- From: Dr. Olaf Hoffmann <Dr.O.Hoffmann@gmx.de>
- Date: Mon, 7 Jan 2013 11:21:04 +0100
- To: www-svg@w3.org
Rik Cabanier: > Thanks for bringing this up again. > We discussed this during a weekly conference call and people were quite > interested. > > I played around with your example page and the results look reasonable. > > The solution needs to work on all types of path types though (including > arc). Do you need any more information than the angle of the control point > and the distance between start and end? > > Rik > You mean elliptical arcs? Well, with the path data notation for segments using the commands A or a, one can use http://www.w3.org/TR/SVG2/implnote.html#ArcParameterizationAlternatives http://www.w3.org/TR/SVG2/implnote.html#ArcConversionCenterToEndpoint http://www.w3.org/TR/SVG2/implnote.html#ArcConversionEndpointToCenter to get a parametrisation of the segment k(s) from s = 0 to 1. To be sure to get the same parametrisation in all implementations, one can define for example the center parametrisation to be relevant with s = (theta - theta1)/(delta theta). The derivative dk(s)/ds is simple to calculate analytically (d cos(bt)/dt= -b sin(bt) and d sin(bt)/dt = b cos(bt)). The implementation notes define equivalences for degenerate cases as well. Therefore one has the required information already to construct the closing cubic curve segment as explained in http://lists.w3.org/Archives/Public/www-svg/2012Dec/0054.html Olaf
Received on Monday, 7 January 2013 10:21:32 UTC