- ABB+92.E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Cruz, A. Greenbaum, S. Hammarling, and D. Sorensen. LA ira CK User's Guide, Release 1.0. SIAM, Philadelphia, 1992. Google ScholarDigital Library
- AS86.W. Auzinger and H.J. Stetter. An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations. In International Series of Numerical Mathematics, volume 86, pages 11-30, 1986.Google Scholar
- BDM89.Z. Bai, J. Demmel, and A. McKenney. On the conditioning of the nonsymmetric eigenproblem: Theory and software. Computer Science Dept. Technical Report 469, Courant Institute, New York, NY, October 1989. (LA- PACK Working Note # 13).Google Scholar
- Ber75.D.N. Bernshtein. The number of roots of a system of equations. Funktsional'nyi A noliz i Ego Prilozheniila, 9(3):1-4, 1975.Google Scholar
- BGW88.C. Bajaj, T. Garrity, and J. Warren. On the applications of multi-equational resultants. Technical Report CSD-TR-826, Department of Computer Science, Purdue University, 1988.Google Scholar
- Can88.J.F. Canny. The Complexity of Robot Motion Planning. ACM Doctoral Dissertation Award. MIT Press, 1988. Google ScholarDigital Library
- CE93.J. Canny and I. Emiris. An efficient algoritllm for the sparse mixed resultant. In Proceedings o.f AAECC, 1993. To appear. Google ScholarDigital Library
- Cra89.J.J. Craig. Introduction to Robotics" Mechanics and Control. Addison-Wesley Publishing Company, 1989. Google ScholarDigital Library
- Dix08.A.L. Dixon. The eliminant of three qualities in two independent variables. Proceedings of London Mathematical Society, 6:49-69, 209-236, 1908.Google Scholar
- GKZ90.I.M. Gelfand, M.M. Kapranov, and A.V. Zelevinsky. Newton polytopes of the cl.x~sical resultant and discriminant. Advances in Mathematics, 84:237-254, 1990.Google ScholarCross Ref
- GL89.G.H. Golub and C.F. Van Loan. Matrix Computations. John Hopkins Press, Baltimore, 1989.Google Scholar
- GLR82.I. Gohberg, P. Lancaster, and L. R odman. Matrix Polynomials. Academic Press, New York, 1982.Google Scholar
- Gol91.D. Goldberg. What every computer scientist should know about floating point arithmetic. ACM Computing Surveys, 23(1):5-48, 1991. Google ScholarDigital Library
- Hof89.C.M. Hoffmann. Geometric and Solid ~llodeling. Morgan Kaufmann, San Mateo, California, 1989. Google ScholarDigital Library
- Hof90.C.M. Hoffmann. A dimensionality paradigm for surface interrogations. Computer Aided Geometric Design, 7:517-532, 1990. Google ScholarDigital Library
- Kaj82.J. Kajiya. Ray tracing parametric patches. Computer Graphics, 16(3):245--254, 1982. Google ScholarDigital Library
- Kra91.G.A. Kramer. Using degrees of freedom analysis to solve geometric constraint system. In Proceedings o/SI/mposium on Solid Modeling Foundationz and CAD/CAM Applications, pages 37'1-378, 1991. Google ScholarDigital Library
- LBD+92.D. Lavender, A. Bowyer, J. Davenport, A. Wallis, and J. Woodwark. Voronoi diagrams of set-theoretic solid models. IEEE Computer Graphics and Applications, pages 69-77, September 1992. Google ScholarDigital Library
- Mac02.F.S. Macaulay. On some formula in elimination. Proceedings ojf London Mathematical Society, pages 3-27, May 1902.Google Scholar
- Man92.D. Manocha. Algebraic and Numeric Techniques .{or Modeling and Robotics. PhD thesis, Computer Science Division, Department of Electrical Engineering and Computer Science, University of California, Berkeley, May 1992. Google ScholarDigital Library
- MC27.F. Morley and A.B. Cable. New results in elimination. American Journal of Mathematics, 49:463-488, 1927.Google ScholarCross Ref
- MC91.D. Manocha and J.F. Canny. A new approach for surface intersection. International Journal of Computational Geometry and Applications, 1(4):491--516, 1991. Special issue on Solid Modeling.Google ScholarCross Ref
- MD92.D. Manocha and J. Demmel. Algorithms for intersecting parametric and algebraic curves. In Graphics Interlace '9~, pages 232-241, 1992. Also available as technical report UCB/CSD 92/698, Computer Science Division, University of California at Berkeley. Google Scholar
- Mor92.A.P. Morgan. Polynomial continuation and its relationship to the symbolic reduction of polynomial systems. In Symbolic and Numerical Computation for Artificial Intelligence, pages 23-45, 1992.Google Scholar
- NSK90.T. Nishita, T.W. Sederberg, and M. Kakimoto. Ray tracing trimmed rational sudace patches. Computer Graphics, 24(4):337-345, 1990. Google ScholarDigital Library
- Owe91.J.C. Owen. Algebraic solution for geometry from dimensional constraints. In Proceedings of Symposium on Solid Modeling Foundations and CAD/CAM Applications, pages 397-407, 1991. Google ScholarDigital Library
- RR92.A.A.G. Requicha and J.R. Rossignac. Solid modeling and beyond. IEEE Computer Graph. ics and Applications, pages 31-44, September 1992. Google ScholarDigital Library
- Sal85.G. Salmon. Lessons lntroducto~ to the Modern Higher Algebra. G.E. Stechert & Co., New York, 1885.Google Scholar
- Sed83.T.W. Sederberg. Implicit and Parametric Curves and Surfaces. PhD thesis, Purdue University, 1983. Google ScholarDigital Library
- SP86.T.W. Sederberg and S.R. Parry. Comparison of three curve intersection algorithms. Computer.Aided Design, 18(1):58--63, 1986. Google ScholarCross Ref
- Ste76.G.W. Stewaxt. Simultaneous iteration for computing invaxiant subspaces of non-hermitian m~trices. Numerische Mathematik, 25:123- 136, 1976.Google ScholarDigital Library
- Stu91.B. Sturmfels. Spaxse elimination theory. In D. Eisenbud and L. Robbiano, editors, Compu. tational Algebraic Geomet~ and Commutative Algebra. Cambridge University Press, 1991.Google Scholar
- SZ92.B. Sturmfels and A. Zelevinsky. Multigraded resultants of sylvester type. Journal of Algebra, 1992.Google Scholar
- Wil59.J.H. Wilkinson. The evaluation of the zeros of ill-conditioned polynomials, parts i and ii. Numer. Math., 1:150-166 and 167-180, 1959.Google ScholarDigital Library
Index Terms
- Solving polynomial systems for curve, surface and solid modeling
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