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COMGEO
2011
ACM

A note on the perimeter of fat objects

8 years 5 months ago
A note on the perimeter of fat objects
In this note, we show that the size of the perimeter of (α, β)-covered objects is a linear function of the diameter. Specifically, for an (α, β)-covered object O, per(O) ≤ c diam(O) αβ sin2 α , for a positive constant c. One easy consequence of the result is that every point on the boundary of such an object sees a constant fraction of the boundary. Locally γ–fat objects are a generalization of (α, β)–covered objects. We show that no such relationship between perimeter and diameter can hold for locally γ-fat objects.
Prosenjit Bose, Otfried Cheong, Vida Dujmovic
Added 13 May 2011
Updated 13 May 2011
Type Journal
Year 2011
Where COMGEO
Authors Prosenjit Bose, Otfried Cheong, Vida Dujmovic
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