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On the Connecting Thickness of Arithmetical Discrete Planes

  • Eric Domenjoud
  • Damien Jamet
  • Jean-Luc Toutant
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)

Abstract

While connected rational arithmetical discrete lines and connected rational arithmetical discrete planes are entirely characterized, only partial results exist for the irrational arithmetical discrete planes. In the present paper, we focus on the connectedness of irrational arithmetical discrete planes, namely the arithmetical discrete planes with a normal vector of which the coordinates are not ℚ-linear dependent. Given v ∈ ℝ3, we compute the lower bound of the thicknesses 2-connecting the arithmetical discrete planes with normal vector v. In particular, we show how the translation parameter operates in the connectedness of the arithmetical discrete planes.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Eric Domenjoud
    • 1
  • Damien Jamet
    • 1
  • Jean-Luc Toutant
    • 2
  1. 1.LoriaUniversité Nancy 1 - CNRSVandœuvre-lès-NancyFrance
  2. 2.LAICIUT Clermont-FerrandAubière CedexFrance

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