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Canal Surfaces Defined by Quadratic Families of Spheres

Chapter

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.

Keywords

Rational Parametrization Minimal Degree Double Point Geometric Design Isotropic Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2008

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