Applications of computational geometry in mechanical engineering design and manufacture

  • Michael J. Pratt
Invited Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1148)


This contribution has a threefold purpose. Firstly, it urges a wider interpretation of ‘Computational Geometry’ than is often taken. Secondly, it emphasizes the importance of the choice of representations as well as algorithms in geometric computing. Thirdly, it provides examples from the author's experience, supporting the opinions expressed.


Tool Path Computational Geometry Polyhedral Approximation Optimal Cutting Condition Numerically Control Program 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    B. Chazelle et al., Application Challenges to Computational Geometry, Technical Report TR-521-96, Princeton University, Princeton, NJ (1996)Google Scholar
  2. 2.
    Degen, W. L. F., Nets with Plane Silhouettes II. To appear in Proc. IMA Conf. Mathematics of Surfaces VII, Dundee, Scotland, 2–4 September 1996. Oxford, England: Oxford University Press (in preparation)Google Scholar
  3. 3.
    Faux, I. D., Pratt, M. J.: Computational Geometry for Design and Manufacture. Chichester, England: Ellis Horwood (1979)Google Scholar
  4. 4.
    Forrest, A. R.: Computational Geometry. Proc. Roy. Soc. Lond. A 321 (1971) 187–195Google Scholar
  5. 5.
    Forrest, A. R.: Computational Geometry — Achievements and Problems. In R. E. Barnhill and R. F. Riesenfeld (eds.) Computer Aided Geometric Design, Academic Press (1974)Google Scholar
  6. 6.
    Fridshal R., Cheng, K.P., Duncan, D., Zucker, W.: Numerical Control Part Program Verification System. In Proc. Conf. on CAD/CAM Technology in Mechanical Engineering, Massachusetts Institute of Technology, March 1982. MIT Press (1982)Google Scholar
  7. 7.
    Guo, B., Representation of Arbitrary Shapes using Implicit Quadrics. The Visual Computer 9 (1993) 267–277CrossRefGoogle Scholar
  8. 8.
    Laporte, H., Nyiri, E., Froumentin, M., Chaillou, C., A Graphics System based on Quadrics. Computers and Graphics 19 (1995) 251–260CrossRefGoogle Scholar
  9. 9.
    Martin, R. R., de Pont, J., Sharrock, T. J., Cyclide Surfaces in Computer Aided Design. In Gregory, J. A. (ed.) The Mathematics of Surfaces. Oxford, England: Oxford University Press (1986)Google Scholar
  10. 10.
    Peternell, M., Pottmann, H., Designing Rational Surfaces with Rational Offsets. Technical Report No. 28, Institut für Geometrie, Technische Universität Wien, Austria (1995)Google Scholar
  11. 11.
    Pratt, M. J., Quartic Supercyclides I: Basic Theory. To appear, Computer Aided Geometric DesignGoogle Scholar
  12. 12.
    Pratt, M. J., Geisow, A. D., Surface/Surface Intersections. In Gregory, J. A. (ed.) The Mathematics of Surfaces. Oxford, England: Oxford University Press (1986)Google Scholar
  13. 13.
    Preparata, F. P., Shamos, M. I., Computational Geometry: An Introduction. New York: Springer-Verlag (1985)Google Scholar
  14. 14.
    Sederberg, T. W., Techniques for Cubic Algebraic Surfaces (Parts 1 and 2). IEEE Computer Graphics & Applications 10 (1990) 5, 14–25 and 6, 12–21Google Scholar
  15. 15.
    TIPS Working Group, TIPS-1: Technical Information Processing System. Institute of Precision Engineering, Hokkaido University, Japan (1978)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Michael J. Pratt
    • 1
    • 2
  1. 1.Center for Advanced TechnologyRensselaer Polytechnic InstituteUSA
  2. 2.Manufacturing Systems Integration DivisionNational Institute of Standards and TechnologyUSA

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