Michael,

Ahh, I was thinking of this, but thought that maybe one could take the magnitude of
the vector returned by that (terribly ugly) formula to get the distance traveled.  I
understand how this is done with vectors now (there is a good page at
http://iq.orst.edu/mathsg/vcalc/arc/arc.html)

Thanks for clarifying
Andrew C


Michael Andrews wrote:

> Hi Andrew,
>
> This is the length of a simple parametric spline where a, b, c and d are
> scalars, yes?
>
> The problem is that it would usually be used to produce a spline in 3d,
> so a, b, c and d would be 3-component vectors. This would probably add a
> whole new level of complexity, something like
>
> f_x := a_x * t^3 + b_x * t^2 + c_x * t + d_x ;
> f_y := a_y * t^3 + ... ;
> f_z := ... ;
>
> int(sqrt(diff(f_x,t)^2 + diff(f_y,t)^2 + diff(f_z,t)^2),t) ;
>
> Try feeding that to Maple and see if it chokes :-)
>
> Bye for now,
>         Mike Andrews.
>
> Andrew Clinton wrote:
> >
> > Exact length of a cubic f(x) = a*x^3 + b*x^2 + c*x + d:
> > http://www.eng.uwaterloo.ca/~ajclinto/test.html
> >
> > assuming you have x=0 and x=1 as the bounds of the segment (and maybe a=1) it
> > would become SLIGHTly simpler, but I still doubt whether there would be any
> > practical use for this mess.
> >
> > Andrew C
> >
> > "Tony[B]" wrote:
> >
> > > How can I get an exact/closely approximated measure of the distance traveled
> > > along a spline and the total length of it? I am using a cubic_spline in
> > > MegaPOV.

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