# Spiral on a hemisphere (chop to sop)

I am trying to create a spiral sop thats following the surface of a half a sphere with 3 pattern chops but i cant get my head around to tweak it into a dome shape…
So far i managed to make it a tube… I guess its just a little change in one of the pattern chops…

spiral.tox (2.0 KB)

I don’t think you’re going to get a super accurate spiral dome with this method, but if you’re going for “close enough” you’re on the right track.

You should leave the number of samples (“Length”) the same on all your Pattern CHOPs and increase the number of cycles on your sine and cosine patterns to be how many times around you want the spiral to go.

Then use the Taper parameter and the Taper Decay Rate to try to get it as close to spherical as you can get. Here’s my stab at it without spending too much time on it:

If you want it more precise / uniform than that, you may have to look into some SOPs that project or “shrinkwrap” a flat spiral onto a sphere, but that’s out of my league

Or go on a deep math dive and start messing with some formulas or something…

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waitwaitwait I figured it out. I’m so dumb - everything is sine waves.

Use a quarter of a sine wave to math the cycling sine and cosine patterns, and then reverse it and that becomes your third dimension, sine the height around half of a sphere is also a sine wave.

Fits perfectly on top of a sphere. I think this is as good as you can get as long as you don’t need to adjust the spiral so more of it happens up at the top… though there might be a more obvious way to do that which I am missing…

base_spiralDome.tox (1022 Bytes)

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Wow! Lovely! Thank You Pete!!
Exactly what I was looking for…
Should have payed more attention in Algebraic geometry back in the days