diameterlike
Diameterlike is an informal term used in geometry and analysis to describe measures of a set’s spatial extent that generalize the usual notion of diameter. The classical diameter of a nonempty bounded subset S of a metric space (X,d) is diam(S) = sup{d(x,y): x,y in S}. Diameterlike quantities broaden this idea by incorporating center, direction, or weighting, yielding a family of related measures rather than a single value.
One common center-based approach defines, for S ⊆ X and a chosen center c in X, D(S,c) =
A directional, or width-based, version is particularly common in Euclidean spaces. For a unit vector u, the
Applications of diameterlike measures appear in shape analysis, computer vision, and geometric tomography, where a single
Note: diameterlike is not a standardized mathematical term; it is used informally to refer to these generalized,