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Gn blending multiple surfaces in polar coordinates

Kan-Le Shi 1 Jun-Hai yong 1 Jia-Guang Sun 1, 2 Jean-Claude Paul 2 
2 CAD - Computer Aided Design
LIAMA - Laboratoire Franco-Chinois d'Informatique, d'Automatique et de Mathématiques Appliquées, Inria Paris-Rocquencourt
Abstract : This paper proposes a method of Gn blending multiple parametric surfaces in polar coordinates. It models the geometric continuity conditions of parametric surfaces in polar coordinates and presents a mechanism of converting a Cartesian parametric surface into its polar coordinate form. The basic idea is first to reparameterize the parametric blendees into the form of polar coordinates. Then they are blended simultaneously by a basis function in the complex domain. To extend its compatibility, we also propose a method of converting polar coordinate blending surface into N NURBS patches. One application of this technique is to fill N-sided holes. Examples are presented to show its feasibility and practicability.
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Kan-Le Shi, Jun-Hai yong, Jia-Guang Sun, Jean-Claude Paul. Gn blending multiple surfaces in polar coordinates. Computer-Aided Design, Elsevier, 2010, 42 (6), pp.479-494. ⟨10.1016/j.cad.2009.11.009⟩. ⟨inria-00517941⟩

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