Testing the quality of manufactured disks and cylinders

Abstract

We consider the problem of testing the roundness of a manufactured object using the finger probing model of Cole and Yap [1]. When the object being tested is a disk and it's center is known, we describe a procedure which uses O(n) probes and O(n) computation time. (Here n = |1/q|, where q is the quality of the object.) When the center of the object is not known, a procedure using O(n) probes and O(n log n) computation time is described. When the object being tested is a cylinder of length l, a procedure is described which uses O(ln 2) probes and O(ln2 log ln) computation time. Lower bounds are also given which show that these procedures are optimal in terms of the number of probes used. © Springer-Verlag Berlin Heidelberg 1998.