On Mon, Aug 12, 2013 at 12:38 PM, Auguste Pop <auguste@...155...> wrote:
On Mon, Aug 12, 2013 at 12:21 AM, Jasper van de Gronde < th.v.d.gronde@...226...> wrote:
On 2013-08-10 07:14, Auguste Pop wrote:
... Should I file a bug report? Please comment.
It is not entirely clear to me in what way the approximation is /wrong/. It is impossible to represent a circular arc using a Bézier curve, and there is thus not one best approximation. In my experience the curves look pretty decent, if you have an example where the approximation is clearly of very bad quality, that would be interesting.
As for the inconsistency, that could indeed be considered a bug. (Although as long as both approximations are of sufficient quality, I wouldn't be too worried.)
I said the approximation is "wrong" because there's no literature or resource that I am aware of comes up with this solution. I know an circular arc can not be represented by a cubic bezier curve losslessly. But with a certain criteria, there's certainly a "best" approximation. The "best" approximation may be very difficult to calculate, so we will finally use some "good" answers. The traditional approximation which puts the middle point of bezier curve on the arc is one of the "good" answers. In any case, the approximation used by "Edit path by nodes" is not "good" nor "best".
Of course, this can not be "wrong" as the error is still relatively slow to human eyes. When inkscape is treated as a design tool, this behavior is acceptable. But as a computer program, it is using the "wrong" equation mathematically.
Best regards,
In order to illustrate how large the error is, I have included a two graphs. These graphs show the absolute error from a point on the bezier curve to the circle. We get the graphs with the assumption that we are approximating a pi/4(45 degrees) arc on an unit circle.
The traditonal.png shows the error when using the traditional method. And the comparison.png shows the both errors from the traditional method and the method i think "wrong". Although the method in question still gives a relatively small error (about one thousandth), it is significantly worse than the traditional method (max error on 10^-6 order).
Best regards,
