Abstract
We propose a symbolic computation algorithm for computing local parametrization of analytic branches and real analytic branches of a curve in n-dimensional space, which is defined by implicit polynomial equations. The algorithm can be used in space curve tracing near a singular point, as an alternative to symbolic computations based on resolutions of singularities.
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References
E. Armando, A. Giovini and G. Niesi. CoCoA User’s Manual, (v. 1.5). Dipartimento di Matematica, Università di Genova, 1991.
A. D. Bruno and A. Soleev. The local uniformization of branches of a curve. Preprint IHES 34, 1990.
P. Cellini, P. Gianni and C. Traverso. Shape of Curves and Surfaces: the Combinatorics In Computer Graphics and Mathematics,EurographicSeminar Series, Springer-Verlag, eds. B. Falcidieno, I. Herman and C. Pienovi, 1992 (present book).
P. Cellini, P. Gianni and C. Traverso. Algorithms for the shape of semialgebraic sets. A new approach. In Proc. AAECC 9, number 539 in Lect. Notes in Comp. Sci., pages 1–18. Springer-Verlag, 1991.
C.L. Bajaj, C.M. Hoffmann, R.E. Lynch and J.E. Hoperoft. Tracing surfaces intersections. Computer Aided Geometric Design, 5: 285–307, 1988.
F. Cucker, L. Pardo, T. Recio, M.F. Roy and M. Raimondo. On the computation of the local and global branches of real algebraic curves. In Proc. AAECC 6, number 356 in Lect. Notes in Comp. Sci., pages 161–181. Springer-Verlag, 1989.
A. Giovini and G. Niesi. CoCoA: A User-Friendly System for Commutative Algebra. In Proc. DISCO 90, number 429 in Lect. Notes in Comp. Sci., pages 20–29. Springer-Verlag, 1990.
W. Groebner. Algebraische Geometrie. Bibliographisches Institut Mannheim, 196870.
C.M. Hoffmann. Algebraic curves. In Mathematical aspects of Scientific Software, number 14 in IMA Volumes in Mathematics and Applications, pages 101–122. Springer-Verlag, 1988.
G. Cardanus jr. POSSO: a report on the expected state of the art in POlynomial System SOlving. in preparation.
Y. Lakshman. On the complexity of computing Groebner bases for zero dimensional polynomial ideals. PhD thesis, Rensselaer Polytechnique Institute, 1991.
W.D. MacMillan. A method for determining the solutions of a system of analytic functions in the neighborhood of a branch point. Math.Ann., 72: 180–202, 1912. 6
J. Maurer. Puiseux expansions for space curves. Manuscripta Math., 32: 91–100, 1980.
T. Mora, G. Pfister, and C. Traverso. An introduction to the tangent cone algorithm. In Issuses in robotics and non-linear geometry. JAI Press, 1991.
T. Mora and C. Traverso. Representing algebraic numbers by Groebner bases. Proc. MEGA 92. (submitted).
C. Traverso. Communication at the workshop Computing in Algebraic Geometry. Cortona, 1991.
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© 1992 EUROGRAPHICS The European Association for Computer Graphics
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Alonso, M.E., Mora, T., Niesi, G., Raimondo, M. (1992). Local Parametrization of Space Curves at Singular Points. In: Falcidieno, B., Herman, I., Pienovi, C. (eds) Computer Graphics and Mathematics. Focus on Computer Graphics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77586-4_5
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DOI: https://doi.org/10.1007/978-3-642-77586-4_5
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