The Community for Technology Leaders
RSS Icon
Issue No.01 - January/February (1993 vol.13)
pp: 79-88
<p>The role of implicit curves and surfaces in computer-aided geometric design (CAGD) are described. The ways in which the study of implicit algebraic curves and surfaces draws on algebraic geometry are reviewed. The implicitization of parametric curves and surfaces, parameterization of implicits, and techniques used to circumvent conversions between implicit and parametric representations are discussed.</p>
Christoph M. Hoffmann, "Implicit Curves and Surfaces in CAGD", IEEE Computer Graphics and Applications, vol.13, no. 1, pp. 79-88, January/February 1993, doi:10.1109/38.180121
1. T.W. Sederberg,Implicit and Parametric Curves and Surfaces for Computer-Aided Geometric Design, doctoral dissertation, Purdue Univ., West Lafayette, Ind., 1983.
2. D. Moore and J. Warren, "Bounded Aspect Ratio Triangulation of Smooth Solids,"Proc. ACM Symp. Foundations of Solid Modeling and CAD/CAM Applications, Austin, Texas, 1991, pp. 455-464.
3. T. Varady, "Rolling Ball Blends in Solid Modeling," inComputer Applications in Production and Engineering, F. Kimura and A. Rolstadas, eds., North Holland, Amsterdam, 1989, pp. 295-308.
4. E. Allgower and S. Gnutzmann, "An Algorithm for Piecewise Linear Approximation of Implicitly Defined Two-Dimensional Surfaces,"SIAM J. Numerical Analysis, Vol. 24, 1987, pp. 452-469.
5. C. Bajaj and J. Ihm, "Hermite Interpolation of Rational Space Curves Using Real Algebraic Surfaces,"Proc. 5th An. ACM Symp. Computational Geometry, Austin, Texas, 1989, pp. 94-103.
6. J. Bloomenthal, "Polygonization of Implicit Surfaces,"Computer-Aided Geometric Design, Vol. 5, 1988, pp. 341-355.
7. W. Dahmen and T.-M. Thamm-Schaar, "Cubicoids: Modeling and Visualization,"Computer-Aided Geometric Design, in press.
8. B. Guo,Modeling Arbitrary Smooth Objects with Algebraic Surfaces, PhD thesis, Dept. of Computer Sciences, Cornell University, 1991.
9. J. Warren, "Blending Algebraic Surfaces,"ACM Trans. Graphics, Vol. 8, 1989, pp. 263-278.
10. S. Abhyankar,Algebraic Geometry for Scientists and Engineers, Mathematical Surveys and Monographs, Vol. 35, American Mathematical Soc., Providence, R.I., 1990.
11. C. M. Hoffmann,Geometric and Solid Modeling: An Introduction. Los Altos, CA: Morgan Kaufmann, 1989.
12. D. Kapur and Y.N. Lakshman, "Elimination Methods: An Introduction," inSymbolic and Numerical Computation: An Integration, B. Donald, D. Kapur, and J. Mundy, eds., Academic Press, New York, 1992.
13. D. Manocha and J. Canny, "Implicitization of Rational Parametric Surfaces," inThe Mathematics of Surfaces(Proc. 4th IMA Conf., 1990), Oxford University Press, England, to appear.
14. J. Gutierrez and T. Recio, "Rational Function Decomposition and Gröbner Bases in the Parameterization of Plane Curves," tech. report, Dept. of Math, University of Cantabria, Santander, Spain, 1991.
15. G. Salmon,Lessons Introductory to the Modern Higher Algebra, G.E. Stechert, New York, 1885.
16. B. Buchberger, "Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory," inMultidimensional Systems Theory, N.K. Bose, ed., D. Reidel Publishing Co., Dordrecht, Germany, 1985, pp. 184-232.
17. M. Kalkbrenner, "Implicitization of Rational Parametric Curves and Surfaces," tech. report, RISC Linz, Linz, Austria, 1990.
18. J. Faugere et al., "Efficient Computation of Zero-Dimensional Gröbner Bases by Change of Ordering," Report 89-52, Lab. Informatique Theorique et Progr., University of Paris 7, July 1989.
19. Wu Wen-Tsün, "Basic Principles of Mechanical Theorem Proving in Geometries,"J. Systems Sciences and Mathematical Sciences, Vol. 4, 1986, pp. 207-235.
20. D. Manocha and J. Canny, "Implicit Represenations of Rational Parametric Surfaces,"J. Symbolic Computation, Vol. 13, 1992, pp. 485-510.
21. D. Manocha and J. Canny, "A New Approach for Surface Intersection,"Int'l J. Computational Geometry and Applications, Vol. 1, No. 4, Dec. 1991, pp, 491-516.
22. C.M. Hoffmann, "Algebraic and Numerical Techniques for Offsets and Blends," inComputations of Curves and Surfaces, S. Micchelli, M. Gasca, and W. Dahmen, eds., Kluwer Academic, Boston, 1990, pp. 499-528.
23. J.-H. Chuang,Surface Approximations in Geometric Modeling, doctoral dissertation, Purdue Univ., West Lafayette, Ind., 1990.
24. W.C. Rheinboldt, "On a Moving-Frame Algorithm and the Triangulation of Equilibrium Manifolds," inBifurcation: Analysis, Algorithms, Applications, T. Küpper, R. Seydel, and H. Troger, eds., Birkhäuser Verlag, Basel, Switzerland, 1987, pp. 256-267.
21 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool