Warp  wrote in message <47ff5d1b@news.povray.org>:
> The easiest (although perhaps not the absolute fastest) solution to
> it is to approximate by adaptive sampling. This means that the next
> point in the spline is searched by first calculating one point at
> a "guessed" distance, then refine that "guess" and calculate another
> point, and so on, all the time approaching the actual point (which will
> never be actually reached, but the end result will be quite close to it).

I think there is something missing in your solution. As far as I know, the
arc length on a spline is not something we can get in closed form. In fact,
that is exactly the cause of the problem in the first place.

Therefore, to compute how much the guessed point if off the desired point,
it is necessary to integrate from the beginning of the curve (or the last
known point). In that case, a simple, linear method is more efficient.

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