N.P. Kopytov, E.A. Mityushov. Universal Algorithm Of Uniform Distribution Of Points On Arbitrary Analitic Surfaces In Three-dimensional Space
Submitted on: Jun 17, 2012, 14:14:28
Natural Sciences / Mathematics / Statistics
Description: The problem of uniform distribution of points on arbitrary analytic surfaces in three-dimensional space is considered. A universal algorithm for uniform distribution of points on analytic surfaces defined by the parametric method is proposed. Neumann's method for generating a two-dimensional random variable by using a known density function of the joint distribution is described. Graphical presentations of the proposed algorithm obtained with the help of Wolfram Mathematica 7.0 are demonstrated. The examples of uniform distribution of points on surfaces of sphere, torus, helicoid, "falling drop" and surface of Klein bottle are presented.
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UNIVERSAL ALGORITHM OF UNIFORM DISTRIBUTION OF POINTS ON ARBITRARY ANALITIC SURFACES IN THREE-DIMENSIONAL SPACE.pdf