{"id":1792,"date":"2024-03-16T11:31:34","date_gmt":"2024-03-16T15:31:34","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2024\/?p=1792"},"modified":"2024-04-04T14:42:55","modified_gmt":"2024-04-04T18:42:55","slug":"lecture-15-discrete-curvature-i-integral_viewpoint","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2024\/2024\/03\/16\/lecture-15-discrete-curvature-i-integral_viewpoint\/","title":{"rendered":"Lecture 15\u2014Discrete Curvature I (Integral Viewpoint)"},"content":{"rendered":"<p>Just as curvature provides powerful ways to describe and analyze smooth surfaces, discrete curvatures provide a powerful way to encode and manipulate digital geometry\u2014and is a fundamental component of many modern algorithms for surface processing. This first of two lectures on discrete curvature from the <em>integral<\/em> viewpoint, i.e., integrating smooth expressions for discrete curvatures in order to obtain curvature formulae suitable for discrete surfaces. In the next lecture, we will see a complementary <em>variational<\/em> viewpoint, where discrete curvatures arise by instead taking derivatives of discrete geometry. Amazingly enough, these two perspectives will fit together naturally into a unified picture that connects essentially all of the standard discrete curvatures for triangle meshes.<\/p>\n<p><a href=\"http:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2019\/03\/DDG_458_SP19_Lecture15_DiscreteCurvatureI-1.pdf\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2019\/03\/DDG_458_SP19_Lecture15_DiscreteCurvatureI.jpg\" alt=\"\" width=\"419\" height=\"243\" \/><\/a><a href=\"https:\/\/brickisland.net\/DDGSpring2021\/wp-content\/uploads\/2019\/03\/DDG_458_SP19_Lecture15_DiscreteCurvatureI-1.pdf\">Here<\/a> are the slides from 2021.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Just as curvature provides powerful ways to describe and analyze smooth surfaces, discrete curvatures provide a powerful way to encode and manipulate digital geometry\u2014and is a fundamental component of many modern algorithms for surface processing. This first of two lectures on discrete curvature from the integral viewpoint, i.e., integrating smooth expressions for discrete curvatures in &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2024\/2024\/03\/16\/lecture-15-discrete-curvature-i-integral_viewpoint\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Lecture 15\u2014Discrete Curvature I (Integral Viewpoint)&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":"","_links_to":"","_links_to_target":""},"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/1792"}],"collection":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/comments?post=1792"}],"version-history":[{"count":4,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/1792\/revisions"}],"predecessor-version":[{"id":2390,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/1792\/revisions\/2390"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/media?parent=1792"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/categories?post=1792"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/tags?post=1792"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}