IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v95y2005i1p23-36.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(04)00168-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. R. C. H. Cheng & G. M. Feast, 1979. "Some Simple Gamma Variate Generators," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 28(3), pages 290-295, November.
    2. Karkazis, J. & Boffey, T. B., 1995. "Optimal location of routes for vehicles transporting hazardous materials," European Journal of Operational Research, Elsevier, vol. 86(2), pages 201-215, October.
    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.
    4. Selim, Shokri Z. & Al-Rabeh, A. H., 1996. "Determining dominant wind directions," European Journal of Operational Research, Elsevier, vol. 90(3), pages 420-426, May.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pang, W. K. & Yang, Z. H. & Hou, S. H. & Leung, P. K., 2002. "Non-uniform random variate generation by the vertical strip method," European Journal of Operational Research, Elsevier, vol. 142(3), pages 595-609, November.
    2. Wolf-Dieter Richter, 2019. "On (p1,…,pk)-spherical distributions," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-18, December.
    3. Mohri, Seyed Sina & Mohammadi, Mehrdad & Gendreau, Michel & Pirayesh, Amir & Ghasemaghaei, Ali & Salehi, Vahid, 2022. "Hazardous material transportation problems: A comprehensive overview of models and solution approaches," European Journal of Operational Research, Elsevier, vol. 302(1), pages 1-38.
    4. P. Daniel Wright & Matthew J. Liberatore & Robert L. Nydick, 2006. "A Survey of Operations Research Models and Applications in Homeland Security," Interfaces, INFORMS, vol. 36(6), pages 514-529, December.
    5. Hisashi Tanizaki, 2008. "A Simple Gamma Random Number Generator for Arbitrary Shape Parameters," Economics Bulletin, AccessEcon, vol. 3(7), pages 1-10.
    6. Sheng Dong & Jibiao Zhou & Changxi Ma, 2020. "Design of a Network Optimization Platform for the Multivehicle Transportation of Hazardous Materials," IJERPH, MDPI, vol. 17(3), pages 1-14, February.
    7. Amirsaman Kheirkhah & HamidReza Navidi & Masume Messi Bidgoli, 2016. "A bi-level network interdiction model for solving the hazmat routing problem," International Journal of Production Research, Taylor & Francis Journals, vol. 54(2), pages 459-471, January.
    8. Diaz-Banez, J. M. & Mesa, J. A. & Schobel, A., 2004. "Continuous location of dimensional structures," European Journal of Operational Research, Elsevier, vol. 152(1), pages 22-44, January.
    9. Liang, Jia-Juan & Bentler, Peter M., 1999. "A t-distribution plot to detect non-multinormality," Computational Statistics & Data Analysis, Elsevier, vol. 30(1), pages 31-44, March.
    10. Kai-Tai Fang & Run-Ze Li, 1997. "Some methods for generating both an NT-net and the uniform distribution on a Stiefel manifold and their applications," Computational Statistics & Data Analysis, Elsevier, vol. 24(1), pages 29-46, March.
    11. Changxi Ma & Wei Hao & Fuquan Pan & Wang Xiang, 2018. "Road screening and distribution route multi-objective robust optimization for hazardous materials based on neural network and genetic algorithm," PLOS ONE, Public Library of Science, vol. 13(6), pages 1-22, June.
    12. Abdelkader Sbihi & Richard W. Eglese, 2007. "The Relationship between Vehicle Routing & Scheduling and Green Logistics - A Literature Survey," Working Papers hal-00644133, HAL.
    13. Ferguson, R.S. & Sprevak, D., 1983. "A model for the simulation of a two MOS-transistor inverter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 25(3), pages 249-258.
    14. Zvi Drezner & George Wesolowsky, 2014. "Covering Part of a Planar Network," Networks and Spatial Economics, Springer, vol. 14(3), pages 629-646, December.
    15. Michael Grabchak, 2021. "On the transition laws of p-tempered $$\alpha $$ α -stable OU-processes," Computational Statistics, Springer, vol. 36(2), pages 1415-1436, June.
    16. Tan, K.C. & Chew, Y.H. & Lee, L.H., 2006. "A hybrid multi-objective evolutionary algorithm for solving truck and trailer vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 172(3), pages 855-885, August.
    17. Hörmann, Wolfgang & Sak, Halis, 2010. "t-Copula generation for control variates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(4), pages 782-790.
    18. Yang, Jun & He, Ping & Fang, Kai-Tai, 2022. "Three kinds of discrete approximations of statistical multivariate distributions and their applications," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    19. Misagh Rahbari & Alireza Arshadi Khamseh & Yaser Sadati-Keneti & Mohammad Javad Jafari, 2022. "A risk-based green location-inventory-routing problem for hazardous materials: NSGA II, MOSA, and multi-objective black widow optimization," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 24(2), pages 2804-2840, February.
    20. Rongrong Li & Yee Leung, 2011. "Multi-objective route planning for dangerous goods using compromise programming," Journal of Geographical Systems, Springer, vol. 13(3), pages 249-271, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:95:y:2005:i:1:p:23-36. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.