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## Re: [Inkscape-devel] Powerstroke wrap-up

 Re: [Inkscape-devel] Powerstroke wrap-up From: Jasper van de Gronde - 2012-10-08 08:35:20 ```On 07-10-12 21:05, Johan Engelen wrote: > On 7-10-2012 7:49, Tavmjong Bah wrote: >> On Sat, 2012-10-06 at 22:26 +0200, Johan Engelen wrote: >>> Hi all, >>> I've lost track of all the problems with powerstroke. >>> Please send me again the bugs you have found (with a test file!) or the >>> UI ideas we definitely need for release. >>> >>> I have been working on "extrapolate by arcs matching path curvature", >>> but I think it will take me too long to make that work reliably before >>> release. There are still too many bumps along that road... I've >>> committed the code, but it is disabled. >> What is your problem with "extrapolate by arcs matching path curvature"? >> I've got a hacked version of Cairo that does the extrapolated >> line-join... but not properly (it only works at 100% zoom at the >> moment). > > Determining the curvature is messy, have not found a good way to do that > yet. In principle, curvature is just the norm of the second derivative w.r.t. arc-length (if you want it signed, you'd probably just have to take the dot product with the unit normal, instead of the norm). Of course, the trick is in the "arc-length" bit, is that where you're getting stuck? One trick you could try is taking an explicit formula like (x'*y'' - y'*x'')/(x'^2+y'^2)^(3/2) and approximating it with a polynomial (which doesn't require any values near the endpoints, where you'll usually get singularities and other problems), then evaluating the polynomial at the endpoints. I haven't tried it, so I'm not sure how well it would work, but my guess is that it could work pretty well. ```