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Spirograph Theory: A Framework for Calculations on Digitized Straight Lines

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2 Author(s)
Dorst, L. ; Pattern Recognition Group, Department of Applied Physics. Delft University of Technology, Delft, The Netherlands. ; Duin, R.P.W.

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.

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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:PAMI-6 ,  Issue: 5 )