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Construction of Cubic Triangular Patches with $C^1$ Continuity around a Corner  

Zhang, Renjiang (Department of Mathematics, College of Science, China Jiliang University)
Liu, Ligang (Department of Mathematics, Zhejiang University)
Wang, Guojin (Department of Mathematics, Zhejiang University)
Ma, Weiyin (Department of Manufacturing Engr. and Engr. Management, City University of Hong Kong)
Publication Information
International Journal of CAD/CAM / v.6, no.1, 2006 , pp. 149-156 More about this Journal
Abstract
This paper presents a novel approach for constructing a piecewise triangular cubic polynomial surface with $C^1$ continuity around a common corner vertex. A $C^1$ continuity condition between two cubic triangular patches is first derived using mixed directional derivatives. An approach for constructing a surface with $C^1$ continuity around a corner is then developed. Our approach is easy and fast with the virtue of cubic reproduction, local shape controllability, $C^2$ continuous at the corner vertex. Some experimental results are presented to show the applicability and flexibility of the approach.
Keywords
Triangular patches; vertex consistency problem; $C^1$ continuity; interpolation;
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