Isn't it a propertie of a cubic-Spline, to be 3-Times
differentiable and also (at every-Point) integratable ???
An Cubic Spline consists of several cubic-functions (every going
through 4 Points) and having at every Point the same
2nd-derivations ....
So there MUST be a way to integrate them ...
or am I completely wrong ???

I just though to have heard this last semester in the
"aproximation-theorie"-lecture ...

I just fear you can not use the pov-Spline to do this for you,
but you have to calculate the Spline yourself, with all its
matrices and so on ...

You know what I mean ???

Chris Colefax <chr### [at] tagpovrayorg> schrieb in im
Newsbeitrag: 39f6a040@news.povray.org...
> I wrote:
> > Due to the maths involved, there is no known way to calculate
the exact
> > length of a cubic spline.  The best method is usually to sum
the linear
> > distances between a number of steps along the spline -
obviously, the more
> > steps, the more accurate the result (at the cost of speed)...
>
> Fabian BRAU <Fab### [at] umhacbe> wrote:
> > If you know the exact form of the function (the spline) you
> > can calculate the length of the spline, this involve a simple
integrale.
> > Actually this is what you do approximately by using straight
line
> > between point.
>
> Yes, it seems obvious that you could integrate the spline
function to find
> the exact length.  But like I said, there is simply no known
way *to*
> integrate the function.  To create my Spline Macro File I
searched and
> re-searched the web for the right formulas, and also started
from first
> principals to derive the functions myself, before attempting
(without
> success) the necessary integration in MathCAD.  I guess it
shows that there
> are limits to our knowledge of mathematics....
>
>

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