B\'ezier Surfaces with Special Coordinate Curve Nets
Received:August 30, 2019  Revised:October 22, 2019
Key Word: B\'ezier surfaces   coordinate curve nets   curvature coordinate nets   shape constraints  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11801490; 11671068; 11501488).
Author NameAffiliation
Lanyin SUN School of Mathematics and Statistics, Xinyang Normal University, Henan 464000, P. R. China 
Chungang ZHU School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
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      B\'ezier surfaces play an important role in Computer-aided Geometric Design (CAGD), and coordinate curve nets are widely discussed in differential geometry. In this paper, we study the B\'ezier surfaces with special coordinate curve nets, such as orthogonal coordinate net, curvature coordinate net and asymptotic coordinate net. In addition, we develop the B\'ezier surfaces which satisfy some shape constraints with the help of energy terms. Moreover, some applicable sufficient conditions based on geometrical structure of control nets are deduced and several representative examples are given.
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