{"action":"created","issue":{"url":"https://api.github.com/repos/Pomax/bezierinfo/issues/66","repository_url":"https://api.github.com/repos/Pomax/bezierinfo","labels_url":"https://api.github.com/repos/Pomax/bezierinfo/issues/66/labels{/name}","comments_url":"https://api.github.com/repos/Pomax/bezierinfo/issues/66/comments","events_url":"https://api.github.com/repos/Pomax/bezierinfo/issues/66/events","html_url":"https://github.com/Pomax/bezierinfo/issues/66","id":224750038,"number":66,"title":"Mention non-intersection/cusp property of centripetal parameterization of Catmul-Rom spline","user":{"login":"JobLeonard","id":259840,"avatar_url":"https://avatars0.githubusercontent.com/u/259840?v=3","gravatar_id":"","url":"https://api.github.com/users/JobLeonard","html_url":"https://github.com/JobLeonard","followers_url":"https://api.github.com/users/JobLeonard/followers","following_url":"https://api.github.com/users/JobLeonard/following{/other_user}","gists_url":"https://api.github.com/users/JobLeonard/gists{/gist_id}","starred_url":"https://api.github.com/users/JobLeonard/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/JobLeonard/subscriptions","organizations_url":"https://api.github.com/users/JobLeonard/orgs","repos_url":"https://api.github.com/users/JobLeonard/repos","events_url":"https://api.github.com/users/JobLeonard/events{/privacy}","received_events_url":"https://api.github.com/users/JobLeonard/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":8,"created_at":"2017-04-27T11:10:37Z","updated_at":"2017-04-28T19:10:11Z","closed_at":null,"body":"As per [my comment on HN](https://news.ycombinator.com/item?id=14198204), it has been proven that for cubic  Catmul-Rom splines. only centripetal parameterization (alpha = 0.5) is guaranteed to never have self-intersections or cusps:\r\n\r\n> In this paper we prove that, for cubic Catmull-Rom curves, centripetal parameterization is the only parameterization in this family that guarantees that the curves do not form cusps or self-intersections within curve segments.\r\n\r\nhttp://www.cemyuksel.com/research/catmullrom_param/catmullrom_cad.pdf\r\n\r\nWhile neither self-intersection or cusps has to be a *technical* bug, it  can be a *visual* one that the artist using them did not intend to have (and which only become visible when zoomed in), so I think it's good to make this part of the \"general knowledge\" for people using such splines."},"comment":{"url":"https://api.github.com/repos/Pomax/bezierinfo/issues/comments/298082622","html_url":"https://github.com/Pomax/bezierinfo/issues/66#issuecomment-298082622","issue_url":"https://api.github.com/repos/Pomax/bezierinfo/issues/66","id":298082622,"user":{"login":"Pomax","id":177243,"avatar_url":"https://avatars1.githubusercontent.com/u/177243?v=3","gravatar_id":"","url":"https://api.github.com/users/Pomax","html_url":"https://github.com/Pomax","followers_url":"https://api.github.com/users/Pomax/followers","following_url":"https://api.github.com/users/Pomax/following{/other_user}","gists_url":"https://api.github.com/users/Pomax/gists{/gist_id}","starred_url":"https://api.github.com/users/Pomax/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Pomax/subscriptions","organizations_url":"https://api.github.com/users/Pomax/orgs","repos_url":"https://api.github.com/users/Pomax/repos","events_url":"https://api.github.com/users/Pomax/events{/privacy}","received_events_url":"https://api.github.com/users/Pomax/received_events","type":"User","site_admin":false},"created_at":"2017-04-28T19:10:11Z","updated_at":"2017-04-28T19:10:11Z","body":"hm, so that would animation contexts? I think with how the sections are ordered at the moment it would make sense to put a path traversal/animation section near the \"Tracing a curve at fixed distance intervals\" section, as that deals with the other aspect of janky animation, although that precedes CR splines..."}}
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