Representation of many-sided polygons and polygonal lines for rapid processing

Abstract

A representation for polygons and polygonal lines is described which allows sets of consecutive sides to be collectively examined. The set of sides are arranged in a binary tree hierarchy by inclusion. A fast algorithm for testing the inclusion of a point in a many-sided polygon is given. The speed of the algorithm is discussed for both ideal and practical examples. It is shown that the points of intersection of two polygonal lines can be located by what is essentially a binary tree search. The algorithm and a practical example are discussed. The representation overcomes many of the disadvantages associated with the various fixed-grid methods for representing curves and regions.