"scott" <sco### [at] spamcom> wrote:
> PM 2Ring wrote:
> > The catenary is the curve formed by a homogeneous chain suspended
> > between two points in a uniform gravity field. It looks like a
> > parabola, but it's mathematically quite different. The equation of a
> >  parabola is just y = a*x*x, a simple quadratic, whereas a catenary is
> >  y = a*cosh(x/a), a transcendental equation.

> How about a comparison between the two for different length chains between
> two points?

Here are two sets of comparisons between parabolas & catenaries, suspended
between the same two points, passing through the same lowest point (almost
:). It was too hard to do them with equal length chains: the _LN_length
parameter in Link.inc does weird things...

The blue chains are parabolas, the red chains are catenaries, using these
links objects:

#declare SC = 0.02;
#declare RodC = cylinder{-x, x, 1 pigment{checker rgb x,rgbt 1} scale SC}
#declare RodP = cylinder{-x, x, 1 pigment{checker rgb z,rgbt 1} scale SC}

I won't post the full source, it's a bit ugly.

Post a reply to this message

Attachments:
Download 'catenaryi3.jpg' (188 KB)

Preview of image 'catenaryi3.jpg'