Uniform line fillings
Evangelos Marakis, Matthias C. Velsink, Lars J. Corbijn van, Willenswaard, Ravitej Uppu, and Pepijn W. H. Pinkse

TL;DR
This paper introduces a method for generating random, homogeneous, and rotationally invariant line fillings in arbitrary dimensions, useful for fabricating metamaterials and optical scattering samples.
Contribution
The authors present a novel algorithm for creating uniform line fillings in any dimension, with proven statistical properties and practical applications in fabrication.
Findings
The method produces homogeneous and isotropic line distributions.
The pore sizes follow a lognormal distribution.
The approach is applicable to 3D optical fabrication.
Abstract
Deterministic fabrication of random metamaterials requires filling of a space with randomly oriented and randomly positioned chords with an on-average homogenous density and orientation, which is a nontrivial task. We describe a method to generate fillings with such chords, lines that run from edge to edge of the space, in any dimension. We prove that the method leads to random but on-average homogeneous and rotationally invariant fillings of circles, balls and arbitrary-dimensional hyperballs from which other shapes such as rectangles and cuboids can be cut. We briefly sketch the historic context of Bertrand's paradox and Jaynes' solution by the principle of maximum ignorance. We analyse the statistical properties of the produced fillings, mapping out the density profile and the line-length distribution and comparing them to analytic expressions. We study the characteristic dimensions…
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