Distances on Real and Digital Planes

  • Michel Marie Deza
  • Elena Deza

Abstract

Any L p -metric (as well as any norm metric for a given norm ∥.∥ on ℝ2) can be used on the plane ℝ2, and the most natural is the L 2-metric, i.e., the Euclidean metric \(d_{\mathrm{E}}(x,y)=\sqrt{(x_{1}-y_{1})^{2}+(x_{2}-y_{2})^{2}}\) which gives the length of the straight line segment [x,y], and is the intrinsic metric of the plane.

Keywords

Voronoi Diagram Facility Layout Manhattan Distance Weighted Path Neighborhood Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Michel Marie Deza
    • 1
  • Elena Deza
    • 2
  1. 1.École Normale SupérieureParisFrance
  2. 2.Moscow State Pedagogical UniversityMoscowRussia

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