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This paper discusses the use of two different approaches for computing the “accessibility” of a surface. These metrics characterize how easily a surface may be touched by a spherical probe. The paper also presents various acceleration techniques for accessibility. The idea of surface accessibility is extended to include “global accessibility” which measures the ability of a spherical probe to enter a structure from outside as well as to fit locally on the surface. The visual effect of shading using accessibility is shown to resemble the patina on certain tarnished surfaces which have then been cleaned.