Numerical implicitization of parametric hypersurfaces with linear algebra

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1930, Issue , 2001, Pages 174-183

  Corless, Robert M ^a   Giesbrecht, Mark W ^a   Kotsireas, Ilias S ^a   Watt, Stephen M ^a  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; LINEAR ALGEBRA;

HUMAN INTERACTIONS; HYPER-SURFACES; IMPLICITIZATION; NUMERICAL LINEAR ALGEBRA; PARAMETRIC CURVE; PARAMETRIC REPRESENTATIONS;

NUMERICAL METHODS;

EID: 84974686158     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44990-6_13     Document Type: Conference Paper

References (28)

1. Shreeram S. Abhyankar and Chanderjit L. Bajaj. Automatic parameterization of rational curves and surfaces iii: Algebraic plane curves. Computer Aided Geometric Design, 5: 309-321, 1988.
2. Cesar Alonso, Jaime Gutierrez, and Tomas Recio. An implicitization algorithm with fewer variables. Computer Aided Geometric Design, 12(3): 251-258, 1995.
3. Bruno Buchberger. Applications of gröbner bases in non-linear computational geometry. In J. R. Rice, editor, Mathematical Aspects of Scientific Software, volume 14 of IMA Volumes in Mathematics and its applications, pages 59-87. Springer-Verlag, 1988.
4. Eng-Wee Chionh and Ronald N. Goldman. Degree, multiplicity, and inversion formulas for rational surfaces usingu -resultants. Computer Aided Geometric Design, 9: 93-108, 1992.
5. George Fix, Chih-Ping Hsu, and Tie Luo. Implicitization of rational parametric surfaces. Journal of Symbolic Computation, 21: 329-336, 1996.
6. Xiao-Shan Gao. Conversion between implicit and parametric representations of algebraic varieties. In Mathematics Mechanization and Applications, Academic Press, pages 1-17, 2000. personal communication, to appear.
7. Xiao-Shan Gao and Shang-Ching Chou. Implicitization of rational parametric equations. Journal of Symbolic Computation, 14: 459-470, 1992.
8. Laureano González-Vega. Implicitization of parametric curves and surfaces by usingm ultidimensional newton formulae. Journal of Symbolic Computation, 23: 137-151, 1997.
9. Gene H. Golub and Charles Van Loan. Matrix Computations. Johns Hopkins, 3rd edition, 1995.
10. L. González-Vega and G. Trujillo. Implicitization of parametric curves and surfaces by usings ymmetric functions. In A.H.M. Levelt, editor, Proc. ISSAC-95, ACM Press, pages 180-186, Montreal, Canada, july 1995.
11. John D. Hobby. Numerically stable implicitization of cubic curves. ACM Transactions on Graphics, 10(3): 255-296, 1991.
12. Christoph M. Hoffmann. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann Publishers, Inc. California, 1989.
13. Hoon Hong. Implicitization of nested circular curves. Journal of Symbolic Computation, 23: 177-189, 1997.
14. Hoon Hong and Josef Schicho. Algorithms for trigonometric curves (simplification, implicitization, parameterization). Journal of Symbolic Computation, 26: 279-300, 1998.
15. Michael Kalkbrener. Implicitization of rational parametric curves and surfaces. In S. Sakata, editor, Proc. AAECC-8, volume 508 of Lecture Notes in Computer Science, pages 249-259, Tokyo, Japan, august 1990.
16. Ziming Li. Automatic implicitization of parametric objects. Mathematics-Mechanization Research Preprints, 4: 54-62, 1989.
17. Sandra Licciardi and Teo Mora. Implicitization of hypersurfaces and curves by the primbasissatz and basis conversion. In Mark Giesbrecht and Joachim von zur Gathen, editors, Proc. ISSAC-94, ACM Press, pages 191-196, Oxford, England, april 1994.
18. Dinesh Manocha and John F. Canny. Algorithm for implicitizing rational parametric surfaces. Computer Aided Geometric Design, 9: 25-50, 1992.
19. Dinesh Manocha and John F. Canny. Implicit representation of rational parametric surfaces. Journal of Symbolic Computation, 13: 485-510, 1992.
20. T. W. Sederberg, D. C. Anderson, and R. N. Goldman. Implicit representation of parametric curves amd surfaces. Computer Vision, Graphics, and Image Processing, 28: 72-84, 1984.
21. T. W. Sederberg, D. C. Anderson, and R. N. Goldman. Implicitization, inversion, and intersection of planar rational cubic curves. Computer Vision, Graphics, and Image Processing, 31: 89-102, 1985.
22. Josef Schicho. Rational parametrization of surfaces. Journal of Symbolic Computation, 26(1): 1-30, 1998.
23. Thomas Sederberg, Ron Goldman, and Hang Du. Implicitizing rational curves by the method of movingalg ebraic curves. Journal of Symbolic Computation, 23(2-3): 153-175, 1997.
24. Thomas W. Sederberg, Takafumi Saito, Dongxu Qi, and Krzysztof S. Klimaszewski. Curve implicitization usingmo vinglin es. Computer Aided Geometric Design, 11(6): 687-706, 1994.
25. J.R. Sendra and F. Winkler. Symbolic parametrization of curves. Journal of Symbolic Computation, 12(6): 607-631, 1991.
26. J.R. Sendra and F. Winkler. Real parametrization of algebraic curves. In J. Calmet and J. Plaza, editors, Proc. AISC’98, volume 1476 of Lecture Notes in Artificial Intelligence, pages 284-295, Plattsburgh, New York, USA, september 1998.
27. John L. Troutman. Variational Calculus with Elementary Convexity. Undergraduate Texts in Mathematics. Springer-Verlag, New York, 1983.
28. Dongming Wang. Reasoning about geometric problems using an elimination method. In Jochen Pfalzgraf and Dongming Wang, editors, Automated Practical Reasoning Algebraic Approaches, Lecture Notes in Computer Science, pages 147-185, Tokyo, Japan, 1995.