clipka <ano### [at] anonymousorg> wrote:


> >      #else
> >           #declare r2 = max (abs(r2), abs(Y));
> >           //#declare r = sqrt(X*X + Y*Y + Z*Z);  <<< comment out

I did a small bit more experimenting.
As previously posted, I got rid of the sphere, but the rest of the spiral became
malformed and had strange discontinuities.

If I _changed_ that line to read #declare r = r2, I got what seemed at this
stage to be acceptable results.

Maybe if I'm able to explore this further in something like Euler math toolbox
or Processing, or K3DSurf, or something else, I'd be able to better see what was
going on and come up with a nicer shape/solution.

> My guess is that it was added deliberately, but that the person who
> added it wasn't aware of all the different spirals that can be created
> by the function, and therefore only regarded one special case.
>
> Look again at this spiral:
>
> http://www.econym.demon.co.uk/isotut/std007.jpg
>
> Now imagine this with a circular (rather than diamond-shaped) cross section.
>
> In that case, the sphere would seem to serve as a neat inner end for the
> spiral.

Yes - I see what you're saying, I just find it a bit odd that it's a sphere of
such different radius than the rest of the spiral.

The comments in the source indicate that the original code was of course written
by Suzuki, and then ported to POV-Ray by F. Lohmueller.  Not sure at what point
the sphere got added in as that central "feature".
Gerd Platl has some archimedian spirals done with K3DSurf that don't seem to
require the sphere - so perhaps it's not really needed.

http://k3dsurf.s4.bizhat.com/k3dsurf-ftopic30-0-asc-30.html

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