Concurrency of line segments in uncertain geometry

Abstract

We examine the derivation of consistent concurrency relations in uncertain geometry. This work extends previous work on parallelism and collinearity. We introduce the concept of a metadomain, which is defined as the set of parameter vectors of lines passing through two domains, where a domain is defined as the uncertainty region of the parameter vector of a line segment. The intersection graph of the metadomains is introduced as the primary tool to derive concurrency relations.