Canal Surfaces Defined by Quadratic Families of Spheres
- 1.1k Downloads
This paper is devoted to quadratic canal surfaces, i.e. surfaces that are envelopes of quadratic families of spheres. They are generalizations of Dupin cyclides but are more flexible as blending surfaces between natural quadrics. The classification of quadratic canal surfaces is given from the point of view of Laguerre geometry. Their properties that are important for geometric modeling are studied: rational parametrizations of minimal degree, Bézier representations, and implicit equations.
KeywordsRational Parametrization Minimal Degree Double Point Geometric Design Isotropic Line
Unable to display preview. Download preview PDF.
- 1.Degen, W., Cyclides, in Handbook of Computer Aided Geometric Design, 2002, p.575-601Google Scholar
- 2.M. Kazakevičiutė , Classification of pairs of natural quadrics from the point of view of Laguerre geometry, Lithuanian Mathematical Journal, 45 (2005), 63–84.Google Scholar
- 3.Krasauskas, R., Minimal rational parametrizations of canal surfaces, Computing, to ap-pear.Google Scholar
- 4.Krasauskas, R. and M. Kazakevičiūtė , Universal rational parametrizations and spline curves on toric surfaces, in: Computational Methods for Algebraic Spline Surfaces, ESF Exploratory Workshop, Springer, 2005, pp. 213-231.Google Scholar