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Is there formula for poly reduction?

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Is there a formula for reducing poly/points down to something that sub divides smoothly?


For example: I have polys that have a total of 18 points that need to be reduced to something like 8 so when I subdivide they round smoothly. But I can't find what the inner number should be to accommodate 4 point poly's. I'm probably not explaining this very well at all. But is there a mathematical function that takes the number of points I'm going from and tells me the number of points I need to go to, in order to make things smooth>? I'm sure this question sucks to most. LOL

reduce from here.jpg

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18 points  (or in fact any even number of points above 8) will smooth correctly under subdivision if they are evenly spaced, so why not just make that center disc 18 segments and bridge or Stitch'n'Sew your existing 18 edges directly to it ? Or am I misunderstanding what you're trying to do ? In fact for the same reason, there is a reasonable argument for not even down-stepping to 18 as you do through the top rim - just patch it all through to a 42 sided disc and it'll be no different to had you done it with 8, except that there will be less opportunity for SDS shading errors caused by uneven poly lengths in your downstepping...


Here's an example of that, with 42 outside edges, but quad patched and brush-relaxed after stitching to a 42 sided center disc...



This is arguably a technically better result than solving down, because in this version there are no complex poles, although of course I concede that on a flat surface this doesn't matter and that it would hardly be a problem to eliminate the center pole on an 8 sided disc :)



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