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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