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On a combination method of VDR and patchwork for generating uniform random points on a unit sphere

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  • Yang, Zhenhai
  • Pang, W.K.
  • Hou, S.H.
  • Leung, P.K.

Abstract

In this paper, we use a combination of VDR theory and patchwork method to derive an efficient algorithm for generating uniform random points on a unit d-sphere. We first propose an algorithm to generate random vector with uniform distribution on a unit 2-sphere on the plane. Then we use VDR theory to reduce random vector Xd with uniform distribution on a unit d-sphere into , such that the random vector (Xd-1,Xd) is uniformly distributed on a unit 2-sphere and Xd-2 has conditional uniform distribution on a (d-2)-sphere of radius , given V=v with V having the p.d.f. . Finally, we arrive by induction at an algorithm for generating uniform random points on a unit d-sphere.

Suggested Citation

  • Yang, Zhenhai & Pang, W.K. & Hou, S.H. & Leung, P.K., 2005. "On a combination method of VDR and patchwork for generating uniform random points on a unit sphere," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 23-36, July.
    • Handle: RePEc:eee:jmvana:v:95:y:2005:i:1:p:23-36
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    3. Szablowski, Pawel J., 1998. "Uniform Distributions on Spheres in Finite DimensionalL[alpha]and Their Generalizations," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 103-117, February.
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    5. Yoshihiro Tashiro, 1977. "On methods for generating uniform random points on the surface of a sphere," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 29(1), pages 295-300, December.
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    Cited by:

    1. Harman, Radoslav & Lacko, Vladimír, 2010. "On decompositional algorithms for uniform sampling from n-spheres and n-balls," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2297-2304, November.

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