A First Look into a Formal and Constructive Approach for Discrete Geometry Using Nonstandard Analysis

  • Laurent Fuchs
  • Gaëlle Largeteau-Skapin
  • Guy Wallet
  • Eric Andres
  • Agathe Chollet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4992)


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.


discrete geometry nonstandard analysis constructive mathematics 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Laurent Fuchs
    • 1
  • Gaëlle Largeteau-Skapin
    • 1
  • Guy Wallet
    • 2
  • Eric Andres
    • 1
  • Agathe Chollet
    • 2
  1. 1.Laboratoire SICUniversité de PoitiersFuturoscope Chasseneuil cédexFrance
  2. 2.Laboratoire LMAUniversité de La RochelleLa Rochelle cedexFrance

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