Abstract
Some methods for generating random points uniformly distributed on the surface of ann-sphere have been proposed to simulate spherical processes on computer. A standard method is to normalize random points inside of the sphere, see M. Muller [5]. Improved methods were given by J. M. Cook [1] and G. Marsaglia [4] in three and four dimensions, and computational methods in higher dimensions by J. S. Hicks and R. F. Wheeling [3] and M. Sibuya [6].
In this paper we shall offer direct methods for generating uniform random points on the surface of a unitn-sphere, which can be easily combined with Marsaglia's idea for getting more improved methods. Our method in even dimensions was obtained by M. Sibuya [6], but a differential-geometric view-point will make analyses simpler, even in odd dimensions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cook, J. M. (1957) Rational formulae for the production of a spherically symmetric probability distribution,Math. Comp.,11, 81–82.
Eisenhart, L. P. (1966).Riemannian Geometry, sixth print, Princeton Univ. Press.
Hicks, J. S. and Wheeling, R. F. (1959) An efficient method for generating uniformly distributed points on the surface of ann-dimensional sphere,Commun. Ass. Comput. Math.,2, 17–19.
Marsaglia, G. (1972). Choosing a point from the surface of a sphere,Ann. Math. Statist.,43, 645–646.
Muller, M. E. (1959). A note on a method for generating points uniformly onN-dimensional spheres,Commun. Ass. Comput. Math. 2, 19–20.
Sibuya, M. (1964). A method for generating uniformly distributed points onN-dimensional spheres,Ann. Inst. Statist. Math.,14, 81–85.
Author information
Authors and Affiliations
About this article
Cite this article
Tashiro, Y. On methods for generating uniform random points on the surface of a sphere. Ann Inst Stat Math 29, 295–300 (1977). https://doi.org/10.1007/BF02532791
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02532791