blender icosphere subdivision\" width=\"1183\" height=\"977\" \/><\/noscript> 1280 triangles<\/figcaption><\/figure>\n<p>&nbsp;<\/li>\n<\/ol>\n<p>There is barely a noticable difference from how icospheres look like when adding them via the Add Mesh menu in Blender:<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium ls_lazyimg\" src=\"https:\/\/leah-lindner.com\/blog\/wp-content\/plugins\/images-lazyload-and-slideshow\/blank_1x1.gif\" file=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/7-BlenderIcosphere.jpg\" alt=\"Blender icosphere\" width=\"1183\" height=\"977\" \/><noscript><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium\" src=\"http:\/\/leah-lindner.com\/img\/blog\/planet_renderer\/icosahedron\/7-BlenderIcosphere.jpg\" alt=\"Blender icosphere\" width=\"1183\" height=\"977\" \/><\/noscript><\/p>\n<p>The nice thing about icosahedrons is that they use equilateral triangles of the same scale everywhere, so they have a nicely distributed amount of surface detail, so it might be quite ideal for rendering of planets.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>For the research on my planet renderer I have been looking into how icospheres are constructed. The process is rather simple:<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[10,9],"tags":[15,26,27,32,40,45],"class_list":["post-184","post","type-post","status-publish","format-standard","hentry","category-planet-renderer","category-tutorial","tag-blender","tag-graduation-work","tag-graphics-programming","tag-lod","tag-planet-renderer","tag-terrain"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/leah-lindner.com\/blog\/wp-json\/wp\/v2\/posts\/184","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/leah-lindner.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/leah-lindner.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/leah-lindner.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/leah-lindner.com\/blog\/wp-json\/wp\/v2\/comments?post=184"}],"version-history":[{"count":0,"href":"https:\/\/leah-lindner.com\/blog\/wp-json\/wp\/v2\/posts\/184\/revisions"}],"wp:attachment":[{"href":"https:\/\/leah-lindner.com\/blog\/wp-json\/wp\/v2\/media?parent=184"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/leah-lindner.com\/blog\/wp-json\/wp\/v2\/categories?post=184"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/leah-lindner.com\/blog\/wp-json\/wp\/v2\/tags?post=184"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}