Position Coding

TL;DR

This paper explores the mathematical foundations of position coding patterns, introduces two existing codes including Anoto, and proposes two new codes utilizing binary wavelets for improved coordinate mapping.

Contribution

It provides a detailed mathematical analysis of position codes and introduces novel codes that incorporate binary wavelets for enhanced encoding capabilities.

Findings

Analysis of Anoto code's mathematical basis

Introduction of two new position codes with wavelet integration

Potential improvements in position encoding accuracy

Abstract

A position coding pattern is an array of symbols in which subarrays of a certain fixed size appear at most once. So, each subarray uniquely identifies a location in the larger array, which means there is a bijection of some sort from this set of subarrays to a set of coordinates. The key to Fly Pentop Computer paper and other examples of position codes is a method to read the subarray and then convert it to coordinates. Position coding makes use of ideas from discrete mathematics and number theory. In this paper, we will describe the underlying mathematics of two position codes, one being the Anoto code that is the basis of "Fly paper". Then, we will present two new codes, one which uses binary wavelets as part of the bijection.