Oriented geometric Objects in Computer Graphics and Numerical Control

Abstract

Conventional natural - language as well as computer - oriented descriptions of geometric constructions by means of geometric relationships (parallelism, tangency, etc.) and attributes (INSIDE, NEAR, MIDDLE, X-LARGE, Y-SMALL, etc.) do not offer a clear and efficient method for selecting a specific object out of a number of possible alternatives. This paper describes a systematic solution to the problem based upon the notions of orientation of geometric objects, of smooth transitions from one object to another (referred to as coherent tangency), and upon locality. Using the notions of object orientation and coherent tangency, some tangent constructions in a plane are developed. The method is shown to employ a minimum set of attributes - at most one, characterizing the intrinsic parameters of geometric objects.