On the Encoding of Arbitrary Geometric Configurations

TLDR

The paper proposes a method to encode arbitrary geometric configurations for computer analysis and manipulation, focusing on a rectangular‑array encoding approach. The rectangular‑array encoding quantizes the slope function into eight standard slopes, enabling efficient representation and manipulation of geometric curves on digital computers. Using this encoding, the authors demonstrate that simple numerical techniques can determine whether a plane curve is open or closed, its connectivity, and enclosed area, and can perform arbitrary scaling, elongation, or rotation, with the rectangular‑array representation proving simple and well suited to current computing and display hardware.

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.