Digital lines and digital convexity

Authors:
Ulrich Eckhardt
Affiliations:
Fachbereich Mathematik, Optimierung und Approximation, Universität Hamburg, Bundesstraße 55, D-20146 Hamburg
Venue:
Digital and image geometry
Year:
2001

Citing 8
Cited 3

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Abstract

Euclidean geometry on a computer is concerned with the translation of geometric concepts into a discrete world in order to cope with the requirements of representation of abstract geometry on a computer. The basic constructs of digital geometry axe digital lines, digital line segments and digitally convex sets. The aim of this paper is to review some approaches for such digital objects. It is shown that digital objects share much of the properties of their continuous counterparts. Finally, it is demonstrated by means of a theorem due to Tietze (1929) that there are fundamental differences between continuous and discrete concepts.