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.

• Type: Journal
• Year: 2011
• Where: COMGEO
• Authors: Prosenjit Bose, Otfried Cheong, Vida Dujmovic
• Keywords: Applied Computing, COMGEO 2011, Constant Fraction, Linear Function, γ–fat Objects