I'm gonna reply to all your posts in one go, since you were carrying on
such a little conversation with yourself ;)

Warp wrote:
> Beware of possible floating point inaccuracies with such small numbers.
This is why your method is better (because the tangential vector is
longer :. less scope for FPI)

Warp wrote:
>   Of course the more mathematically oriented people would like an exact
> result instead of just an approximation... :)
Well, the only limit on the accuracy is that imposed by the system
itself (specifically FPI as you pointed out), so a more accurate
solution would probably have no further benefit anyway?

Warp wrote:
>   By the way, I think that this gives a better approximation:
Yeah, it does.

>   Suppose that we want to calculate the tangent of the spline at the
> time value T.
Which we do. ;P

>   Take a small value, which we will call Epsilon (could be for example
> 10e-5 or something similar).
> My constants.inc has EPSILON=1e-7, but of course it doesn't matter so long as it's
small.
> 
>   This given a better approximation because the resulting vector will be
> closer to the true tangent, and could even be exactly the tangent.
> 'Spline(T+Epsilon)-Spline(T)', however, can never be exactly the tangent.
Yeah, this method *is* better. I think the only reason I thought of the
other one was because the pure mathematical definition of the tangent
comes from that (with EPSILON -> 0), which makes the maths easier.
Of course, we can't use EPSILON=0 here, so obviously your method works
better.

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