Density functions of periodic sequences.

21^st October 2022, 14:00
Vitaly Kurlin
MIF

Abstract

The past work at SoCG 2021 introduced an infinite sequence of density functions, which are continuous isometry invariants of a periodic point set. For any integer k>=0, the k-th density function of a variable radius measures the fractional volume of the ambient space covered by exactly k balls centred at all given points. These density functions are highly non-trivial even in dimension 1 for periodic sequences of points in the line. The new work at DGMM 2022 fully describes the density functions of any periodic sequence and their symmetry properties. The explicit description confirms coincidences of density functions for a pair of non-isometric sequences that were previously computed via finite samples.