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Aressera

Equal-area partition of unit sphere

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I'm working on an application that needs to compute a histogram over the surface of a sphere. In order to do this I have to partition the surface of the sphere into pieces that are equal area (or fairly close). The shape of a piece does not matter as long as it covers the same area. I also need to be able to parameterize the partitioning scheme so that I can iterate over the pieces in an efficient manner without having to store their bounds.

I've tried looking into equal area cylindrical projections but I can't seem to get anything to work correctly. Polar distortion is not a problem, so any sort of cylindrical projection could work. I just need to parameterize the latitude generation it so that the area of each rectangular/triangular piece is more or less equal.

Does anyone have a tips for solving this issue?

P.S. the end goal is to use each piece of the sphere to generate a certain number of rays (depending on the histogram) that start at the sphere's center and pass through the bounds of that piece.

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An easy way to do this would be to divide the sphere into slices of equal width, and then each slice into an equal number of sectors.

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An easy way to do this would be to divide the sphere into slices of equal width, and then each slice into an equal number of sectors.


Thanks, that seems to work well enough and is a lot simpler than what I was trying to do.

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