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The chord-length distribution of a polyhedron.

ABSTRACT: The chord-length distribution function [γ''(r)] of any bounded polyhedron has a closed analytic expression which changes in the different subdomains of the r range. In each of these, the γ''(r) expression only involves, as transcendental contributions, inverse trigonometric functions of argument equal to R[r, Δ₁], Δ₁ being the square root of a second-degree r polynomial and R[x, y] a rational function. As r approaches δ, one of the two end points of an r subdomain, the derivative of γ''(r) can only show singularities of the forms |r - δ|^-n and |r - δ|^-m+1/2, with n and m appropriate positive integers. Finally, the explicit analytic expressions of the primitives are also reported.

SUBMITTER: Ciccariello S

PROVIDER: S-EPMC7331884 | biostudies-literature | 2020 Jul

REPOSITORIES: biostudies-literature

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The chord-length distribution of a polyhedron.

Ciccariello Salvino S

Acta crystallographica. Section A, Foundations and advances 20200601 Pt 4

The chord-length distribution function [γ''(r)] of any bounded polyhedron has a closed analytic expression which changes in the different subdomains of the r range. In each of these, the γ''(r) expression only involves, as transcendental contributions, inverse trigonometric functions of argument equal to R[r, Δ<sub>1</sub>], Δ<sub>1</sub> being the square root of a second-degree r polynomial and R[x, y] a rational function. As r approaches δ, one of the two end points of an r subdomain, the deri ...[more]

PMID: 32608363

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