Gn blending multiple surfaces in polar coordinates

Authors:
Kan-Le Shi;Jun-Hai Yong;Jia-Guang Sun;Jean-Claude Paul
Affiliations:
School of Software, Tsinghua University, Beijing 100084, PR China and Department of Computer Science and Technology, Tsinghua University, Beijing 100084, PR China and Key Laboratory for Informatio ...;School of Software, Tsinghua University, Beijing 100084, PR China and Key Laboratory for Information System Security, Ministry of Education of China, Beijing 100084, PR China and Tsinghua National ...;School of Software, Tsinghua University, Beijing 100084, PR China and Key Laboratory for Information System Security, Ministry of Education of China, Beijing 100084, PR China and Tsinghua National ...;School of Software, Tsinghua University, Beijing 100084, PR China and Key Laboratory for Information System Security, Ministry of Education of China, Beijing 100084, PR China and Tsinghua National ...
Venue:
Computer-Aided Design
Year:
2010

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Abstract

This paper proposes a method of G^n 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.