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Stereology of Dihedral Angles II: Distribution Function
James A. Reeds and James P. Butler
SIAM Journal on Applied Mathematics
Vol. 47, No. 3 (Jun., 1987), pp. 678-687
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2101808
Page Count: 10
You can always find the topics here!Topics: Geometric angles, Sine function, Elliptic functions, Geometric planes, Parameterization, Mathematical integrals, Ellipses, Distribution functions, Power series, Greens theorem
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A field of randomly dispersed dihedrals in space is sliced by a plane. This results in a field of angles in the slicing plane whose sizes A will be random, even if the original dihedrals all have the same nonrandom size α. In this paper we derive explicit formulas for the distribution function and density function of A in terms of easily computable elliptic integrals, and use these formulas to study the asymptotic behavior of the distribution and density near α.
SIAM Journal on Applied Mathematics © 1987 Society for Industrial and Applied Mathematics