POV is powerful enough for getting all the piecewise polynomial coefficients
from declared spline. For cubic spline we can calculate four points on every
time interval, get all four coefficients from this 4x4 linear system and
then get exact tangent function for every time interval. These coefficients
can be used outside POV.

Of course, this will be approximation too, because of limited accuracy. The
best way is just to find out these figures directly from original set of
points, but it seems that in this case we need to solve linear systems of
higher order, than 4(still possible with SDL, however).







"Disnel" <dis### [at] itamcascz> wrote in message
news:3C7### [at] itamcascz...
>
> Thank to all, you are right and I think, that it will be sufficient.
>
> But I wanted to ask if there is some way to get exact tangent (another
> than reimplementing POV spline in POV language, of course ;-) The answer
> is probably not.

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