On Tue, Dec 20, 2011 at 2:42 AM, Alvin Penner <penner@...2467...> wrote:
yes, you are correct, the conversion from elliptical arc to cubic Bézier
curves is not lossless. There have been some bug reports concerning this:
The behaviour in Inkscape is, typically, to try to make sure that the angle
of the arc over which the Bezier curve is fit is never more than 90 degrees.
If it is, then multiple Beziers will be used. The Bezier curve is applied so
that it touches the elliptical arc tangentially at both endpoints of the arc
and also at the midpoint as well. The resulting error will be so small that
it should not be noticeable on a normal display.
Thank you for your explanation. I understand that the approximation
can be rather accurate when the elliptical arc is small. It may even
be identical pixel to pixel when rasterized for printing. However, the
problem is when we draw a circle with large radius, like 30,000
pixels, for high resolution large canvas, the final printed output is
no longer identical. Seems adding a huge amount of points on the
circle and simplify the largely over-defined curve maybe the only way
out right now. Hopefully the two step approximation would produce a
better result than a static conversion.