Distances on Real and Digital Planes

  • Michel Marie Deza
  • Elena Deza


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.


Voronoi Diagram Facility Layout Manhattan Distance Weighted Path Neighborhood Sequence 
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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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