Journal of Algorithms
A complete roundness classification procedure
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Efficient approximation and optimization algorithms for computational metrology
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Computing Constrained Minimum-Width Annuli of Point Sets
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Testing the Quality of Manufactured Balls
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Property Testing with Geometric Queries
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
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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(ln2) 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.