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Re: SVG2 - suggestion for a new path command to close a subpath smoothly

From: Dr. Olaf Hoffmann <Dr.O.Hoffmann@gmx.de>
Date: Mon, 7 Jan 2013 11:21:04 +0100
To: www-svg@w3.org
Message-Id: <201301071121.04401.Dr.O.Hoffmann@gmx.de>
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 GMT

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