A general rule for disk and hemisphere partition into equal-area cells

A new general rule is presented to define procedures in order to cut a disk or a hemisphere into an imposed number of equal-area cells. The system has several degrees of freedom that can be fixed, for instance, by enforcing the cells aspect ratios. Therefore, the cells can have very comparable forms, i.e. close to the square. This kind of method is effectively useful because it is not possible to build exact dense uniform distributions of points on the sphere. However, it will be shown that it is easy to cover the sphere, the hemisphere or the disk with equal-area cells. This capability makes easy, for instance, the implementation of stratified sampling in Monte Carlo methods. Moreover, the use of different azimuthal projections allows to link problems initially stated either on the hemisphere or within the circle. (C) 2012 Elsevier B.V. All rights reserved.