Partition a sphere

Hi,

I'm trying to partition a sphere into an arbitrary number of symmetrical pieces - I've started by using the XY, XZ, and YZ planes and splitting, followed by rotating them (45, 30, ...) degrees.

However, the split operation eventually fails for this approach. Can anybody suggest a better way to do this?

Attachments:

partition.gh, 15 KB

Replies to This Discussion

Permalink Reply by Hyungsoo Kim on October 22, 2015 at 2:34pm

Hi.

I think this way is not so bad.

Attachments:

partition_re.gh, 12 KB

Permalink Reply by Nik Willmore on October 22, 2015 at 3:16pm

Can there be gaps between the sphere surface pieces?

Permalink Reply by Hyungsoo Kim on October 22, 2015 at 4:59pm

Solid or faces with gaps...

Attachments:

partition_rev2.gh, 20 KB

Permalink Reply by Hyungsoo Kim on October 22, 2015 at 5:05pm

Be as careful as possible to apply this one to massive numbers.

Permalink Reply by Christopher Edgemon on October 22, 2015 at 4:36pm

Thanks Hyungsoo, that image looks great. I'll check out the definition tomorrow when I have access to my Windows machine.

Nik, gaps between the surface pieces would be fine, as long as they're relatively small in comparison to the pieces - ideally, I'd like to be able to make a massive number of partitions.

Permalink Reply by Nik Willmore on October 27, 2015 at 6:54pm

I'm sorry I don't have more time for this right now, since it's exactly what I might otherwise delve very deeply into.

What is time and space and matter and thought?

This problem relates to that, being so simple.

I thought to use Kangaroo 1 or 2 versions to fluidly lock exact numbers of particles on a sphere (etc.) surface and let simulated physics let them repel one another apart, with your required symmetry being thus an emergent property, then expand each point particle out as an expanding circle upon the surface constraint that butts up against each other as a polygon upon the surface with the straight edges of the polygon perhaps being obtained by yet another tweak during the dynamism of the butting.

God and the Devil both are in the details though, where Philosophy crashes its motorcycle. It might be very elegant. It might be tweaky. But doesn't it after all require an "organic" approach rather than a pedantically mathematical one? After all, mathematics so far can't even solve the three-body problem, of three points that are attracted to each other, orbiting 'round each other in 3D space.

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