Spirograph Theory: A Framework for Calculations on Digitized Straight Lines

Authors:
L. Dorst;R. P. W. Duin
Affiliations:
Pattern Recognition Group, Department of Applied Physics. Delft University of Technology, Delft, The Netherlands.;Pattern Recognition Group, Department of Applied Physics. Delft University of Technology, Delft, The Netherlands.
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
1984

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Abstract

Using diagrams called ``spirographs'' a general theory is developed with which one can easily perform calculations on various aspects of digitized straight lines. The mathematics of the theory establishes a link between digitized straight lines and the theory of numbers (Farey series, continued fractions). To show that spirograph theory is a useful unification, we derive two previously known advanced results within the framework of the theory, and new results concerning the accuracy in position of a digitized straight line as a function of its slope and length.