{"id":1965,"date":"2022-04-05T01:00:16","date_gmt":"2022-04-05T05:00:16","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2022\/?p=1965"},"modified":"2022-01-17T15:53:05","modified_gmt":"2022-01-17T20:53:05","slug":"lecture-20-conformal-geometry","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2022\/2022\/04\/05\/lecture-20-conformal-geometry\/","title":{"rendered":"Lecture 19: Conformal Geometry"},"content":{"rendered":"<p>A basic task in geometric algorithms is finding <em>mappings<\/em> between surfaces, which can be used to transfer data from one place to another.  A particularly nice class of algorithms (both from a mathematical and computational perspective) are <em>conformal<\/em> mappings, which preserve angles between vectors, and are generally very well-behaved.  In this lecture we&#8217;ll take a look at smooth characterizations of conformal maps, which will ultimately inspire the way we talk about conformal maps in the discrete\/computational setting.<\/p>\n<p>The video covering both this and the next lecture (on discrete aspects of conformal maps) can be found <a href=\"https:\/\/www.youtube.com\/watch?v=4YHmaoQoT9s\">here<\/a>.<\/p>\n<p><a href=\"http:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/04\/DDG_458_SP19_Lecture19_ConformalGeometryI.pdf\"><img loading=\"lazy\" src=\"http:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/04\/DDG_458_SP19_Lecture19_ConformalGeometryI_icon.jpg\" alt=\"\" width=\"419\" height=\"243\" class=\"alignnone size-full wp-image-1966\" srcset=\"https:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/04\/DDG_458_SP19_Lecture19_ConformalGeometryI_icon.jpg 838w, https:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/04\/DDG_458_SP19_Lecture19_ConformalGeometryI_icon-300x174.jpg 300w, https:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/04\/DDG_458_SP19_Lecture19_ConformalGeometryI_icon-768x445.jpg 768w\" sizes=\"(max-width: 419px) 85vw, 419px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A basic task in geometric algorithms is finding mappings between surfaces, which can be used to transfer data from one place to another. A particularly nice class of algorithms (both from a mathematical and computational perspective) are conformal mappings, which preserve angles between vectors, and are generally very well-behaved. In this lecture we&#8217;ll take a &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2022\/2022\/04\/05\/lecture-20-conformal-geometry\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Lecture 19: Conformal Geometry&#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\/1965"}],"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=1965"}],"version-history":[{"count":4,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1965\/revisions"}],"predecessor-version":[{"id":3370,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1965\/revisions\/3370"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/media?parent=1965"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/categories?post=1965"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/tags?post=1965"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}