{"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":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.8 - aioseo.com -->\n\t<meta name=\"description\" content=\"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\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"jgmoxness\"\/>\n\t<link rel=\"canonical\" href=\"https:\/\/theoryofeverything.org\/theToE\/2017\/10\/18\/perspective-enhanced-ncube-projections-to-3d\/\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 4.9.8\" \/>\n\t\t<meta property=\"og:locale\" content=\"en_US\" \/>\n\t\t<meta property=\"og:site_name\" content=\"Visualizing a Theory of Everything! - Dedicated to the pursuit of beauty and Truth in Nature!\" \/>\n\t\t<meta property=\"og:type\" content=\"article\" \/>\n\t\t<meta property=\"og:title\" content=\"Perspective Enhanced HyperCube Projections to 3D - Visualizing a Theory of Everything!\" \/>\n\t\t<meta property=\"og:description\" content=\"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\" \/>\n\t\t<meta property=\"og:url\" content=\"https:\/\/theoryofeverything.org\/theToE\/2017\/10\/18\/perspective-enhanced-ncube-projections-to-3d\/\" \/>\n\t\t<meta property=\"article:published_time\" content=\"2017-10-18T20:57:39+00:00\" \/>\n\t\t<meta property=\"article:modified_time\" content=\"2017-10-18T23:52:25+00:00\" \/>\n\t\t<meta name=\"twitter:card\" content=\"summary\" \/>\n\t\t<meta name=\"twitter:title\" content=\"Perspective Enhanced HyperCube Projections to 3D - Visualizing a Theory of Everything!\" \/>\n\t\t<meta name=\"twitter:description\" content=\"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. 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There is an enhanced perspective applied to vertex location as well. 4Cube 4Cube 3D StereoLithography (STL) model for 3D Printing 5Cube 5Cube 3D StereoLithography"},"aioseo_meta_data":{"post_id":"4788","title":null,"description":null,"keywords":null,"keyphrases":null,"primary_term":null,"canonical_url":null,"og_title":null,"og_description":null,"og_object_type":"default","og_image_type":"default","og_image_url":null,"og_image_width":null,"og_image_height":null,"og_image_custom_url":null,"og_image_custom_fields":null,"og_video":null,"og_custom_url":null,"og_article_section":null,"og_article_tags":null,"twitter_use_og":false,"twitter_card":"default","twitter_image_type":"default","twitter_image_url":null,"twitter_image_custom_url":null,"twitter_image_custom_fields":null,"twitter_title":null,"twitter_description":null,"schema":{"blockGraphs":[],"customGraphs":[],"default":{"data":{"Article":[],"Course":[],"Dataset":[],"FAQPage":[],"Movie":[],"Person":[],"Product":[],"ProductReview":[],"Car":[],"Recipe":[],"Service":[],"SoftwareApplication":[],"WebPage":[]},"graphName":"","isEnabled":true},"graphs":[],"defaultGraph":"","defaultPostTypeGraph":""},"schema_type":"default","schema_type_options":null,"pillar_content":false,"robots_default":true,"robots_noindex":false,"robots_noarchive":false,"robots_nosnippet":false,"robots_nofollow":false,"robots_noimageindex":false,"robots_noodp":false,"robots_notranslate":false,"robots_max_snippet":null,"robots_max_videopreview":null,"robots_max_imagepreview":"large","priority":null,"frequency":null,"local_seo":null,"limit_modified_date":false,"created":"2022-04-06 04:22:24","updated":"2025-06-10 15:49:17"},"aioseo_breadcrumb":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"https:\/\/theoryofeverything.org\/theToE\" title=\"Home\">Home<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">\u00bb<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"https:\/\/theoryofeverything.org\/theToE\/topics\/physics\/\" title=\"Physics\">Physics<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">\u00bb<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\tPerspective Enhanced HyperCube Projections to 3D\n\t\t<\/span><\/div>","aioseo_breadcrumb_json":[{"label":"Home","link":"https:\/\/theoryofeverything.org\/theToE"},{"label":"Physics","link":"https:\/\/theoryofeverything.org\/theToE\/topics\/physics\/"},{"label":"Perspective Enhanced HyperCube Projections to 3D","link":"https:\/\/theoryofeverything.org\/theToE\/2017\/10\/18\/perspective-enhanced-ncube-projections-to-3d\/"}],"_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}]}}