> Are you suggesting a formula that returns the distance of a cubic spline
at
> a particular point?  If so, it's my understanding (after a lot of research
> and many attempts while developing my Spline Macro File -
> http://www.geocities.com/ccolefax/spline) that there is no known
analytical
> solution to this problem.  If you have indeed found one, I for one would
be
> very interested!

I should have read ahead in the arc-length section of my calculus text - the
bit where it says there is often no way of solving the integral required
because of the difficulty in finding the appropriate antiderivative.

Having got stuck into the maths I've found that the problem boils down to
finding the antiderivative of the square-root of a polynomial of degree
(n-2)^2, where n is the number of control points in the spline.  In the most
common case (for me anyway) of 4 points, the polynomial is a 4th degree.  I
can't think of how to do that, but I'll ask someone in the maths department
at uni if I can't nut it out over the weekend.

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