{"id":25,"date":"2009-02-28T09:31:00","date_gmt":"2009-02-28T09:31:00","guid":{"rendered":"http:\/\/www.fun-engineering.net\/blogs\/funeng\/2009\/02\/28\/3-d_convex_hull\/"},"modified":"2009-02-28T09:31:00","modified_gmt":"2009-02-28T09:31:00","slug":"3-d-convex-hull","status":"publish","type":"post","link":"https:\/\/fun-engineering.net\/blogs\/funeng\/2009\/02\/28\/3-d-convex-hull\/","title":{"rendered":"3-D Convex Hull"},"content":{"rendered":"<p>I&#8217;m working on developing a 3-D convex hull algorithm in Mathematica for the 4-colour rhombohedral lattice. Right now I&#8217;m trying to grasp how to store the connectness or topology of the convex shell.<br \/>\n<!--more--><\/p>\n<p>I have an ordered list of vertices. I need an adjacency matrix, which indicates which vertex is connected to which other vertex. A web reference for this is:<br \/>\n<a title=\"Link to http:\/\/en.wikipedia.org\/wiki\/Adjacency_matrix\" href=\"http:\/\/en.wikipedia.org\/wiki\/Adjacency_matrix\">http:\/\/en.wikipedia.org\/wiki\/Adjacency_matrix<\/a><br \/>\n(original link, which was no longer available, replaced 20 May 2012)<br \/>\nA great thing about the adjacency matrix is that it incorporates the direction of each connecting link. This allows me to distinguish between a forward link and a backward link.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I&#8217;m working on developing a 3-D convex hull algorithm in Mathematica for the 4-colour rhombohedral lattice. Right now I&#8217;m trying to grasp how to store the connectness or topology of the convex shell.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[33],"class_list":["post-25","post","type-post","status-publish","format-standard","hentry","category-mathematics-2","tag-convex-hull"],"_links":{"self":[{"href":"https:\/\/fun-engineering.net\/blogs\/funeng\/wp-json\/wp\/v2\/posts\/25","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fun-engineering.net\/blogs\/funeng\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/fun-engineering.net\/blogs\/funeng\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/fun-engineering.net\/blogs\/funeng\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fun-engineering.net\/blogs\/funeng\/wp-json\/wp\/v2\/comments?post=25"}],"version-history":[{"count":0,"href":"https:\/\/fun-engineering.net\/blogs\/funeng\/wp-json\/wp\/v2\/posts\/25\/revisions"}],"wp:attachment":[{"href":"https:\/\/fun-engineering.net\/blogs\/funeng\/wp-json\/wp\/v2\/media?parent=25"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/fun-engineering.net\/blogs\/funeng\/wp-json\/wp\/v2\/categories?post=25"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/fun-engineering.net\/blogs\/funeng\/wp-json\/wp\/v2\/tags?post=25"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}