On the Encoding of Arbitrary Geometric Configurations

Abstract

A method is described which permits the encoding of arbitrary geometric configurations so as to facilitate their analysis and manipulation by means of a digital computer. It is shown that one can determine through the use of relatively simple numerical techniques whether a given arbitrary plane curve is open or closed, whether it is singly or multiply connected, and what area it encloses. Further, one can cause a given figure to be expanded, contracted, elongated, or rotated by an arbitrary amount. It is shown that there are a number of ways of encoding arbitrary geometric curves to facilitate such manipulations, each having its own particular advantages and disadvantages. One method, the so-called rectangular-array type of encoding, is discussed in detail. In this method the slope function is quantized into a set of eight standard slopes. This particular representation is one of the simplest and one that is most readily utilized with present-day computing and display equipment.