Computer Graphics Tools for Rendering Algebraic Surfaces and for Geometry of Order

  • Thomas F. Banchoff
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 17)


New developments in interactive computer graphics make it possible for mathematicians to approach old subjects in fresh ways. Occasionally the new approaches reveal additional insights into things already well understood from other viewpoints. This note give several examples of projects developed in collaboration with undergraduate students at Brown University in courses related to differential geometry. In each case, computer graphics techniques are used to investigate some geometric phenomenon, and in each case the difficulties encountered by the program reveal some feature of geometric interest.


Computer Graphic Algebraic Surface Projection Direction Interactive Computer Graphic Quartic 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.


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  1. 1.
    Banchoff, T. and Kuiper, N., Geometrical class and degree for surfaces in three space, J. Diff. Geom. 16 (1981), 559–576.MATHMathSciNetGoogle Scholar
  2. 2.
    Fisher, G. (Editor), “Mathematical Models; Commentary,” Vieweg-Verlag, Braunschweig/Wiesbaden, 1986.Google Scholar
  3. 3.
    Goursat, E., Étude des surfaces qui admettent tous les plans de symétrie d’un polyèdre régulier, Ann. Sci. Ec. Norm. Sup. (3) 4 (1987), 159–200.MathSciNetGoogle Scholar
  4. 4.
    Hirzebruch, F., Singularities of algebraic surfaces and characteristic numbers, Max Planck Inst, für Math. (1984 Bonn).Google Scholar
  5. 5.
    Juel, C., Die elementare ringfläche vierter Ordnung, D. Kgl. Danske Vidensk. Selsk. Skrifter, naturvidensk. og mathem. afd. 8, Raekke 1.4 (1916), 182–197.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • Thomas F. Banchoff
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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