New uniform grids on the sphere

Abstract

<i>Aims. <i/>A method for constructing new uniform grids on the sphere is given.<i>Methods. <i/>We define a bijection in , which maps squares onto discs and preserves areas. Then we use this bijection, combined with Lambert azimuthal projection, for lifting uniform grids from the square to the sphere.<i>Results. <i/>We can obtain uniform spherical grids that allow a hierarchical data manipulation and have an isolatitudinal distribution of cells. Compared with HEALPix grids, nowadays the most used in astronomy and astrophysics, our grids have the advantage of allowing easier implementation, and in addition one can move approximating functions from the square to the sphere by a simple technique.