The Secret of Gambling with Irregular Dice: Estimating the Face Statistics of Polyhedra

  • Péter L. Várkonyi

Abstract

This paper is devoted to the description of a new geometric algorithm to estimate the “face statistics” of an irregularly-shaped polyhedron, i.e. the probability that it rests on a given face after being dropped onto a horizontal surface. A recently  published paper of the author discussed existing and new methods to estimate this probability, together with a comparison of their reliability, and the challenges of benchmarking them against data obtained via computer simulation. The present work focuses on a new estimation algorithm, with computational complexity linearly proportional to the number of vertices. The main industrial application area of this result is automated assembly: the throughput of a part feeder is heavily influenced by the face statistics of the parts processed by the feeder.
Keywords: face statistics, polyhedra, gambling, part feeding
Published online
2014-12-22
How to Cite
Várkonyi, P. (2015) “The Secret of Gambling with Irregular Dice: Estimating the Face Statistics of Polyhedra”, Periodica Polytechnica Architecture, 46(1), pp. 1-5. https://doi.org/10.3311/PPar.7607.
Section
Articles