"Kenneth" <kdw### [at] gmailcom> wrote:
> Thanks
> for taking the time to work it out.

Sure thing.  It wasn't too bad once I had enough time to look it over from a
fresh perspective.

> I do notice that the functions don't yet
> produce 'tapering' of the spiral at the start and end points (i.e, tapering to a
> fine point)-- but that's a minor quibble right now, and actually gives us more
> opportunities for experimentation, function-wise. And, so far, I haven't seen a
> need for a sphere shape at the center; only a bit of isosurface accuracy
> adjustment instead. Perhaps the sphere requirement applies to other more complex
> spiral cross-sections (or tapering).

Well, the thing that I did notice, is that there IS tapering - x-z-wise.  The
y-component remains constant, but the spirals get pinched off so that you have a
vertical y-edge.  If you closely, I believe the same thing happens with the
original function, which is presumably what the sphere was intended to cover up.

I haven't experimented enough to gain enough perspective on the various parts of
the function[s] to see why, or how it get changed - if it can.  But have some
vague ideas for further experiments.

> Meanwhile... here's a spiral doodle just for the fun of it, that looks like a
> rubber mat, draped over an invisible rod.

Ha!  That's excellent.  I played around with trying to cram everything into one
super-function using select(), and I got something similar, but it's symmetric
around the axis of rotation and looks like yours - where the tubes blend
together.

I'm wondering if the idiosyncrasies of this shape are best addressed by a
parametric rather than an isosurface.  Implicit / closed form equations can be
pretty difficult to grapple with sometimes, whereas separating the x, y, and
z-components can be easier, more tunable, and seem to be a lot more readable /
intuitive.

I'm glad you're having fun and producing some fun-looking shapes.  I'll bet
they'd look great in glass.  A light probe, radiosity and photons would probably
make for long render times, but pretty sharp looking scenes.

Also, I was looking at some seashell sites, and taking a slice out of your open
surface might be something to try, as would wireframing / grid-texturing it,
either with uv-mapping or tightly-banded color/texture/material maps (with rbgt
1).

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