bulia byak wrote:
On 5/14/05, bulia byak <buliabyak@...400...> wrote:
The distance between nodes in 2 is ideally calculated as "distance along path", here's the formula: http://www.cit.gu.edu.au/~anthony/info/graphics/bezier.curves
Actually, for the purpose of comparing lengths, you don't need all that math. Just sum the length of both Bezier handles that define the segment, plus the distance between the ends of these handles (in other words, sum the three of the four sides of the quadrilateral into which the bezier curve is inscribed). This is a good first approximation of the curve length, at least it should be sufficient for comparing lengths of segments.
I'm sure that would be faster and I may have to resort to it. I think that website leaves something to be desired. At least it does for me.
As far as I can tell the code in the Gravensen approximation does not implement what the description says. It is basically what you describe above.
The code in the Simpson method uses a point2d struct right in an equation. Since I don't know C, I don't know exactly what that means, but it seems to be nonsense. And now that I have something implmented It tries to sqrt a negative number in the "balf" function. I don't know enough math to figure out how the implementation is wrong.
So I think I will do just as you suggest. I still wouldn't mind having a good bezier arc length function sitting around for use in future projects. So if anyone would be willing to take a look at my Simpson approximation code and tell me what is wrong, I would much appreciate it.
Oh, and did you try the interpolation extension with paths of multiple subpaths?
Aaron Spike