Testing the Quality of Manufactured Disks and Cylinders

We consider the problem of testing the roundness of a manufactured object using the finger probing model of Cole and Yap [2]. 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 = j1=qj, 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(ln²) probes and O(ln 2 log ln) computation time. Lower bounds are also given which show that these procedures are optimal in terms of the number of probes used

Testing the Quality of Manufactured Disks and Cylinders

1 Introduction The field of metrology is concerned with measuring the quality of manufactured objects. A basic task in metrology is that of determining whether a given manufactured object is of acceptable quality. Usually this involves probing the surface of the object using a measuring device such as a coordinate measuring machine to get a set S of sample points, and then verifying, algorithmically, how well S approximates an ideal object. A special case of this problem is determining whether an object is round, or circle like. For our purposes, an object I is good if the boundary of I can be contained in an annulus of inner radius 1 \Gamma ffl and outer radius 1 + ffl, for some quality parameter ffl? 0, and is bad otherwise. See Fig. 1 for examples of good and bad objects. We call this problem the roundness classification problem