“An interactive computer graphics approach to surface representation” by Wu, Abel and Greenberg

  • ©Sheng-Chuan Wu, John F. Abel, and Donald P. Greenberg

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Title:

    An interactive computer graphics approach to surface representation

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Abstract:


    An interactive computer graphics method has been developed for the rapid generation of arbitrary shaped three-dimensional surfaces. The method is a synthesis of spline theory and algorithms, an interactive means for man-machine communication, and software for static or dynamic graphics display. The basic technique employed is a modified lofting method in which sectional curves are represented by uniform B-splines and the surface is interpolated between sections by Cardinal splines. Among the features of this method are algorithm, which enable interactive modification of the B-spline representation of the sectional curves. At all stages of the process, the spatial information is graphically displayed to the user. Complex surfaces can be created by the combination of a number of shapes that have been separately generated and automatically joined. The system has been successfully interfaced to a variety of analytical routines for structural, medical and graphical applications.

References:


    1. Ahlberg, J.H., Nilson, E.N., and Walsh, J.L. The Theory of Splines and Their Applications. Academic Press, New York, 1967.
    2. Bezier, P. Numerical Control, Mathematics and Applications. Wiley, London, 1972.
    3. Coons, S.A. Surfaces for computer-aided design of space forms. MAC-TR-41, Proj. MAC, M.I.T., Cambridge, Mass., June 1967. 
    4. Forrest, A.R. Mathematical principles for curve and surface representation. Proc. Conf. on Curved Surfaces in Engineering, Cambridge, England, March 1972, pp. 5-13.
    5. Gordon, W.J. Spline-blended surface interpolation through curve networks. J. Math. Mech. 18, 10 (1969), 931-952.
    6. Gordon, W.J., and Riesenfeld, R.F. B-spline curves and surfaces. Computer Aided Geometric Design, R.E. Barnhill and R.F. Riesenfeld, Eds., Academic Press, New York, 1974, pp. 95- 126.
    7. Greenberg, D.P. An interdisciplinary laboratory for graphics research and applications. Proc. Fourth Annual Conf. on Computer Graphics, Interactive Techniques, and Image Processing, July 1977, pp. 90-97 (available from ACM, New York). 
    8. Riesenfeld, R.F. “Applications of B-spline approximation to geometric problems of computer aided design,” Ph.D. Th., Syracuse U., Syracuse, N.Y., 1973. 
    9. Rogers, D.F., and.Adams, J.A., Mathematical Elements for Computer Graphics. McGraw-Hill, New York, 1976. 

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