On 6/26/07, bulia byak <buliabyak@...400...> wrote:
Can you check if the increased precision fixes any of these bugs, at least partially?
http://sourceforge.net/tracker/index.php?func=detail&aid=1723167&gro...
This one says rotating a circle by 36 degrees results in something of different width than the the original. That's still going to happen even with an improved approximation (unless you special case your approximation for 36 degrees :-)
With the current approximation, a 45 degree rotation turns a width 500 circle into a width of about 499.92. Maximum diameter is at about 18 degrees and that's about 500.11.
With the full constant, the 45 degree width would be exact, everywhere else would be higher. That's what the full constant does, it makes the bez touch the ideal circle at 45 degree angles. Really, that doesn't necessarily mean either minimum peak error or minimal error in the integral sense. In fact with the "correct" constant, it overshoots the radius *everywhere* except multiples of 45 degrees, and has a max radius of 500.136. So in that sense the current approximation is more optimal since the max error is smaller, and since it's sometime bigger and sometimes smaller, it probably has a smaller integrated error.
http://sourceforge.net/tracker/index.php?func=detail&aid=1449053&gro...
I don't think it will help much there either. It'll still be an approximation, so dicing up circles, rotating them, and trying to line them up will still reveal inaccuracies to the tune of 2 parts per 10000.
So 0.552 actually seems to be a pretty good choice after looking at it closer. There's probably some number in that vicinity that really does minimize either max error or integrated error, or RMS error. But it's not going to be a whole lot better -- and they're probably all different numbers -- and I don't happen to know any of those numbers. :-)
--bb