“An application of color graphics to the display of surface curvature” by Dill

  • ©John C. Dill

Conference:


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Title:

    An application of color graphics to the display of surface curvature

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Abstract:


    In developing a mathematical representation for a surface, designers currently must use line drawing graphics to examine the curvature of a line in a plane, a two-dimensional analysis. By combining a result from differential geometry with the use of color raster graphics, the method described in this paper provides a means for the designer to examine surface curvature, a three-dimensional analysis. In particular, a formulation for the Gaussian and average curvatures is given and it is shown how these indicate the presence or absence of protrusions, hollows, etc. in a surface, i.e., how, where, and by how much the surface curves. Showing a fourth variable, curvature in this case, over a three-dimensional surface is difficult, if not impossible with traditional line drawing computer graphics. The method described solves this problem by using color as a fourth dimension. Examples are given, including both known shapes (torus) and automotive parts (hood, fender).

References:


    1. Forrest, A.R. “On the rendering of surfaces.” SIGGRAPH ’79 Proceedings 13(2), August 1979.
    2. Jones, J.I. “A system for designing and approximating aesthetically smooth curves with interactive graphic controls.” Ph.D. Thesis, U. of Detroit, 1970.
    3. Gordon, W.J. “Spline-blended surface interpolation through curve networks.” J. Math. & Mechanics 18(10), 931-952, 1969.
    4. Struik, D.J. Differential Geometry. Addison-Wesley, Cambridge, 1950.
    5. Christiansen, H. “Application of continuous tone computer generated images in structural mechanics.” In: Structural Mechanics Computer Programs – Surveys, Assessments and Availability (Pilkey, Saczalski and Schaefler, eds.), U. Press of Virginia, 1974.
    6. Rodriguez, R.N. “Multivariate Burr III distributions. Part I. Theoretical properties.” Research Publication GMR-3232, General Motors Research Laboratories, Warren, Michigan, 1980.
    7. Dill, J.C. “An overview of CADANCE – a computer graphics system at General Motors.” Research Publication GMR-3150, General Motors Research Laboratories, Warren, Michigan, 1980.


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