Arithmetization of a circular arc

Authors:
Aurélie Richard;Guy Wallet;Laurent Fuchs;Eric Andres;Gaëlle Largeteau-Skapin
Affiliations:
Laboratoire XLIM-SIC, Université de Poitiers, Futuroscope Chasseneuil cedex, France;Laboratoire MIA, Université de La Rochelle, La Rochelle cedex, France;Laboratoire XLIM-SIC, Université de Poitiers, Futuroscope Chasseneuil cedex, France;Laboratoire XLIM-SIC, Université de Poitiers, Futuroscope Chasseneuil cedex, France;Laboratoire XLIM-SIC, Université de Poitiers, Futuroscope Chasseneuil cedex, France
Venue:
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Year:
2009

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Abstract

In this paper, we present an arithmetization of the Euler's integration scheme based on infinitely large integers coming from the nonstandard analysis theory. Using the differential equation that defines circles allows us to draw two families of discrete arc circles using three parameters, the radius, the global scale and the drawing scale. These parameters determine the properties of the obtained arc circles. We give criteria to assure the 8-connectivity. A global error estimate for the arithmetization of the Euler's integration scheme is also given and a first attempt to define the approximation order of an arithmetized integration scheme is provided.