On 12/9/2010 12:55 PM, Warp wrote:
> yoyodunno<nomail@nomail>  wrote:
>> Is there something I can do to make the distance values constant over each time
>> value in the spline so that the animation has constant speed, which will also
>> let me make multiple carts.
>
>    Distributing points at even distances on a spline is a non-trivial problem
> because of how a spline is calculated. I don't know if there exists a
> closed form expression for this (in other words, a single non-recursive
> formula which can be used to calculate a point at a given length from the
> beginning of the spline without resorting to an iterative approximation)...

About a decade ago I looked into something like this.  Measuring the 
length of a section of spline involves the integral of the length of the 
differential of the...  Uh, it's complicated.  Even for a quadratic 
spline the integral is hairy enough, and I suppose for a cubic spline 
it's downright ugly.  The iterative solution is much neater and simpler 
to understand.

Regards,
John

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