Advertisement

Design Methods of Free-Form Surfaces and their Integration into the Solid Modeling Package GEOMAP-III

  • Fumihiko Kimura

Abstract

Two powerful methods are shown for the construction of complex solid shapes with free-form surfaces: local modification operations for constructing rough shapes and their smoothing, and complete set operations among curved objects. For actually realizing these methods, it is necessary to develop a basic theory for treating problems which cannot be solved thoroughly by the conventional theories, such as smooth connection of surface patches under various restrictive conditions, and generation of irregular (nonrectangular) surface patches. Some theoretical results are described which are based on the control point approach of Bezier and which are useful for these problems. The two methods are integrated into our comprehensive solid modeling package GEOMAP-III which is soon to be operational and which will serve as a basis for sophisticated shape design and integrated CAD/CAM systems.

Keywords

Control Point Surface Patch Bezier Curve IEEE Computer Graphic Bezier Surface 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Bézier 1972]
    P. E. Bézier, Numerical Control—Mathematics and Applications, John Wiley and Sons, London, England, 1972.MATHGoogle Scholar
  2. [Barnhill and Böhm 1983]
    R. E. Barnhill and W. Böhm, eds., Surfaces in Computer Aided Geometric Design, North-Holland Publishing Company, Amsterdam, Netherlands, 1983.MATHGoogle Scholar
  3. [Barnhill and Riesenfeld 1974]
    R. E. Barnhill and R. F. Riesenfeld, eds., Computer Aided Geometric Design, Academic Press, New York, New York, 1974.MATHGoogle Scholar
  4. [Braid et al. 1980]
    I. C. Braid, R. C. Hillyard, and I. A. Stroud, “Stepwise Construction of Polyhedra in Geometric Modeling,” Mathematical Methods in Computer Graphics and Design, Academic Press, London, England, 1980, pp. 123–141.Google Scholar
  5. [Catmull and Clark 1978]
    E. Catmull and J. Clark, “Recursively Generated B-Spline Surfaces on Arbitrary Topological Meshes,” Computer Aided Design, Vol. 10, No. 6, November 1978, pp. 350–355.CrossRefGoogle Scholar
  6. [Chiyokura and Kimura 1983]
    H. Chiyokura and F. Kimura, “Design of Solids with Free-Form Surfaces,” ACM Computer Graphics, Vol. 17, No. 3 (SIGGRAPH ’83 Conference Proceedings, Detroit, Michigan, July 25–29, 1983 ) pp. 289–298.Google Scholar
  7. [Doo 1978]
    D. Doo, “Subdivision Algorithm for Smoothing Down Irregular Shaped Polyhedrons,” IEEE Proceedings of the International Conference on Interactive Techniques in Computer Aided Design, Bologna, Italy, September 21–23, 1978, pp. 157–165.Google Scholar
  8. [Faux and Pratt 1979]
    I. D. Faux and M. J. Pratt, Computational Geometry for Design and Manufacture, Ellis Horwood Limited, London, England, 1979.MATHGoogle Scholar
  9. [Forrest 1978]
    A. R. Forrest, “A Unified Approach to Geometric Modeling,” ACM Computer Graphics, Vol. 12, No. 3 (SIGGRAPH ’78 Conference Proceedings, Atlanta, Georgia, August 23–25, 1978 ) pp. 264–269.Google Scholar
  10. [Goldman 1983]
    R. N. Goldman, “Quadrics of Revolution,” IEEE Computer Graphics and Applications, Vol. 3, No. 2, March/April 1983, pp. 68–76.Google Scholar
  11. [Higashi et al 1983]
    M. Higashi, I. Kohzen, and J. Nagasaka, “An Interactive CAD System for Construction of Shapes with High-Quality Surfaces,” Proceedings of CAPE ’83, Amsterdam, Netherlands, April 25–28, 1983, pp. 371–389.Google Scholar
  12. [Hosaka and Kimura 1977]
    M. Hosaka and F. Kimura, “An Interactive Geometrical Design System with Handwriting Input,” Proceedings of the 1977 IFIP Congress, Toronto, Canada, August 1977, pp. 167–172.Google Scholar
  13. [Hosaka and Kimura 1978]
