Optimized design of Bezier surface through Bezier geodesic quadrilateral

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:273

Article

Yang, Huogen^1,2  Wang, Guozhao¹ 

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[2] Jiangxi Univ Sci & Technol, Fac Sci, Ganzhou 341000, Peoples R China

关键词: Bezier surface;    Interpolation;    Geodesic quadrilateral;    Optimized design;   

DOI  :  10.1016/j.cam.2014.06.017

来源: Elsevier

【 摘 要 】

This paper studies constructing polynomial Bezier surface that interpolates a Bezier curvilinear quadrilateral as boundary geodesics. The construction consists of two parts. First, from the given corner data (i.e., position, tangent and curvature at the corner of each curve), four quintic Bezier curvilinear quadrilateral with minimum strain energy is constructed to satisfy the constraints of the crossing geodesics on a surface. Second, a polynomial Bezier surface of degree (7,7) is constructed to interpolate the quadrilateral as boundary geodesics of the constructed surface. We identify the precise degrees of freedom in terms of the control points. And the constructed surface that adheres to the NURBS standard and employs geometric shape handles can be readily incorporated into commercial CAD systems. The method is illustrated by several computational examples. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free