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.
Partially supported by the ANR program ANR-06-MDCA-008-05/FOGRIMMI.
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Fuchs, L., Largeteau-Skapin, G., Wallet, G., Andres, E., Chollet, A. (2008). A First Look into a Formal and Constructive Approach for Discrete Geometry Using Nonstandard Analysis. In: Coeurjolly, D., Sivignon, I., Tougne, L., Dupont, F. (eds) Discrete Geometry for Computer Imagery. DGCI 2008. Lecture Notes in Computer Science, vol 4992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79126-3_4
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