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Characterization of convex and pointisable interval relations by diagrammatic methods

Kulpa Z., Le T. L.

Machine Graphics and Vision

2000

Vol. 9, No. 1/2

221-231

In the paper diagrammatic methods are used to demonstrate equivalence of different characterizations of convex and pointisable interval relations. The diagrammatic tools used are introduced: the MR-diagram for interval space, the W-diagram for representing arrangement interval relations, and the conjunction and lattice diagrams. Two theorems on characterizations on convex and pointisable relation classes are given. The proof of the first theorem has been published by Kulpa elsewhere; the second theorem on pointisable relations is proven in this paper with the help of the diagrammatic tools introduced.