Chebyshev distance (L-infinity metric)

E656653

L-infinity metric Minkowski distance distance metric mathematical concept

Chebyshev distance (L-infinity metric) is a distance measure on a grid or in n-dimensional space defined as the maximum absolute difference along any coordinate axis between two points.

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Observed surface forms (1)

Surface form	Occurrences
Chebyshev distance	1

Statements (50)

Predicate	Object
instanceOf	L-infinity metric ⓘ Minkowski distance ⓘ distance metric ⓘ mathematical concept ⓘ
alsoKnownAs	L-infinity distance ⓘ L∞ metric ⓘ chessboard distance ⓘ maximum metric ⓘ
applicationDomain	approximation theory ⓘ chess ⓘ clustering ⓘ computational geometry ⓘ grid-based pathfinding ⓘ image processing ⓘ operations research NERFINISHED ⓘ pattern recognition ⓘ robot motion planning ⓘ
ballVolumeGrowth	proportional to radius^n in R^n ⓘ
coordinateDependence	depends on chosen coordinate axes ⓘ
definedOn	grids ⓘ lattices ⓘ n-dimensional real vector space ⓘ
definition	For x,y in R^n, d(x,y) = max_i \|x_i - y_i\| NERFINISHED ⓘ
field	discrete geometry ⓘ functional analysis ⓘ metric geometry ⓘ
greaterOrEqualThan	Euclidean distance on R^n ⓘ Manhattan distance on R^n is not always comparable ⓘ
inducedByNorm	L-infinity norm ⓘ
isLimitOf	Minkowski p-metrics as p -> infinity ⓘ
isMetric	true ⓘ
metricInequality	d_1(x,y)/n <= d_infinity(x,y) ⓘ d_infinity(x,y) >= d_2(x,y)/sqrt(n) ⓘ
metricSpaceType	norm-induced metric ⓘ
MinkowskiParameter	p = infinity ⓘ
namedAfter	Pafnuty Chebyshev NERFINISHED ⓘ
relationToChess	minimum number of king moves between squares ⓘ
satisfiesProperty	identity of indiscernibles ⓘ non-negativity ⓘ symmetry ⓘ triangle inequality ⓘ
symmetryGroup	hypercube symmetry group ⓘ
topologyInduced	same as L1 metric on R^n ⓘ same as L2 metric on R^n ⓘ
unitBallShape	hypercube ⓘ
unitBallShapeIn2D	square aligned with coordinate axes ⓘ
unitBallShapeIn3D	cube aligned with coordinate axes ⓘ
usedFor	defining neighborhoods in grid-based images ⓘ estimating worst-case coordinate deviation ⓘ measuring distance on square grids ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Moore neighborhood → distanceMetric → Chebyshev distance (L-infinity metric) ⓘ

Pafnuty Chebyshev → notableWork → Chebyshev distance (L-infinity metric) ⓘ

this entity surface form: Chebyshev distance