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<H1>L<sub>m</sub> distance</H1>
<P>
(definition)

<P>
<strong>Definition:</strong>
The generalized distance between two points.  In a plane with point p<sub>1</sub> at (x<sub>1</sub>, y<sub>1</sub>) and p<sub>2</sub> at (x<sub>2</sub>, y<sub>2</sub>), it is  (|x<sub>1</sub> - x<sub>2</sub>|<sup>m</sup> +  |y<sub>1</sub> - y<sub>2</sub>|<sup>m</sup>)<sup>1/m</sup>.
<P><strong>See also</strong>
<a href="euclidndstnc.html" tppabs="http://hissa.nist.gov/dads/HTML/euclidndstnc.html"><em>Euclidean distance</em></a>, <a href="rectilinear.html" tppabs="http://hissa.nist.gov/dads/HTML/rectilinear.html"><em>rectilinear</em></a>, <a href="manhttndstnc.html" tppabs="http://hissa.nist.gov/dads/HTML/manhttndstnc.html"><em>Manhattan distance</em></a>.
<P><em>Note:
This is easily generalized to higher dimensions. Euclidean distance is L<sub>2</sub> distance.  Rectilinear or Manhattan distance is L<sub>1</sub> distance.   L<sub> <img src="infty.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/infty.gif"  border=0 height=6  width=13 alt="infinity"></sub> distance is max(|x<sub>1</sub> - x<sub>2</sub>| +  |y<sub>1</sub> - y<sub>2</sub>|). Adapted from [CLR, page 912].</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>

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Entry modified Fri Oct 15 10:07:56 1999.<BR>
HTML page formatted Wed Dec 22 09:35:45 1999.

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