Anisotropic Poisson Processes of Cylinders
Malte Spiess, Evgeny Spodarev
TL;DR
This paper studies stationary anisotropic Poisson processes of cylinders in Euclidean space, providing explicit formulas for key characteristics useful for practical applications.
Contribution
It derives explicit formulas for the capacity functional, covariance, contact distribution, volume fraction, and surface intensity of anisotropic Poisson cylinder processes.
Findings
Explicit formulas for capacity functional and covariance
Analytical expressions for contact distribution and volume fraction
Formulas applicable in practical modeling scenarios
Abstract
Main characteristics of stationary anisotropic Poisson processes of cylinders (dilated k-dimensional flats) in d-dimensional Euclidean space are studied. Explicit formulae for the capacity functional, the covariance function, the contact distribution function, the volume fraction, and the intensity of the surface area measure are given which can be used directly in applications.
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Taxonomy
TopicsPoint processes and geometric inequalities · Textile materials and evaluations · Advanced Theoretical and Applied Studies in Material Sciences and Geometry