Contour codes of isothetic polygons

Abstract

An isothetic polygonal arc is one that has all its sides oriented in two orthogonal directions, so that all its angles are right angles. Such an arc is determined (up to congruence) by specifying a “code” sequence of the form α₁A₁α₂ … α_m−1A_m−1α_m, where the α's are positive real numbers representing side lengths, and the A's are single bits that specify whether the arc turns left or right between one side and the next. In this paper we develop basic properties of this code and show how to derive various geometric properties of the arc (or the region it bounds, if it is closed) directly from the code.