RT Journal Article T1 Parametric generalized offsets to hypersurfaces A1 Arrondo Esteban, Enrique A1 Sendra, Juana A1 Sendra, J. Rafael AB 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. PB Academic Press SN 0747-7171 YR 1997 FD 1997-03-02 LK https://hdl.handle.net/20.500.14352/57182 UL https://hdl.handle.net/20.500.14352/57182 LA eng NO .|.|Farouki, R.T. (1992). Pythagorean-hodograph curves in practical use, in geometry processing for designand 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 GeometricDesign 7 83{99..|.|Farouki, R.T., Ne®, C.A. (1990b). Algebraic properties of plane o®set curves. Computer Aided GeometricDesign 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, InstitutfÄur Geometrie, Technische UniversitÄat Wien..|.|Pottmann, H., (1995). Rational curves and surfaces with rational o®sets, Computer Aided GeometricDesign 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 inthree 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. NO DGICYT NO Universidad de Alcalá NO DGICYT DS Docta Complutense RD 28 abr 2024