{"id":1959,"date":"2022-03-31T01:00:16","date_gmt":"2022-03-31T05:00:16","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2022\/?p=1959"},"modified":"2022-01-17T15:58:04","modified_gmt":"2022-01-17T20:58:04","slug":"lecture-19-discrete-laplacian","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2022\/2022\/03\/31\/lecture-19-discrete-laplacian\/","title":{"rendered":"Lecture 19\u2014The Discrete Laplacian"},"content":{"rendered":"<p>In the last lecture we introduced the Laplace operator from the smooth point of of view; in this lecture we talk about how to discretize it, and show that from computational point of view it really is the &mdash;Swiss army knife&mdash; of geometry processing algorithms&mdash;essentially playing the role of the discrete Fourier transform from classical signal processing.<\/p>\n<p>You can find a video lecture for these slides, from a talk given by Etienne Vouga, <a href=\"https:\/\/youtu.be\/IwS-mRhPDGg?t=3139\">here<\/a>.  (We&#8217;ll have our own lecture in-class!  This one is just for reference\/for anyone who is sick, etc.)<\/p>\n<p><a href=\"http:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/04\/SwissArmyLaplacian.pdf\"><img loading=\"lazy\" src=\"http:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/04\/DDG_458_SP19_Lecture17_LaplaceBeltramiI_icon.jpg\" alt=\"\" width=\"838\" height=\"486\" class=\"alignnone size-full wp-image-1960\" srcset=\"https:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/04\/DDG_458_SP19_Lecture17_LaplaceBeltramiI_icon.jpg 838w, https:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/04\/DDG_458_SP19_Lecture17_LaplaceBeltramiI_icon-300x174.jpg 300w, https:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/04\/DDG_458_SP19_Lecture17_LaplaceBeltramiI_icon-768x445.jpg 768w\" sizes=\"(max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 984px) 61vw, (max-width: 1362px) 45vw, 600px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In the last lecture we introduced the Laplace operator from the smooth point of of view; in this lecture we talk about how to discretize it, and show that from computational point of view it really is the &mdash;Swiss army knife&mdash; of geometry processing algorithms&mdash;essentially playing the role of the discrete Fourier transform from classical &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2022\/2022\/03\/31\/lecture-19-discrete-laplacian\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Lecture 19\u2014The Discrete Laplacian&#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":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1959"}],"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=1959"}],"version-history":[{"count":6,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1959\/revisions"}],"predecessor-version":[{"id":3373,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1959\/revisions\/3373"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/media?parent=1959"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/categories?post=1959"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/tags?post=1959"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}