THE DESIGN OF BEZIER SURFACE THROUGH QUINTIC BEZIER ASYM PTOTIC QUADRILATERAL  

作　　者：Hui Wang Chungang Zhu Caiyun Li 

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China [2]School of Mathematical and Physical Sciences,Dalian University of Technology,Panjin 124221,China

出　　处：《Journal of Computational Mathematics》2019年第5期721-738,共18页计算数学（英文）

基　　金：The authors are grateful to the reviewers for their helpful comments and suggestions. This work is partly supported by the National Natural Science Foundation of China (Nos. 11671068, 11271060, 11401077).

摘　　要：The asymptotic curve is widely used in astronomy, mechanics and numerical optimization. Moreover, it shows great application potentials in architecture. We focus on the problem how to cover bounded asymptotic curves by a freeform surface. The paper presents the necessary and sufficient conditions for quadrilateral with non-inflection being asymptotic boundary curves of a surface. And then, with given corner data, we model quintic Bezier asymptotic quadrilateral interpolated by a smooth Bezier surface of bi-eleven degree. We handle the available degrees of freedom during the construction to get an optimized result. Some representative surfaces bounded by asymptotic curves with lines or inflections are also discussed by examples. The presented interpolation scheme for the construction of tensor-product Bezier surfaces is compatible with the CAD systems.

关 键 词：ASYMPTOTIC CURVES BEZIER SURFACE INTERPOLATION QUADRILATERAL 

分 类 号：O1[理学—数学]