{"id":1969,"date":"2023-04-03T11:07:15","date_gmt":"2023-04-03T15:07:15","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2023\/?p=1969"},"modified":"2023-03-13T12:25:38","modified_gmt":"2023-03-13T16:25:38","slug":"lecture-21-discrete-conformal-geometry","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2023\/2023\/04\/03\/lecture-21-discrete-conformal-geometry\/","title":{"rendered":"Lecture 20: Discrete Conformal Geometry"},"content":{"rendered":"

In this lecture we’ll attempt to translate several smooth characterizations of conformal maps into the discrete setting. We’ll also see how each of these attempts leads to a different class of computational algorithms, with different trade offs. Although conformal maps are often associated with angle preservation, we’ll see that preserving angles at the discrete level results in a theory that is far to rigid<\/em>: i.e., it does not capture any of the interesting structure of smooth conformal geometry. Instead, we’ll see how less-obvious starting points (such as patterns of circles, or preservation of length cross ratios<\/em>) lead to some deep and beautiful connections between the classic smooth picture, and the discrete, combinatorial picture.<\/p>\n

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In this lecture we’ll attempt to translate several smooth characterizations of conformal maps into the discrete setting. We’ll also see how each of these attempts leads to a different class of computational algorithms, with different trade offs. Although conformal maps are often associated with angle preservation, we’ll see that preserving angles at the discrete level … Continue reading “Lecture 20: Discrete Conformal Geometry”<\/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,"_links_to":"","_links_to_target":""},"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/posts\/1969"}],"collection":[{"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/comments?post=1969"}],"version-history":[{"count":3,"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/posts\/1969\/revisions"}],"predecessor-version":[{"id":2273,"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/posts\/1969\/revisions\/2273"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/media?parent=1969"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/categories?post=1969"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/tags?post=1969"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}