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.


> 
> Tony[B] <ben### [at] panamac-comnet> 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.
> 
> 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).  In MegaPOV you
> should be able to do this quite simply using a while loop (the following
> presumes your spline clock ranges from 0 to 1):
> 
>    #declare MySpline = spline {cubic_spline ..... }
>    #declare Length = 0;
> 
>    #declare C = 0; #while (C <= 100)
>       #declare P1 = MySpline(C/100);
>       #if (C > 0) #declare Length = Length + vlength(P1 - P0); #end
>       #declare P0 = P1;
>    #declare C = C + 1; #end
> 
> Also, a very rough approximation can be calculated if know the bezier hull
> points of the spline.  My own Spline Macro file uses a combination of both
> methods, so you can return the total length of a spline, return a point at a
> specified distance along a spline, or even specify a list of points and a
> length, and have the macro tension the spline through the points to fit the
> desired length.

Post a reply to this message