city-block metric
The city-block metric, defined on ℝn, is
d(a,b)=n∑i=1|bi-ai| |
where a and b are vectors in ℝn with a=(a1,…,an) and b=(b1,…,bn).
In two dimensions and with discrete-valued vectors, when we can picture the set of points in ℤ×ℤ as a grid, this is simply the number of edges between points that must be traversed to get from a to b within the grid. This is the same problem as getting from corner a to b in a rectilinear downtown area, hence the name “city-block metric.”
Title | city-block metric |
---|---|
Canonical name | CityblockMetric |
Date of creation | 2013-03-22 12:12:57 |
Last modified on | 2013-03-22 12:12:57 |
Owner | akrowne (2) |
Last modified by | akrowne (2) |
Numerical id | 9 |
Author | akrowne (2) |
Entry type | Definition |
Classification | msc 54E35 |
Synonym | city-block distance |
Synonym | taxicab metric |