Concurrency Relations between Digital Planes

Abstract

Abstract. In this paper we examine concurrency relations between planes whose position is not precisely known. The simplest case consists of four planes, where we have to determine whether the four planes can be forced to pass through one common intersection point by moving them slightly within specified limits. We prove that if such a concurrency relation is possible then it can be found in a finite number of steps by a simple geometrical construction. This result remains valid for larger collections of planes, with multiple concurrency relations, provided each pair of relations shares at most one plane, and the relations do not form cycles.