math - Is there any constant time spatial indexing of points on the surface of a sphere with balanced partitioning? -

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a simple way index points in sphere use polar coordinates. is, find index of point, convert polar coordinates , apply formula polar_ang * width + azimuthal_ang. problem strategy isn't evenly spaced - indices near center of sphere have bigger areas near top.

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is there alternative indexing strategy equally simple better partitioning properties?

use subdivided icosahedron. there 12 vertices , 20 triangular faces. each of these faces can subdivided grids of smaller triangles arbitrarily small size. not subdivided triangles have equal area, range of possible areas bounded.


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