Spirograph Theory: A Framework for Calculations on Digitized Straight Lines

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.

[1]  F. Groen,et al.  Freeman-code probabilities of object boundary quantized contours , 1978 .

[2]  AZRIEL ROSENFELD,et al.  Digital Straight Line Segments , 1974, IEEE Transactions on Computers.

[3]  A. Hurwitz,et al.  Ueber die angenäherte Darstellung der Zahlen durch rationale Brüche , 1894 .

[4]  Carlo Arcelli,et al.  On the parallel generation of straight digital lines , 1978 .

[5]  Li-De Wu,et al.  On the Chain Code of a Line , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  R. Brons,et al.  Linguistic Methods for the Description of a Straight Line on a Grid , 1974, Comput. Graph. Image Process..

[7]  E. T..  An Introduction to the Theory of Numbers , 1946, Nature.

[8]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.