Topological Relations of Arrow Symbols in Complex Diagrams

Yohei Kurata and Max Egenhofer
Diagrams 2006: Fourth International Conference on the Theory and Application of Diagrams, Stanford, CA
D. Barker-Plummer, R. Cox, and N. Swoboda (eds.), Lecture Notes in Computer Science, Vol. 4045, Springer, pp. 112-126, June 2006.

Abstract

Illustrating a dynamic process with an arrow-containing diagram is a widespread convention in peopleÕs daily communications. In order to build a basis for capturing the structure and semantics of such diagrams, this paper formalizes the topological relations between two arrow symbols and discusses the influence of these topological relations on the diagramÕs semantics. Topological relations of arrow symbols are established by two types of links, intersections and common references, which are further categorized into nine types based on the combination of the linked parts. The topological relations are captured by the existence/non-existence of these nine types of intersections and common references. Then, this paper demonstrates that arrow symbols with different types of intersections typically illustrate two actions with different interrelations, whereas the arrow symbols with common references illustrate a pair of semantics that may be mutually exclusive or synchronized.

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