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

  • ©Joshua Z. Levin




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



    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.


    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.

ACM Digital Library Publication:

Overview Page: