Distances on Real and Digital Planes

Michel Marie Deza and Elena Deza
Additional contact information
Michel Marie Deza: Ecole Normale Supérieure
Elena Deza: Moscow State Pedagogical University

Chapter Chapter 19 in Encyclopedia of Distances, 2016, pp 365-381 from Springer

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

Keywords: Voronoi Diagram; Manhattan Distance; Link Distance; Neighborhood Sequence; Euclidean Length (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-52844-0_19

Ordering information: This item can be ordered from
http://www.springer.com/9783662528440

DOI: 10.1007/978-3-662-52844-0_19

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().