On the Connectedness of Rational Arithmetic Discrete Hyperplanes

  • Damien Jamet
  • Jean-Luc Toutant
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4245)


While connected arithmetic discrete lines are entirely characterized by their arithmetic thickness, only partial results exist for arithmetic discrete hyperplanes in any dimension. In the present paper, we focus on 0-connected rational arithmetic discrete planes in ℤ3. Thanks to an arithmetic reduction on a given integer vector n, we provide an algorithm which computes the thickness of the thinnest 0-connected arithmetic plane with normal vector n.


Normal Vector Integer Point Integer Vector Translation Parameter Metic Plane 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Damien Jamet
    • 1
  • Jean-Luc Toutant
    • 2
  1. 1.LORIA – INRIA LorraineVillers-lès-NancyFrance
  2. 2.LIRMM – CNRS UMR 5506Université Montpellier IIMontpellierFrance

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