Although it's not completely relevant to your parabola question, I used 
a caternary to model hanging cables in my povcomp image and it seemed to 
work out pretty well.  The source code is linked to from the viewing 
page, feel free to use it in any way without restriction if you like. 
Although I didn't use spheres, I used cylinders with spheres at joints 
due to the sheer number of cables simulated, with a simple algorithm 
that increases the number of cylinders in each cable depending on the 
distance to the viewer.  I also tried sphere sweeps based on splines 
generated from points along the cable, but got some weird artifacts I 
couldn't figure out.  The biggest problem was figuring out how to hang a 
rope between two arbitrary points that hung down with a specific amount 
of slack, as well as trying to recall decade old math lessons :)

http://www.povcomp.com/entries/181.php

If you have any questions, ask away.

Regards,

Peter D.

Tim McMurdo wrote:
> I need to know how to equally space objects on a curve formed by a parabola.
> The vertex will be at the origin, so that should simplify matters (I
> believe this means that the formula for the curve itself will be a simple
> aX^2).
> 
> What I am going to use this for is to place spheres along a parabola to
> create rope. I would use a cantenary but I want to be able to reflect the
> stiffness of the rope. I figure a parabola is the way to go as I can adjust
> the fatness of the curve using a. At a given point (X,Y), the curve will be
> nearly vertical.
> 
> My problem is figuring out how to evenly space the spheres along the curve.
> 
> Any takers?
> 
> Tim
> 
>

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