Arrondo Esteban, Enrique and Sendra, Juana and Sendra, J. Rafael
(1997)
*Parametric generalized offsets to hypersurfaces.*
Journal of symbolic computation, 23
.
pp. 267-285.
ISSN 0747-7171

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Official URL: http://www.sciencedirect.com/science/journal/07477171

## Abstract

In this paper we extend the classical notion of offset to the concept of generalized offset to hypersurfaces. In addition, we present a complete theoretical analysis of the rationality and unirationality of generalized offsets. Characterizations for deciding whether the generalized offset to a hypersurface is parametric or it has two parametric components are given. As an application, an algorithm to analyse the rationality of the components of the generalized offset to a plane curve or to a surface, and to compute rational parametrizations of its rational components, is outlined.

Item Type: | Article |
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Uncontrolled Keywords: | Curves |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 14853 |

References: | .|.|Farouki, R.T. (1992). Pythagorean-hodograph curves in practical use, in geometry processing for design and manufacturing. Barnhill, R.E., ed., SIAM, Philadelphia. pp 3{33. .|.|Farouki, R.T., Ne®, C.A. (1990a). Analytic properties of plane o®set curves. Computer Aided Geometric Design 7 83{99. .|.|Farouki, R.T., Ne®, C.A. (1990b). Algebraic properties of plane o®set curves. Computer Aided Geometric Design 7 100{127. .|.|Farouki, R.T., Ne®, C.A. (1997), Hermite interpolation by Pythagorean-hodograph quintics. Math. Comp., to appear. .|.|Farouki, R.T., Sakkalis, T. (1990). Pythagorean hodographs. IBM J. Res. Develop. 34, 736{752. .|.|Harris, J. (1992). Algebraic geometry: a ¯rst course. Springer-Verlag. .|.|Ho®man, C. (1990). Algebraic and numerical techniques for o®sets and blends. Dahmen, W., et al., eds, Computation of Curves and Surfaces. (Kluwer) pp. 499{528. .|.|LÄu, W. (1995a). O®set-rational parametric plane curves, Computer Aided Geometric Design 12, 601{617. .|.|LÄu, W. (1995b). Rational parametrizations of quadrics and their o®sets. Technical Report No. 24, Institut fÄur Geometrie, Technische UniversitÄat Wien. .|.|Pottmann, H., (1995). Rational curves and surfaces with rational o®sets, Computer Aided Geometric Design 12, 175{192. .|.|Pottmann, H., LÄu, W., Ravani, B. (1995). Rational ruled surfaces and their o®sets. Technical Report No. 23, Institut fÄur Geometrie, Technische UniversitÄat Wien. .|.|Salmon, G. (1960). A Treatise on the Higher Plane Curves. New York, Chelsea. .|.|Schicho, J. (1995). Rational Parametrization of Algebraic Surfaces. Symbolic Solution of an equation in three variables. Ph.D. Thesis, University Linz, Austria. .|.|Sendra, J. (1996). M¶etodos Algor¶³tmicos para variedades o®set. Ph.D. Thesis, Universidad de Alcal¶a, Spain. In preparation. .|.|Sendra, J.R., Sendra, J. (1995). On the rationality of o®set curves. Techn. Rep. RISC 95-02 Univ. Linz. .|.|Sendra, J.R., Winkler, F. (1991). Symbolic parametrization of curves. J. Symbolic Computation 12/6, 607{631. .|.|Winkler, F. (1996). Polynomial Algorithms in Computer Algebra. Springer-Verlag, ACM Press. |

Deposited On: | 18 Apr 2012 10:32 |

Last Modified: | 06 Feb 2014 10:10 |

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