{"id":3847,"date":"2018-02-11T11:14:38","date_gmt":"2018-02-11T19:14:38","guid":{"rendered":"https:\/\/bendwavy.org\/wp\/?p=3847"},"modified":"2019-03-11T21:02:47","modified_gmt":"2019-03-12T05:02:47","slug":"meander","status":"publish","type":"post","link":"https:\/\/bendwavy.org\/wp\/?p=3847","title":{"rendered":"meander"},"content":{"rendered":"

(Previously: 2014<\/a>, 2011<\/a>, 2010<\/a>; also, less closely related, 2015<\/a>)<\/p>\n

I tried to smoothen a stroke by shifting each dot toward the Euler spiral (aka clothoid, aka Cornu spiral) determined by its four nearest neighbors. That didn’t work so well: small wiggles were removed, but big ones were magnified.
\n
\n Which reminds me that I considered naming the project Meander, but then thought no, the point is to remove<\/em> meanders. (For now I’m calling it Thalweg<\/a>, until a better name occurs to me.)<\/p>\n

The flaw in my thinking is that I don’t want any<\/em> Euler spiral, I want one in which curvature changes as slowly as possible: that is, one that is locally very like a circle.<\/p>\n

So the logical thing to do is to shift the dot toward the circle defined by three<\/em> neighbors; or rather, since that would introduce an undesirable asymmetry, the circle that fits the two immediate neighbors exactly and misses the next two by equal distances. I haven’t worked out how to do that; I’ll probably simply fit two circles and split the difference.<\/p>\n

I’m also working on another approach: fit two curves exactly to alternating dots, and adjust each dot according to the other curve. Though this uses piecewise Euler spirals, I hope the discipline of global constraints will prevent the exuberance seen above.<\/p>\n","protected":false},"excerpt":{"rendered":"

(Previously: 2014, 2011, 2010; also, less closely related, 2015) I tried to smoothen a stroke by shifting each dot toward the Euler spiral (aka clothoid, aka Cornu spiral) determined by its four nearest neighbors. That didn’t work so well: small … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[72],"tags":[],"class_list":["post-3847","post","type-post","status-publish","format-standard","hentry","category-curve-fitting"],"_links":{"self":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/3847","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3847"}],"version-history":[{"count":4,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/3847\/revisions"}],"predecessor-version":[{"id":4004,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/3847\/revisions\/4004"}],"wp:attachment":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3847"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3847"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3847"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}