A first look into a formal and constructive approach for discrete geometry using nonstandard analysis

Authors:
Laurent Fuchs;Gaëlle Largeteau-Skapin;Guy Wallet;Eric Andres;Agathe Chollet
Affiliations:
Laboratoire SIC, Université de Poitiers, Futuroscope Chasseneuil cédex, France;Laboratoire SIC, Université de Poitiers, Futuroscope Chasseneuil cédex, France;Laboratoire LMA, Université de La Rochelle, La Rochelle cedex, France;Laboratoire SIC, Université de Poitiers, Futuroscope Chasseneuil cédex, France;Laboratoire LMA, Université de La Rochelle, La Rochelle cedex, France
Venue:
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Year:
2008

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Abstract

In this paper, we recall the origins of discrete analytical geometry developed by J-P. Reveillès [1] in the nonstandard model of the continuum based on integers proposed by Harthong and Reeb [2,3]. We present some basis on constructive mathematics [4] and its link with programming [5,6]. We show that a suitable version of this new model of the continuum partly fits with the constructive axiomatic of R proposed by Bridges [7]. The aim of this paper is to take a first look at a possible formal and constructive approach to discrete geometry. This would open the way to better algorithmic definition of discrete differential concepts.