A note on the perimeter of fat objects

作者：Bose Prosenjit^*; Cheong Otfried; Dujmovic Vida

来源：Computational Geometry-Theory and Applications, 2011, 44(1): 1-8.

DOI：10.1016/j.comgeo.2010.06.002

• Realistic inputs
• Fat objects
• Visibility
• Perimeter
• Fractals

In this Note, we show that the size of the perimeter of (alpha, beta)-covered objects is a linear function of the diameter. Specifically, for an (alpha, beta)-covered object O, per(O) <= c diam(O)/alpha beta sin(2)alpha , 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 gamma-fat objects are a generalization of (alpha, beta)-covered objects. We show that no such relationship between perimeter and diameter can hold for locally gamma-fat objects.

• 出版日期2011-1