“Multi-Dimensional Function Display Using a Color Scale” by Staudhammer

  • ©John Staudhammer




    Multi-Dimensional Function Display Using a Color Scale


Session Title: Hardware Session



    Similar to the use of color on maps to indicate height information on a two-dimensional display, color can be used to convey a sense of the fourth dimension in a three-dimensional display. The information then appears as a set of color dots arranged in three dimensions. A color display system then shows sections of this assembly, much like a series of stacked colored maps.

    A particularly simple implementation occurs when the fourth-dimension variable is of limited range, such as in the display of complex-variable functions. By showing magnitude of the function as height and phase angles as colors, colored three-dimensional surfaces may be used to depict such functions vividly. The choice of the phase-angle color-scale determines the ease of reading off details from this display.


    1. J. Staudhammer, “Circuit Analysis by Digital Computer,” Prentice-Hall, Inc., 1975.
    2. J. G. Truxal, “Automatic Feedback Control System Synthesis,” McGraw-Hill, Inc., 1955.
    3. H. S. Carslaw and J. C. Jaeger, “Operational Methods in Applied Mathematics,” Oxford University Press, 1953.
    4. J. Staudhammer and D. J. Ogden, “Computer Graphics for Half-Tone Three-Dimensional Object Images,” Computers and Graphics, in print.
    5. J. F. Eastman and J. Staudhammer, “Computer Display of Colored Three-Dimensional Objects,” Proc. Second Annual Symposium on Computer Architecture, Houston, January 1975.
    6. J. F. Eastman and J. Staudhammer, “Interactive Verification of Roadbed Topologies,” presented at this conference.

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