{"id":1739,"date":"2022-02-24T01:00:16","date_gmt":"2022-02-24T06:00:16","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2022\/?p=1739"},"modified":"2022-01-17T16:14:39","modified_gmt":"2022-01-17T21:14:39","slug":"lecture-11-discrete-curves","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2022\/2022\/02\/24\/lecture-11-discrete-curves\/","title":{"rendered":"Lecture 11: Discrete Curves"},"content":{"rendered":"<p><a href=\"https:\/\/www.youtube.com\/watch?v=IyJnd_LvGRI&#038;list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS&#038;index=14\"><img loading=\"lazy\" src=\"http:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/02\/DDG_458_SP19_Lecture11_DiscreteCurves_icon.jpg\" alt=\"\" width=\"419\" height=\"243\" \/><\/a><\/p>\n<p>This lecture presents the discrete counterpart of the previous lecture on smooth curves.  Here we arrive at a discrete version of the fundamental theorem for plane curves: a discrete curve is completely determined by its discrete parameterization (a.k.a. edge lengths) and its discrete curvature (a.k.a. exterior angles).  We&#8217;ll also cook up a discrete version of the fundamental theorem for space curves, and give a bunch of neat examples of discrete curves in geometry processing and physical simulation.<\/p>\n<ul>\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=IyJnd_LvGRI&#038;list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS&#038;index=14\">Video<\/a><\/li>\n<li><a href=\"http:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2020\/03\/DDG_11_DiscreteCurves.pdf\">Slides<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>This lecture presents the discrete counterpart of the previous lecture on smooth curves. Here we arrive at a discrete version of the fundamental theorem for plane curves: a discrete curve is completely determined by its discrete parameterization (a.k.a. edge lengths) and its discrete curvature (a.k.a. exterior angles). We&#8217;ll also cook up a discrete version of &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2022\/2022\/02\/24\/lecture-11-discrete-curves\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Lecture 11: Discrete Curves&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_links_to":"","_links_to_target":""},"categories":[7,3],"tags":[],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1739"}],"collection":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/comments?post=1739"}],"version-history":[{"count":4,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1739\/revisions"}],"predecessor-version":[{"id":3274,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1739\/revisions\/3274"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/media?parent=1739"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/categories?post=1739"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/tags?post=1739"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}