W3C home > Mailing lists > Public > www-svg@w3.org > June 2008

Re: Arc Segment Implementation Notes ...

From: Dr. Olaf Hoffmann <Dr.O.Hoffmann@gmx.de>
Date: Thu, 26 Jun 2008 11:46:16 +0200
To: www-svg@w3.org
Message-Id: <200806261146.16619.Dr.O.Hoffmann@gmx.de>

I think, the missing arc commands are more related to a tiny profile than to
version 1.2, because they are not available in SVG tiny 1.1 too:
http://www.w3.org/TR/SVGMobile/#sec-shapes


As many other shapes elliptical arcs cannot be exactly expressed with
cubic curves.
Depending on the accuracy requirements, an author can compute
a set of cubic curve fragments to replace an elliptical arc approximately.
Typically a good approach is to demand that position and derivates fit
together at the end of cubic curve fragments joined together to an
approximation of an elliptical arc.
How many curve fragments are needed to get the desired 
accuracy obviously depends on the requirements of the author,
therefore there cannot be a general rule to do this approximation.
However, the rule described above is an even more general 
rule how to approximate any continuously differentiable  curve 
with a cubic curve, but this needs some calculations, either analytical
or numerical.
I needed for some reasons already a cubic curve replacement
for an ellipse, circle and some other shapes like spirals, atomic
transition dipole moment shapes, therefore I already did this with 
a small PHP script analytically or numerically and it is not really 
a big issue if one is familiar with basic analytics. 
Received on Thursday, 26 June 2008 09:48:36 GMT

This archive was generated by hypermail 2.3.1 : Friday, 8 March 2013 15:54:39 GMT