Geodesic
Uniform distribution of points on hypersurfaces: simulation of random equiprobable rotations
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 1, pp. 29-35

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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: random points on a hypersphere
Mots-clés : uniform distribution of points on hypersurfaces, quaternions, random rotations. 
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     title = {Uniform distribution of points on hypersurfaces: simulation of random equiprobable rotations},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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N. P. Kopytov; E. A. Mityushov. Uniform distribution of points on hypersurfaces: simulation of random equiprobable rotations. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 1, pp. 29-35. http://geodesic.mathdoc.fr/item/VUU_2015_25_1_a3/