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《Journal of Nanjing University of Aeronautics & Astronautics》 1993-05
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On the Geometric Continuity between Adjacent Rational Bezier Surface Patches

Kang Baosheng Zhou Rurong (Etepartment of Mechanical Engineering)  
Geometric continuity (GCk-Continuity) is widely recognized as the appropriate way to fit together two adjacent surface patches in CAGD. It avoids dependence on the parametrizetion and provides additional parameters for modelling the shapes. This paper considers two adjacent rational Bezier surface patches with a common boundary edge along which they have to join smoothly. We give the explicit representations of GC1 continuity conditions,and GC1 adjudging conditions. In terms of these conditions,a simple and small program can be written that takes as input the Bezier points and weights of the two patches, and produces as output either "Yes" or "No".indicating the presence or absence of a common tangent plane. For the case of non-GC1 continuity,the given conditions provide an approach which can be used to modify the two patches symmetrically so as to obtain GC1 smoothly compositive surf aces. Furthermore, some sufficient conditions for practical application are developed.
【Fund】: 国家自然科学基金
【CateGory Index】: O18;;TB115
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