Covering rational ruled surfaces
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- by J. Rafael Sendra, David Sevilla and Carlos Villarino PDF
- Math. Comp. 86 (2017), 2861-2875
Abstract:
We present an algorithm that covers any given rational ruled surface with two rational parametrizations. In addition, we present an algorithm that transforms any rational surface parametrization into a new rational surface parametrization without affine base points and such that the degree of the corresponding maps is preserved.References
- William W. Adams and Philippe Loustaunau, An introduction to Gröbner bases, Graduate Studies in Mathematics, vol. 3, American Mathematical Society, Providence, RI, 1994. MR 1287608, DOI 10.1090/gsm/003
- Carlos Andradas and Tomás Recio, Plotting missing points and branches of real parametric curves, Appl. Algebra Engrg. Comm. Comput. 18 (2007), no. 1-2, 107–126. MR 2280313, DOI 10.1007/s00200-006-0032-7
- Y.-B. Bai, J.-H. Yong, C.-Y. Liu, X.-M. Liu, and Y. Meng, Polyline approach for approximating Hausdorff distance between planar free-form curves, Comput.-Aided Des. 43 (2011), no. 6, 687–698.
- Chandrajit L. Bajaj and Andrew V. Royappa, Finite representations of real parametric curves and surfaces, Internat. J. Comput. Geom. Appl. 5 (1995), no. 3, 313–326. MR 1339190, DOI 10.1142/S0218195995000180
- Xiao Shan Gao and Shang-Ching Chou, On the normal parameterization of curves and surfaces, Internat. J. Comput. Geom. Appl. 1 (1991), no. 2, 125–136. MR 1132800, DOI 10.1142/S0218195991000116
- X.-D. Chen, W. Ma, G. Xu, and J.-C. Paul, Computing the Hausdorff distance between two B-spline curves, Comput.-Aided Des. 42 (2010), 1197–1206.
- David Cox, John Little, and Donal O’Shea, Ideals, varieties, and algorithms, 3rd ed., Undergraduate Texts in Mathematics, Springer, New York, 2007. An introduction to computational algebraic geometry and commutative algebra. MR 2290010, DOI 10.1007/978-0-387-35651-8
- Y.-J. Kim, Y.-T. Oh, S.-H. Yoon, M.-.S Kim, and G. Elber, Precise Hausdorff distance computation for planar freeform curves using biarcs and depth buffer, Vis. Comput. 26 (2010), nos. 6–8, 1007–1016.
- Li-Yong Shen and Sonia Pérez-Díaz, Characterization of rational ruled surfaces, J. Symbolic Comput. 63 (2014), 21–45. MR 3165726, DOI 10.1016/j.jsc.2013.11.003
- A. Seidenberg, Constructions in algebra, Trans. Amer. Math. Soc. 197 (1974), 273–313. MR 349648, DOI 10.1090/S0002-9947-1974-0349648-2
- J. Rafael Sendra, Normal parametrizations of algebraic plane curves, J. Symbolic Comput. 33 (2002), no. 6, 863–885. MR 1921714, DOI 10.1006/jsco.2002.0538
- J. Rafael Sendra, David Sevilla, and Carlos Villarino, Covering of surfaces parametrized without projective base points, ISSAC 2014—Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2014, pp. 375–380. MR 3239949, DOI 10.1145/2608628.2608635
- J. Rafael Sendra, David Sevilla, and Carlos Villarino, Some results on the surjectivity of surface parametrizations, Computer algebra and polynomials, Lecture Notes in Comput. Sci., vol. 8942, Springer, Cham, 2015, pp. 192–203. MR 3335575, DOI 10.1007/978-3-319-15081-9_{1}1
- Dongming Wang, A simple method for implicitizing rational curves and surfaces, J. Symbolic Comput. 38 (2004), no. 1, 899–914. MR 2094561, DOI 10.1016/j.jsc.2004.02.004
Additional Information
- J. Rafael Sendra
- Affiliation: Department of Physics and Mathematics, Research Group asynacs, University of Alcalá, E-28871 Alcalá de Henares, Madrid, Spain
- MR Author ID: 260673
- Email: Rafael.Sendra@uah.es
- David Sevilla
- Affiliation: University Center of Mérida, University of Extremadura, Av. Santa Teresa de Jornet 38, E-06800 Mérida, Badajoz, Spain
- MR Author ID: 700228
- Email: sevillad@unex.es
- Carlos Villarino
- Affiliation: Department of Physics and Mathematics, Research Group asynacs, University of Alcalá, E-28871 Alcalá de Henares, Madrid, Spain
- MR Author ID: 683262
- Email: Carlos.Villarino@uah.es
- Received by editor(s): October 20, 2014
- Received by editor(s) in revised form: April 26, 2016
- Published electronically: March 3, 2017
- © Copyright 2017 by the authors
- Journal: Math. Comp. 86 (2017), 2861-2875
- MSC (2010): Primary 14Q10, 68W30
- DOI: https://doi.org/10.1090/mcom/3193
- MathSciNet review: 3667027