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Home » Issues » Archive of Issues » 2015 - 1 issue » pp. 29-35

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Russia Yekaterinburg
Year
2015
Volume
25
Issue
1
Pages
29-35
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Section Mathematics
Title Uniform distribution of points on hypersurfaces: simulation of random equiprobable rotations
Author(-s) Kopytov N.P.a, Mityushov E.A.a
Affiliations Ural Federal Universitya
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
UDC 519.21
MSC 60D05
DOI 10.20537/vm150104
Received 27 December 2014
Language English
Citation Kopytov N.P., Mityushov E.A. Uniform distribution of points on hypersurfaces: simulation of random equiprobable rotations, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 1, pp. 29-35.
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