Spiral Tessellation on the Sphere

In this paper we describe a tessellation of the unit sphere in the 3-dimensional space realized using a spiral joining the north and the south poles. This tiling yields to a one dimensional labeling of the tiles covering the whole sphere and to a 1-dimensional natural ordering on the set of tiles of the tessellation. The correspondence between a point on the sphere and the tile containing it is derived as an analytical function, allowing the direct computation of the tile. This tessellation exhibits some intrinsic features useful for general applications: absence of singular points and efficient tiles computation. Moreover, this tessellation can be parametrized to obtain additional features especially useful for spherical coordinate indexing: tiles with equal area and good shape uniformity of tiles. An application to spherical indexing of a database is presented, it shows an assessment of our spiral tiling for practical uses