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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2015, Volume 25, Issue 1, Pages 29–35 (Mi vuu462)  

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Uniform distribution of points on hypersurfaces: simulation of random equiprobable rotations

N. P. Kopytov, E. A. Mityushov

Department of Theoretical Mechanics, Ural Federal University, pr. Mira, 19, Yekaterinburg, 620002, Russia

Abstract: The paper describes a universal method for simulation of uniform distributions of points on smooth regular surfaces in Euclidean spaces of various dimensions. The authors give an interpretation of a set of possible values of Rodrigues–Hamilton parameters used to describe a rigid rotation as a set of points of a three-dimensional hypersphere in four-dimensional Euclidean space. The relationship between random equiprobable rotations of a rigid body and a uniform distribution of points on the surface of a three-dimensional hypersphere in four-dimensional Euclidean space is established.

Keywords: uniform distribution of points on hypersurfaces, random points on a hypersphere, quaternions, random rotations.

Full text: PDF file (336 kB)
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UDC: 519.21
MSC: 60D05
Received: 27.12.2014
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Citation: N. P. Kopytov, E. A. Mityushov, “Uniform distribution of points on hypersurfaces: simulation of random equiprobable rotations”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:1 (2015), 29–35

Citation in format AMSBIB
\Bibitem{KopMit15}
\by N.~P.~Kopytov, E.~A.~Mityushov
\paper Uniform distribution of points on hypersurfaces: simulation of random equiprobable rotations
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2015
\vol 25
\issue 1
\pages 29--35
\mathnet{http://mi.mathnet.ru/vuu462}
\elib{http://elibrary.ru/item.asp?id=23142048}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. A. Mityushov, N. E. Misyura, S. A. Berestova, “Plavnoe peremeschenie tverdogo tela v prostranstve orientatsii po kratchaishei traektorii cherez uzly odnorodnoi reshetki na gruppe $SO(3)$”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:1 (2017), 138–145  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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