Optimized design of B-B surface through Bézier geodesic trilateral(过Bézier测地三边形的B-B曲面优化设计)

Abstract

This paper proposed an optimal design algorithm for three end-to-end quintic Bezier curves which satisfy the geodesic trilateral constraints, and interpolates the Bernstein-Bézier parametric surface (referred to as B-B surface) as surface boundary geodesics. The algorithm is realized by determining the surface control points step by step. Firstly, the boundary geodesic interpolation condition is used to determine the two rows of control points of the surface boundary line and adjacent boundary line; Secondly, two methods of minimizing surface Bending energy functional and Dirichlet energy functional are given to optimize the remaining control points of the surface. The constructed B-B surface has a total degree of 8 and has the characteristics of minimum energy optimization. The experimental results show the feasibility and effectiveness of the algorithm.(对满足测地三边形约束的3条首尾相连的五次Bézier曲线，提出了插值以该三边形曲线为曲面边界测地线的Bernstein-Bézier参数曲面（简称B-B曲面）优化设计算法。首先由边界测地线插值条件确定曲面边界线及邻接边界线的2排控制顶点；然后给出极小化曲面Bending能量泛函和Dirichlet能量泛函优化确定曲面内部剩余的控制顶点；通过分步优化方法确定曲面控制顶点实现算法。所构造的B-B曲面全次数为8，具有能量极小最优特性。实验结果表明，算法是可行和有效的。)

Keywords

• bernstein-bézier surface(b-b曲面)
• interpolation(插值)
• geodesic(测地线)
• optimization design(优化设计)