Aha! I see that now. This is close to how I calculate things in animations, but I'm
not
familiar with this form. Now that I get it, it's probably easier than what I normally
do. My
formula would look like

S double prime of x = [ [ ( x - x sub i ) * ( z sub i +1 - z sub i ) ] / (x sub i +1 -
x sub
1)  ] + z sub i

which is probably harder to integrate.

Thanks for the tip. I'm getting closer. I understand what you're acheiving here, which
is a
plus on my side.

Josh

Serge LAROCQUE wrote:

> > I don't quite follow the linear relationship for S double prime sub i that you
list on
> > the top of page two.
>
> Ok. S'' is the second derivative of the spline. It is shown in Figure 1. I know,
it's not
> much to look at :-). Perhaps I should have made the graph a bit bigger with more
points.
> But basically, we want second derivative continuity from segment to segment, and for
a
> cubic, that means that it must change linearly from point to point. The equation can
be
> easily derived by applying the algorithm for finding the equation of a line based on
2
> pairs of (x,y) coordinates [with (x sub i,z sub i) and (x sub i+1,z sub i+1]. After,
you do
> a bit of algebraic manipulation to get it in the form of S'' = A*(x-x sub i) + B*(x
sub i+1
> - x), [rather than S'' = K*x + M ] and you get the equation. I have done this check
myself
> to make sure it was correct :-).
>
> One thing to note is that at this point you don't even know what S'' is equal to at
each
> point. You assume they are z sub i. You find their value when you solve the system
of
> equations. Once that is solved, you're in business and you can form your
polynomials, one
> for each interval.

--
Josh English
eng### [at] spiritonecom
"May your hopes, dreams, and plans not be destroyed by a few zeros."

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