    M. Hosaka and F. Kimura, “Synthesis Methods of Curves and Surfaces in Interactive CAD,” IEEE Proceedings of the International Conference on Interactive Techniques in Computer Aided Design, Bologna, Italy, September 21–23, 1978, pp. 151–156.Google Scholar
  14. [Hosaka and Kimura 1980]
    M. Hosaka and F. Kimura, “A Theory and Methods for Three Dimensional Free-Form Shape Construction,” Journal of Information Processing, Vol. 3, No. 3, Information Processing Society of Japan, 1980, pp. 140–151.Google Scholar
  15. [Hosaka and Kimura 1981]
    M. Hosaka and F. Kimura, “Interactive Input Methods for Free-Form Shape Design,” Man-Machine Communication in CAD/CAM, North-Holland Publishing Company, Amsterdam, Netherlands, 1981, pp. 103–118.Google Scholar
  16. [Hosaka and Kimura 1982]
    M. Hosaka and F. Kimura, “Methods of Surface Synthesis in GEOMAP-III,” Proceedings of MICAD ’82, Paris, France, 1982, p. 268–280.Google Scholar
  17. [Hosaka et al. 1974]
    M. Hosaka, F. Kimura and N. Kakishita, “A Unified Method for Processing Polyhedra,” Proceedings of the 1974 IFIP Congress, Stockholm, Sweden, August 1974, pp. 768–772.Google Scholar
  18. [IEEE 1982]
    IEEE Special Issue on Solid Modeling, IEEE Computer Graphics and Applications, Vol. 2, No. 2, March 1982.Google Scholar
  19. [Kawabe et al. 1980a]
    S. Kawabe, F. Kimura, and T. Sata, “Generation of NC Commands for Sculptured Surface Machining for 3-Coordinate Measuring Data,” Annals of the CIRP, Vol. 29, No. 1, 1980, pp. 369–372.CrossRefGoogle Scholar
  20. [Kawabe et al. 1980b]
    S. Kawabe, F. Kimura, and T. Sata, “Automatic Generation of NC Commands for a 3-Coordinate Measuring Machine,” Proceedings of ICPE, Tokyo, Japan, 1980, pp. 941–946.Google Scholar
  21. [Kawabe et al. 1983]
    S. Kawabe, S. Shimura, M. Miyashita, F. Kimura, and T. Sata, “Programming for Machining Based on Workpiece Models in Computers,” Annals of the CIRP, Vol. 32, No. 1, 1983, pp. 351–355.CrossRefGoogle Scholar
  22. [Kimura et al. 1982]
    F. Kimura, Y. Yamaguchi, Y. Sasaki, K. Kido, and M. Hosaka, “Construction and Uses of an Engineering Data Base in Design and Manufacturing Environments,” File Structures and Data Bases for CAD, North-Holland Publishing Company, Amsterdam, Netherlands, 1982, pp. 95–116.Google Scholar
  23. [Kimura et al. 1983a]
    F. Kimura, T. Sata, and M. Hosaka, “Integration of Design and Manufacturing Activities based on Object Modeling,” Advances in CAD/CAM (PROLAMAT ’82), North-Holland Publishing Company, Amsterdam, Netherlands, 1983, pp. 375–385.Google Scholar
  24. [Kimura et al. 1983b]
    F. Kimura, S. Kawabe, T. Sata, and M. Hosaka, “A Study on Product Modeling for Integration of CAD/CAM,” Integration of CADI CAM, North-Holland Publishing Company, Amsterdam, Netherlands, 1983, pp. 227–251.Google Scholar
  25. [Mäntylä and Sulonen 1982]
    M. Mäntylä and R. Sulonen, “GWB: A Solid Modeler with Euler Operators,” IEEE Computer Graphics and Applications, Vol. 2, No. 7, September 1982, pp. 17–31.CrossRefGoogle Scholar
  26. [Riesenfeld 1973]
    R. F. Riesenfeld, “Application of B-Spline Approximations to Geometric Problems of Computer Aided Design,” Ph.D. Dissertation, Syracuse University, Syracuse, New York, May 1973.Google Scholar
  27. [Sarraga 1983]
    R. F. Sarraga, “Algebraic Methods for Intersection of Quadric Surfaces in GMSolid,” Computer Vision, Graphics, and Image Processing, Vol. 22, No. 2, May 1983, pp. 222–238.CrossRefGoogle Scholar
  28. [Sata et al. 1981]
    T. Sata, F. Kimura, and A. Amano, “Robot Simulation System as a Task Programming Tool,” Proceedings of lSIR, Tokyo, Japan, 1981, pp. 595–602.Google Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • Fumihiko Kimura
    • 1
  1. 1.University of TokyoTokyoJapan

Personalised recommendations