Smoothing a Rock by Chipping

TL;DR

This paper models how repeated small chipping at corners smooths and reduces a polygonal rock, revealing the resulting anisotropic shapes and their fluctuations over multiple realizations.

Contribution

It introduces an idealized model for polygonal rock smoothing through corner chipping, analyzing shape evolution and variability.

Findings

Shapes quickly reach a well-defined form for each realization.

Significant fluctuations exist between different realizations.

Facet lengths and corner angles are broadly distributed.

Abstract

We investigate an idealized model for the size reduction and smoothing of a polygonal rock due to repeated chipping at corners. Each chip is sufficiently small so that only a single corner and a fraction of its two adjacent sides are cut from the object in a single chipping event. After many chips have been cut away, the resulting shape of the rock is generally anisotropic, with facet lengths and corner angles distributed over a broad range. Although a well-defined shape is quickly reached for each realization, there are large fluctuations between realizations.