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On the tangent model for the density of lines and a Monte Carlo method for computing hypersurface area

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  • El Khaldi Khaldoun

    (Department of Computer Science, Notre Dame University-Louaize, Zouk Mosbeh, Lebanon)

  • Saleeby Elias G.

    (Department of Mathematics and Natural Science, American University of Iraq,Sulaimani, Iraq)

Abstract

Methods to estimate surface areas of geometric objects in 3D are well known. A number of these methods are of Monte Carlo type, and some are based on the Cauchy–Crofton formula from integral geometry. Employing this formula requires the generation of sets of random lines that are uniformly distributed in 3D. One model to generate sets of random lines that are uniformly distributed in 3D is called the tangent model (see [4]). In this paper, we present an extension of this model to higher dimensions, and we examine its performance by estimating hypersurface areas of n-ellipsoids. Then we apply this method to estimate surface areas of hypersurfaces defined by Fermat-type varieties of even degree.

Suggested Citation

  • El Khaldi Khaldoun & Saleeby Elias G., 2017. "On the tangent model for the density of lines and a Monte Carlo method for computing hypersurface area," Monte Carlo Methods and Applications, De Gruyter, vol. 23(1), pages 13-20, March.
    • Handle: RePEc:bpj:mcmeap:v:23:y:2017:i:1:p:13-20:n:2
    DOI: 10.1515/mcma-2017-0100
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    References listed on IDEAS

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    1. 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. El Khaldi Khaldoun & Saleeby Elias G., 2020. "On the density of lines and Santalo’s formula for computing geometric size measures," Monte Carlo Methods and Applications, De Gruyter, vol. 26(4), pages 315-323, December.

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