Abstract
In this paper, first, we provide a resultant-based implicitization method for revolution surfaces, generated by non necessarily rational curves. Secondly, we analyze the offsetting problem for revolution surfaces, proving that the offsetting and the revolution constructions are commutative. Finally, as a consequence of this, the (total and partial) degree formulas for the generic offset to an irreducible plane curve, given in our previous papers, are extended to the case of offsets to surfaces of revolution.
This work has been partially supported by Research Project MTM2008-04699-C03-01 of the Spanish Ministerio de Ciencia e Innovación.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Agoston, M.K.: Computer Graphics and Geometric Modeling: Implementation and Algorithms. Springer, Heidelberg (2005)
Arrondo, E., Sendra, J., Sendra, J.R.: Parametric generalized offsets to hypersurfaces. Journal of Symbolic Computation 23(2-3), 267–285 (1997)
Cox, D.A., Little, J.B., O’Shea, D.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 2nd edn. Springer, Heidelberg (1997)
Farin, G.E.: Curves and Surfaces for CAGD: A Practical Guide. Morgan Kaufmann, San Francisco (2001)
Harris, J.: Algebraic Geometry: A First Course. Springer, Heidelberg (1992)
Patrikalakis, N.M., Maekawa, T.: Shape Interrogation for Computer Aided Design and Manufacturing. Springer, Heidelberg (2002)
San Segundo, F., Sendra, J.R.: Degree formulae for offset curves. J. Pure Appl. Algebra 195(3), 301–335 (2005), doi:10.1016/j.jpaa.2004.08.026
San Segundo, F., Sendra, J.R.: The offset degree problem for surfaces of revolution. In: Proceedings of the XIth Encuentro de Algebra Computacional y Aplicaciones(EACA 2008), Universidad de Granada, pp. 65–68 (2008)
San Segundo, F., Sendra, J.R.: Partial degree formulae for plane offset curves. Journal of Symbolic Computation 44(6), 635–654 (2009), doi:10.1016/j.jsc.2008.10.002
Sendra, J.R., Sendra, J.: Algebraic analysis of offsets to hypersurfaces. Mathematische Zeitschrift 234(4), 697–719 (2000)
Sendra, J.R., Winkler, F., Pérez-Díaz, S.: Rational Algebraic Curves—A Computer Algebra Approach. Springer, Heidelberg (2007)
van der Waerden, B.L.: Algebra. Springer, Heidelberg (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
San Segundo, F., Sendra, J.R. (2011). Offsetting Revolution Surfaces. In: Sturm, T., Zengler, C. (eds) Automated Deduction in Geometry. ADG 2008. Lecture Notes in Computer Science(), vol 6301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21046-4_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-21046-4_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21045-7
Online ISBN: 978-3-642-21046-4
eBook Packages: Computer ScienceComputer Science (R0)