Surface Intersections

  • Mamoru Hosaka
Part of the Computer Graphics — Systems and Applications book series (COMPUTER GRAPH.)

Abstract

Interference calculation of surfaces is an important basic procedure in CAD/CAM technology. It appears in various processes such as set operations in solid modelling, surface modelling, cutter path calculation for NC machining, and calculations in robot motion. Efficiency and robustness of its solutions are required especially for those of free-form surfaces, because the degree of intersection curves becomes so high that their analytical methods are generally hopeless and the numerical methods become unstable where the normal vectors of interfering surfaces on their intersecting curves become nearly parallel.

Keywords

Curve Surface Section Curve Tangential Plane Surface Patch Intersection Curve 
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. [1]
    Phillips, M.B., Odel, G.M.: An algorithm for locating and displaying the intersection of two arbitrary surfaces. IEEE Computer Graphics and Applications 9: 48–55, 1984CrossRefGoogle Scholar
  2. [2]
    Dokken, T.: Finding intersections of B-spline represented geometies using recursive subdivision techniques. Computer Aided Geometric Design 2 (1–3): 37–48, 1985MathSciNetGoogle Scholar
  3. [3]
    Pfeifer, H-U.: Methods used for intersecting geometrical entities in the GPM. module for volume geometry. Computer Aided Design 17 (7): 311–318, 1985CrossRefGoogle Scholar
  4. [4]
    Houghton, E.G.: Implementation of a divide-and-conquer method for intersection of parametic surfaces. Computer Aided Geometric Design 2 (1–3): 173–183, 1985MATHCrossRefGoogle Scholar
  5. [5]
    Miller, J.R.: Sculptured surfaces in solid models: issues and alternative approaches. IEEE Computer Graphics and Applications 12: 37–48, 1986CrossRefGoogle Scholar
  6. [6]
    Barnhill, R.E., Farin, G., Jordan, M., Piper, R.R.: Surface/suface intersection. Computer Aided Geometric Design 4 (1–2): 3–16, 1987MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Bajaj, C.L., Hoffmann, C.M., Lynch, R.E.: Tracing surface intersections. Computer Aided Geometric Design 5 (4): 295–307, 1988MathSciNetCrossRefGoogle Scholar
  8. [8]
    Hosaka, M.: *Connection and interference of surfaces. In: Proc. symp. on graphics and CAD’87: IPS Japan 1988, pp. 57–66Google Scholar
  9. [9]
    Hosaka, M., Kushimoto, T., Gonda, H.: *Connection and interference of surfaces. In: Proc. symp. on graphics and CAD’88 IPS Japan: 1988, pp. 121–131Google Scholar
  10. [10]
    Hoffmann, C.M.: Geometric and solid modeling, San Mateo CA: Morgan Kaufmann 1989Google Scholar
  11. [11]
    Higashi, M, Mori, T., Hosaka, M.: Interference calculation of surfaces based on their geometric properties. In: Kimura, F., Rolstadas, A.(eds.): Computer Applications in Production and Engineering CAPE’89: Amsterdam: Elsevier 1989, pp. 275–282Google Scholar
  12. [12]
    Aziz, M.A., Bata, R., Bhat. S.: Bézier surface/surface intersection IEEE Computer Graphics and Applications 1: 50–58, 1990CrossRefGoogle Scholar
  13. [13]
    Hosaka, H., Kushimoto, T.: *New methods of intersection tracing of curves surfaces. In: Proc. symp. on design JSPE: 1990, pp. 1–3, pp. 7–9Google Scholar
  14. [14]
    Stoer, J., Bulirsch, R.: Introduction to numerical analysis. New York: Springer-Verlag 1980Google Scholar
  15. [15]
    Press, W.H., Flannery, B.P., Teukolsky, S. A., Vetterling, W.T.: Numerical recipies in C. Cambridge: Cambridge University Press 1988Google Scholar
  16. [16]
    Burden, R.L., Faires, J.D.: Numerical analysis-4th edition. PWS-ICENT, 1989Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Mamoru Hosaka
    • 1
  1. 1.Tokyo Denki UniversityChiyoda-ku, TokyoJapan

Personalised recommendations