Basic Theory of Surfaces

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


Quadric surfaces, especially bodies of revolution such as spheres, cylinders, cones, or also ruled surfaces have been widely used in engineering products. This is because their geometric properties are easily specified by their designers and the shapes are easily manufactured by machines. On the other hand, free-form surfaces have only been used in special cases and their design and manufacture have required special talent and skill. But in recent years their uses have increased because of strong demands for high performance and aesthetic quality in engineering products. And computers have been used for their design and manufacture. Accordingly, various mathematical expressions of free-forms for engineering use have been developed.


Basic Vector Tangent Vector Gaussian Curvature Principal Curvature Principal Direction 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Coxeter, H.S.M.: Introduction to geometry. 2nd edition, John Wiley 1969Google Scholar
  2. [2]
    Hosaka, M.: *Theory of curve and surface synthesis and their smooth fitting. J. IPS Japan 10 (3): 121–131, 1969Google Scholar
  3. Hosaka, M.: English abstract, Information Processing in Japan 9: 60–68, 1969MathSciNetMATHGoogle Scholar
  4. [3]
    Enomoto, H. et al.: *Computer experiment on global properties of structure lines of images using graphic display and its consideration). J. IPS Japan 17 (7): 641–649, 1976Google Scholar
  5. [4]
    Kajiya, J.T.: Ray tracing parametric patches. Computer Graphics (Proc. Siggraph’82) 16 (3): 224–254, 1984Google Scholar
  6. [5]
    Sederberg, T.W., Anderson, D.C., Goldman, R.N.: Implicit representation of parametric curves and surfaces. Computer Vision, Graphics and Image Processing 28: 72–84, 1984CrossRefGoogle Scholar
  7. [6]
    Goldman, R.N., Sederberg, T.W., Anderson, D.C.: Vector elimination: a technique for implicitization, inversion and intersection of planar parametric rational polynomial curves. Computer Aided Geometric Design 1 (4): 327–356, 1984MATHCrossRefGoogle Scholar
  8. [7]
    Sederberg, T.W.: Planar piecewise algebraic curves. Computer Aided Geometric Design 1 (3): 241–255, 1984MATHCrossRefGoogle Scholar
  9. [8]
    Poeschle, R.: Detecting surface irregularities using isophotes. Computer Aided Geometric Design 1 (2): 163–168, 1984CrossRefGoogle Scholar
  10. [9]
    Tiller, W., Hanson, E.G.: Offsets of two-dimensional profiles. IEEE Computer Graphics and Applications 9: 36–46, 1984CrossRefGoogle Scholar
  11. [10]
    Satterfield, S.D., Rogers, D.F.: A procedure for generating contour lines from a B spline surface. IEEE Computer Graphics and Applications 4: 71–75, 1985CrossRefGoogle Scholar
  12. [11]
    Farouki, R., Rajan, V.: Exact offset procedures for simple solids. Computer Aided Geometric Design 2 (4): 257–294, 1985MATHCrossRefGoogle Scholar
  13. [12]
    Beck, J.M., Farouki, R.T., Hind, J.K.: Surface analysis methods. IEEE Computer Graphics and Applications 6 (12): 18–36, 1986CrossRefGoogle Scholar
  14. [13]
    Klok, F.: Two moving coordinate frames for sweeping along 3D trajectory. Computer Aided Geometric Design 3 (3): 217–229, 1986MathSciNetMATHCrossRefGoogle Scholar
  15. [14]
    Farouki, R.: The approximation of non-degenerate offset surface. Computer Aided Geometric Design 2 (1): 15–44, 1986CrossRefGoogle Scholar
  16. [15]
    Rossignac, J.R., Requicha, A.A.G.: Offsetting operations in solid modelling. Computer Aided Geometric Design 3 (2): 129–148, 1986MATHCrossRefGoogle Scholar
  17. [16]
    Stoer, J., Bulirsch, R.: Introduction to numerical analysis. New York: Springer-Verlag 1980Google Scholar
  18. [17]
    Press, W. H., Flannery, B.P., Teukolsky, S.A., Vetterling W.T.: Numerical Recipies in C Cambridge: Cambridge University Press 1988Google Scholar
  19. [18]
    Higashi, M., Kushimoto, T., Hosaka, M.: On formulation and display for visualizing features and evaluating quality of free-form surfaces. In: Vandoni, C.E., Duce, D.A.(eds): Proc. Eurographics’90 1990, pp. 299–309Google Scholar
  20. [19]
    Love, A.E.H.: Treatise on the mathematical theory of elasticity. Cambridge: Cambridge University Press 1934, pp. 401–410Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

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

Personalised recommendations