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Issue No.05 - September/October (1990 vol.10)
pp: 12-21
ABSTRACT
<p>A survey of some techniques that may have potential for free-form modeling with algebraic surfaces is continued. Classical results as well as several recent innovations are included. Specific attention is paid to cubic algebraic surfaces, although many of the ideas presented have application to algebraic surfaces of any degree. Topics addressed include piecewise constructions, interpolation to points and space curves, and parameterization.</p>
CITATION
Thomas W. Sederberg, "Techniques for Cubic Algebraic Surfaces", IEEE Computer Graphics and Applications, vol.10, no. 5, pp. 12-21, September/October 1990, doi:10.1109/38.59032
REFERENCES
1. T.W. Sederberg, "Techniques for Cubic Algebraic Surfaces, Part One,"CG&A, Vol. 10, No. 4, July 1990, pp. 14-25.
2. J. Warren,On Algebraic Surfaces Meeting with Geometric Continuity, doctoral dissertation, Cornell Univ., Ithaca, N.Y., 1986.
3. T.W. Sederberg, "Piecewise Algebraic Surface Patches,"Computer Aided Geometric Design, Vol. 2, Nos. 1-3, Sept. 1985, pp. 53-59.
4. T.W. Sederberg, "Planar Piecewise Algebraic Curves,"Computer Aided Geometric Design, Vol. 1, No. 3, Dec. 1984, pp. 241-255.
5. P. Alfeld, "A Trivariate Clough-Tocher Scheme for Tetrahedral Data," Tech. Report 2702, Mathematics Research Center, Univ. of Wisconsin, Madison, Wis., 1984.
6. A. Geisow,Surface Interrogations, doctoral dissertation, Univ. of East Anglia, Norwich, U.K., 1983.
7. N.M. Patrikalakis and G.A. Kriezis, "Representation of Piece-wise Continuous Algebraic Surfaces in Terms of B-Splines,"The Visual Computer, Vol. 5, No. 6, Dec. 1989, pp. 360-374.
8. W. Dahmen, "Smooth Piecewise Quadric Surfaces," inMathematical Methods in Computer Aided Geometric Design, T. Lyche and L.L. Schumaker, eds., Academic Press, Boston, 1989, pp. 181-193.
9. T.W. Sederberg and J.P. Snively, "Parametrization of Cubic Algebraic Surfaces," inThe Mathematics of Surfaces II, R.R. Mar tin, ed., Clarendon Press, Oxford, U.K., 1987, pp. 299-319.
10. S.S. Abhyankar and C. Bajaj, "Automatic Parametrization of Rational Curves and Surfaces II: Cubics and Cubicoids,"Computer-Aided Design, Vol. 19, No. 9, Nov. 1987, pp. 499-502.
11. A. Henderson,The Twenty-Seven Lines Upon the Cubic Surface, Cambridge Univ. Press, Cambridge, U.K., 1911.
12. J. Warren, "The Effect of Base Points on Rational Bezier Surfaces," Tech. Report TR90-122, Computer Science Dept., Rice Univ., Houston, Texas, 1990.
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