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For curiosity: It's possible to segment a sphere into equal area rectangles, plus circular caps. This is based on the arguably surprising relation between spher

by mxfh 10y ago

For curiosity: It's possible to segment a sphere into equal area rectangles, plus circular caps. This is based on the arguably surprising relation between sphere area and the corresponding area on a cylinder of the same height as described in this article [1]. Paul Leopardi describes a neat 33 equal area region tiling, Recursive Zonal Equal Area Sphere, in his talk [2]. [1] http://blog.zacharyabel.com/2012/01/slicing-spheres/ http://blog.zacharyabel.com/2012/01/slicing-spheres/ Especially this animation: http://i1.wp.com/blog.zacharyabel.com/wp-content/uploads/2012/01/stab-hemisphere.gif?zoom=2&resize=300%2C299 http://i1.wp.com/blog.zacharyabel.com/wp-content/uploads/201... [2] http://maths-people.anu.edu.au/~leopardi/ORNL-2014-Leopardi-sphere-talk.pdf http://maths-people.anu.edu.au/~leopardi/ORNL-2014-Leopardi-... Matlab Code: http://eqsp.sourceforge.net/ http://eqsp.sourceforge.net/

jacobolus 10y ago
Your link #1 is about the volume of a ball, not the surface area of a sphere. There are hundreds of different ways of segmenting a sphere. Your link #2 a relatively obscure one which is potentially worth evaluating for some uses (e.g. you start with a fine latitude/longitude grid but want to group your data into coarser histogram bins, and you them to have equal area), but is pretty far removed from the mostly hexagonal tilings in the OP. For a summary of some other methods, I recommend Popko’s book Divided Spheres, http://www.dividedspheres.com http://www.dividedspheres.com