Re: [Inkscape-devel] Recent change to ellipse to path conversion method?
On 20-Oct-2013 14:35, Nathan Hurst wrote:
There have been papers published on ways to do this efficiently in
general (one search term is geometric interpolation). Nobody has
implemented a competitive algorithm. I would recommend modifying the
ellipse code to use the known approximation directly rather than going
via sbasis (or equivalently, generating the approximation in sbasis
form rather than using sin,cos in which case
Geom::cubicbezierpath_from_sbasis should be the identity).
Recapitulating:
1. The original ellipse -> bezier conversion used one of the worked out
solutions which are calculated directly from the ellipse parameters.
Probably something like this:
http://www.spaceroots.org/documents/ellipse/
It produced four beziers for any ellipse. These met the needs of most
users.
2. Higher precision curve drawing of ellipses was required by some end
users for CAD purposes, so the method was changed. This resulted in the
default bezier representation of an ellipse being more complex (>4
beziers) than needed for general use. The new method uses a fit
parameter which must be changed in a major way from its default value in
order to return to beziers similar to (1), and there is currently no way
to do this in the GUI. (Unsure: that same parameter is used for other
curve -> bezier conversions? Does the end user need to be able to
adjust the fit parameter?)
So far so good?
The issue then is how to allow those who need it to obtain a higher
precision conversion to beziers without requiring that the average user
know anything about it. I suggest that the usual solution to this sort
of problem, as applied to Inkscape, would be to modify the toolbar for
elliptical drawing to add a "precision" field that normally reads
"Default", with other options perhaps called "CAD Low","CAD
Medium","CAD
High". Each corresponds to a parameter value, but that is not shown to
the end user, in case things need to be changed around again at some
point in future. Exposing the parameter value is unlikely to be helpful
to most users, since it probably will not correspond in a simple way to
an easily comprehended measure of error. The bezier generating code
looks at this parameter, and when it sees the one corresponding to
"Default" it uses the original algorithm, for all of the others it uses
Geom::cubicbezierpath_from_sbasis.
In terms of usability that should be fine, and adding the control will
not be hard. However, algorithmically I am guessing that
Geom::cubicbezierpath_from_sbasis is not as efficient as using some
partially precalculated method which uses the a/b ratio of the ellipse
in question, at least for whole ellipses. For circles in particular
symmetry suggests that there must be an extremely efficient method of
determining the best set of Beziers for a given measure of fit.
Regards,
David Mathog
mathog@...1176...
Manager, Sequence Analysis Facility, Biology Division, Caltech