Attached is a modified version of the files src\2geom\sbasis-to-bezier.cpp, and *.h. The original call to the routine : sbasis_to_bezier(bez, B, 4) has been replaced with a call to a new routine : sbasis_to_cubic_bezier(bez, B) in order to improve the conversion from sbasis to cubic bezier. In the original routine the cubic bezier was specified by fitting the four variables : dx/dt(0), dy/dt(0), dx/dt(1), dy/dt(1), where t is the independent variable in the parametric representation. In the new routine the bezier is specified by fitting the four variables dx/dy(0), dx/dy(1), x(0.5), y(0.5). Numerical tests have shown that the original routine, if applied to a circular arc, will yield a bezier curve whose control arms have a length

d/r = theta/3

where

d = Bezier control arm length r = radius theta = angle of arc.

This is a correct zeroth order result for small theta, but is not appropriate for large theta. Numerical tests using the new routine on a circular arc yield a bezier control arm length that is consistent with

d/r = 4*tan(theta/4)/3

This is identical to the formula that is currently being used in the routine sp_genericellipse_set_shape (src\sp-ellipse.cpp) to render those ellipses that have sodipodi attributes associated with them. When applied to LP Bug 653315, file p.svg, this patch appears to resolve the rendering problem shown there.

Alvin Penner

http://old.nabble.com/file/p30327020/sbasis-to-bezier.cpp sbasis-to-bezier.cpp http://old.nabble.com/file/p30327020/sbasis-to-bezier.h sbasis-to-bezier.h