How to obtain a lattice basis from a discrete projected space

Authors:
Nicolas Normand;Myriam Servières;JeanPierre Guédon
Affiliations:
IRCCyN/IVC, École polytechnique, University of Nantes, Nantes;IRCCyN/IVC, École polytechnique, University of Nantes, Nantes;IRCCyN/IVC, École polytechnique, University of Nantes, Nantes
Venue:
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Year:
2005

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Abstract

Euclidean spaces of dimension n are characterized in discrete spaces by the choice of lattices. The goal of this paper is to provide a simple algorithm finding a lattice onto subspaces of lower dimensions onto which these discrete spaces are projected. This first obtained by depicting a tile in a space of dimension n – 1 when starting from an hypercubic grid in dimension n. Iterating this process across dimensions gives the final result.