“A parametric algorithm for drawing pictures of solid objects bounded by quadric surfaces” by Levin

  • ©Joshua Z. Levin

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Title:

    A parametric algorithm for drawing pictures of solid objects bounded by quadric surfaces

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Abstract:


    An algorithm for drawing pictures of three-dimensional objects, with surfaces made up of patches of quadric surfaces, is described.The emphasis of this algorithm is calculating the intersections of quadric surfaces. A parameterization scheme is used. Each quadric surface intersection curve (QSIC) is represented as a set of coefficients and parameter limits. Each value of the parameter represents at most two points, and these may easily be distinguished. This scheme can find the co-ordinates of points of even quartic (fourth-order) intersection curves, using equations of no more than second order.Methods of parameterization for each type of QSIC are discussed, as well as surface bounding and hidden surface removal.

References:


    1. Braid, I.C. The synthesis of solids bounded by many faces. Comm. ACM 18, 4 (April 1975), 209-216. 
    2. Comba, P.G. A procedure for detecting intersections of threedimensional objects. J. ACM 15, 3 (July 1968), 354-366. 
    3. Dresden, A. Solid Analytical Geometry and Determinants. Dover, New York, 1964.
    4. Levin, J.Z. A parametric algorithm for drawing pictures of solid objects bounded by quadric surfaces. Tech. Rep. CRL-46, School of Eng., Rensselaer Polytechnic Inst., Troy, N.Y., 1976.
    5. Loutrel, P. A solution to the hidden-line problem for computer-drawn polyhedra. IEEE Trans. Computers C-19, 3 (March 1970), 205-213.
    6. Mahl, R. Visible surface algorithm for quadric patches. IEEE Trans. Computers C-21, (Jan. 1972), 1-4.
    7. Metelli, F. The perception of transparency. Scientific American 230, 4 (April 1974), 90-98.
    8. Newman, W.M., and Sproull, R.F. Principles of Interactive Computer Graphics. McGraw-Hill, New York, 1973, Appendix II, pp. 467–480. 
    9. Bui-Tuong Phong. Illumination for computer generated pictures. Comm. ACM 18, 6 (June 1975), 311-317. 
    10. Weiss, R.A. BE VISION, a package of IBM 7090 FORTRAN programs to draw orthographic views of combinations of plane and quadric surfaces. J. ACM 13, 2 (April 1966), 194-204. 
    11. Woon, P.Y. A computer procedure for generating visible-line drawings of solids bounded by quadric surfaces. Tech. Rep. 403-15, Dep. Electr. Eng., School of Eng. and Sci., New York U., New York, Nov. 1970.
    12. Woon, P.Y., and Freeman, H. A procedure for generating visible-line projections of solids bounded by quadric surfaces. Information Processing 71, Vol. 2, North-Holland Pub. Co., Amsterdam, 1971, pp. 1120-1125.

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