Distances on Real and Digital Planes

Michel Marie Deza and Elena Deza
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Michel Marie Deza: École Normale Supérieure
Elena Deza: Moscow State Pedagogical University

Chapter Chapter 19 in Encyclopedia of Distances, 2013, pp 323-338 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-3-642-30958-8_19

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