{"id":4788,"date":"2017-10-18T13:57:39","date_gmt":"2017-10-18T20:57:39","guid":{"rendered":"http:\/\/theoryofeverything.org\/theToE\/?p=4788"},"modified":"2017-10-18T16:52:25","modified_gmt":"2017-10-18T23:52:25","slug":"perspective-enhanced-ncube-projections-to-3d","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2017\/10\/18\/perspective-enhanced-ncube-projections-to-3d\/","title":{"rendered":"Perspective Enhanced HyperCube Projections to 3D"},"content":{"rendered":"<p>These objects are projected using an {x,y,z} orthonormal basis. For n={5,6,7} I add a small delta (.2) to {x,y,z} basis vectors in columns {n-2,n-1,n} in order to keep vertices from overlapping. There is an enhanced perspective applied to vertex location as well.<\/p>\n<h4 style=\"text-align: center;\">4Cube<\/h4>\n<p><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/4-cube0.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4790\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/4-cube0.png\" alt=\"\" width=\"250\" height=\"251\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/4-cube0.png 250w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/4-cube0-150x150.png 150w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/><\/a><br \/>\n<a href=\"http:\/\/theoryofeverything.org\/TOE\/JGM\/models\/4-cube0.stl\">4Cube 3D StereoLithography (STL) model for 3D Printing<\/a><\/p>\n<h4 style=\"text-align: center;\">5Cube<\/h4>\n<p><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/5-cube0.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4791\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/5-cube0.png\" alt=\"\" width=\"250\" height=\"251\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/5-cube0.png 250w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/5-cube0-150x150.png 150w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/><\/a><br \/>\n<a href=\"http:\/\/theoryofeverything.org\/TOE\/JGM\/models\/5-cube0.stl\">5Cube 3D StereoLithography (STL) model for 3D Printing<\/a><\/p>\n<h4 style=\"text-align: center;\">6Cube<\/h4>\n<p><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/6-cube0.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4791\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/6-cube0.png\" alt=\"\" width=\"250\" height=\"251\" \/><\/a><br \/>\n<a href=\"http:\/\/theoryofeverything.org\/TOE\/JGM\/models\/6-cube0.stl\">6Cube 3D StereoLithography (STL) model for 3D Printing<\/a><\/p>\n<h4 style=\"text-align: center;\">7Cube<\/h4>\n<p><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/7-cube0.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4792\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/7-cube0.png\" alt=\"\" width=\"250\" height=\"251\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/7-cube0.png 250w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/7-cube0-150x150.png 150w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/><\/a><br \/>\n<a href=\"http:\/\/theoryofeverything.org\/TOE\/JGM\/models\/7-cube0.stl\">7Cube 3D StereoLithography (STL) model for 3D Printing<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>These objects are projected using an {x,y,z} orthonormal basis. For n={5,6,7} I add a small delta (.2) to {x,y,z} basis vectors in columns {n-2,n-1,n} in order to keep vertices from overlapping. There is an enhanced perspective applied to vertex location as well. 4Cube 4Cube 3D StereoLithography (STL) model for 3D Printing 5Cube 5Cube 3D StereoLithography &hellip; <a href=\"https:\/\/theoryofeverything.org\/theToE\/2017\/10\/18\/perspective-enhanced-ncube-projections-to-3d\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Perspective Enhanced HyperCube Projections to 3D<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[4,14],"class_list":["post-4788","post","type-post","status-publish","format-standard","hentry","category-physics","tag-e8","tag-math"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/4788","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/comments?post=4788"}],"version-history":[{"count":5,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/4788\/revisions"}],"predecessor-version":[{"id":4809,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/4788\/revisions\/4809"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=4788"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=4788"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=4788"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}