{"id":465,"date":"2008-03-15T13:11:50","date_gmt":"2008-03-15T21:11:50","guid":{"rendered":"http:\/\/www.elbeno.com\/blog\/?p=465"},"modified":"2008-03-15T13:17:50","modified_gmt":"2008-03-15T21:17:50","slug":"even-more-on-ellipses-and-splines","status":"publish","type":"post","link":"https:\/\/www.elbeno.com\/blog\/?p=465","title":{"rendered":"Even more on ellipses and splines"},"content":{"rendered":"

Honestly, they’re incredibly interesting. Anyway, I’ll skip straight to the pi\u00c3\u00a8ce de r\u00c3\u00a9sistance<\/i>:<\/p>\n

\"Ellipse<\/a><\/p>\n

This is a 4-curve cubic B\u00c3\u00a9zier spline modulated onto an ellipse. The ellipse [a=4, b=3] is at an angle of π\/4. C1 continuity of the complete curve is preserved. The flickr set<\/a> tells the story of how I got here.<\/p>\n

This is around 450 lines of my naive lisp, including class definitions and test code. So Gary, this is your g-code challenge!<\/p>\n

The lisp code is object oriented (oh, and so much nicer than C++’s so-called object orientation). I rewrote the earlier code now that I knew what I was doing, and I added lines and polylines to the mix too (see the flickr set) so I can easily modulate whatever edge I want. You’ll notice if you look closely at the earlier<\/a> attempts<\/a> that they had a bit of a problem with c1 continuity, which is now fixed with the new code.<\/p>\n

In closing, thanks<\/a>, Zach<\/a>!<\/p>\n","protected":false},"excerpt":{"rendered":"

Honestly, they’re incredibly interesting. Anyway, I’ll skip straight to the pi\u00c3\u00a8ce de r\u00c3\u00a9sistance: This is a 4-curve cubic B\u00c3\u00a9zier spline modulated onto an ellipse. The ellipse [a=4, b=3] is at an angle of π\/4. C1 continuity of the complete curve is preserved. The flickr set tells the story of how…<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13,11,8],"tags":[],"class_list":["post-465","post","type-post","status-publish","format-standard","hentry","category-lisp","category-maths","category-programming"],"_links":{"self":[{"href":"https:\/\/www.elbeno.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/465","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.elbeno.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.elbeno.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.elbeno.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.elbeno.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=465"}],"version-history":[{"count":0,"href":"https:\/\/www.elbeno.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/465\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.elbeno.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=465"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.elbeno.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=465"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.elbeno.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=465"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}