Edward Coffey <e.c### [at] ugradunimelbeduau> wrote:
> 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.

When I said there was no known solution, I meant quite literally that no-one
has been able to solve this problem since the first invention/discovery of
the various cubic spline functions!  I'd certainly applaud your efforts to
be the first, but it seems that approximation works well for just about
everyone who's had a need for finding the length of a cubic spline segment -
so don't lose any sleep over it...

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