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Testing the Quality of Manufactured Balls

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Algorithms and Data Structures (WADS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1663))

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Abstract

We consider the problem of testing the roundness of a manufactured ball, using the finger probing model of Cole and Yap [4]. When the center of the object is known, a procedure requiring O(n 2) probes and O(n 2) computation time is described. (Here n = |1/q|, where q is the quality of the object.) When the center of the object is not known, the procedure requires O(n 2) probes and O(n 4) computation time. We also give lower bounds that show that the number of probes used by these procedures is optimal.

This work was funded in part by the Natural Sciences and Engineering Research Council of Canada.

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References

  1. P. Agarwal, B. Aronov, and M. Sharir. Line transversals of balls and smallest enclosing cylinder in three dimensions. In 8th ACM-SIAM Symposium on Data Structures and Algorithms (SODA), pages 483–492, 1997.

    Google Scholar 

  2. P. Bose and P. Morin. Testing the quality of manufactured balls. Technical Report TR-98-08, Carleton University School of Computer Science, 1998.

    Google Scholar 

  3. P. Bose and P. Morin. Testing the quality of manufactured disks and cylinders. In Proceedings of the Ninth Annual International Symposium on Algorithms and Computation (ISAAC’98), pages 129–138, 1998.

    Google Scholar 

  4. R. Cole and C. K. Yap. Shape from probing. Journal of Algorithms, 8:19–38, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  5. M. deBerg, P. Bose, D. Bremner, S. Ramaswami, and G. Wilfong. Computing constrained minimum-width annuli of point sets. In Proceedings of the 5th Workshop on Data Structures and Algorithms, pages 25–36, 1997.

    Google Scholar 

  6. C. A. Duncan, M. T. Goodrich, and E. A. Ramos. Efficient approximation and optimization algorithms for computational metrology. In 8th ACM-SIAM Symposium on Data Structures and Algorithms (SODA), pages 121–130, 1997.

    Google Scholar 

  7. H. Ebara, N. Fukuyama, H. Nakano, and Y. Nakanishi. Roundness algorithms using the Voronoi diagrams. In 1st Canadian Conference on Computational Geometry, page 41, 1989.

    Google Scholar 

  8. Q. Fu and C. K. Yap. Computing near-centers in any dimension. Unpublished manuscript, 1998.

    Google Scholar 

  9. J. Garcia and P. A. Ramos. Fitting a set of points by a circle. In ACM Symposium on Computational Geometry, 1997.

    Google Scholar 

  10. V. B. Le and D. T. Lee. Out-of-roundness problem revisited. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(3):217–223, 1991.

    Article  Google Scholar 

  11. K. Mehlhorn, T. Shermer, and C. Yap. A complete roundness classiffication procedure. In ACM Symposium on Computational Geometry, pages 129–138, 1997.

    Google Scholar 

  12. P. Ramos. Computing roundness in practice. In European Conference on Computational Geometry, pages 125–126, 1997.

    Google Scholar 

  13. U. Roy and X. Zhang. Establishment of a pair of concentric circles with the minimum radial separation for assessing rounding error. Computer Aided Design, 24(3):161–168, 1992.

    Article  MATH  Google Scholar 

  14. E. Schomer, J. Sellen, M. Teichmann, and C. K. Yap. Efficient algorithms for the smallest enclosing cylinder. In 8th Canadian Conference on Computational Geometry, pages 264–269, 1996.

    Google Scholar 

  15. K. Swanson. An optimal algorithm for roundness determination on convex polygons. In Proceedings of the 3rd Workshop on Data Structures and Algorithms, pages 601–609, 1993.

    Google Scholar 

  16. C. K. Yap. Exact computational geometry and tolerancing metrology. In David Avis and Jit Bose, editors, Snapshots of Computational and Discrete Geometry, Vol. 3. 1994.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Carleton University, Ottawa, Canada, K1S 5B6

    Prosenjit Bose & Pat Morin

Authors
  1. Prosenjit Bose
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  2. Pat Morin
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Canada, K1S 5B6

    Frank Dehne  & Jörg-Rüdiger Sack  & 

  2. School of Computer Science, Simon Fraser University, Burnaby, BC, Canada, V5A 1S6

    Arvind Gupta

  3. Center for Geometric Computing Providence, Brown University, RI, 02912-1910, USA

    Roberto Tamassia

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© 1999 Springer-Verlag Berlin Heidelberg

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Bose, P., Morin, P. (1999). Testing the Quality of Manufactured Balls. In: Dehne, F., Sack, JR., Gupta, A., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1999. Lecture Notes in Computer Science, vol 1663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48447-7_16

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  • DOI: https://doi.org/10.1007/3-540-48447-7_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66279-2

  • Online ISBN: 978-3-540-48447-9

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