过Bézier三边形测地线的有理多项式Coons曲面片重构  

Reconstruction of rational polynomial Coons surface patches throuth Bézier triangular geodesic

作　　者：王淑娟 杨火根[1] 柴莹 WANG Shu-juan;YANG Huo-gen;CHAI Ying(Faculty of Science,Jiangxi University of Science and Technology,Ganzhou 341000,Jiangxi,China)

机构地区：[1]江西理工大学理学院,江西赣州341000

出　　处：《山东大学学报（理学版）》2022年第6期102-110,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12161043);江西省自然科学基金资助项目(20192BAB201007)。

摘　　要：对满足一定约束的五次Bézier三边形曲线,提出4种有理多项式Coons曲面构造格式,使得所构造的曲面插值三边形曲线为边界测地线。首先,分析插值曲面沿边界测地线的跨界切矢在角点处的相容性约束;其次基于重心坐标表示的有理Hermite多项式基,设计插值两相邻边界测地线的插值算子;最后,给出插值三边形测地线的有理多项式Coons曲面构造格式。本文提出的过Bézier三边形测地线的Coons曲面构造算法简便易实现,计算结果表明算法的可行性。For the quintic Bézier triangular curve that satisfies certain constraints, four rational polynomial Coons surfaces which interpolate the triangular curve as the geodesics is proposed. Firstly, the corner compatibility constraints of the cross-boundary tangent vector of the interpolated surface along the boundary geodesics are analyzed. Secondly, based on the rational Hermite polynomial basis represented by the barycentric coordinate, the interpolation operator for interpolating two adjacent boundary geodesics is designed. Finally, the construction scheme of rational polynomial Coons surface for interpolating triangular geodesics is presented. The construction algorithm of Coons surface through Bézier triangular geodesics proposed in this paper is simple and easy to implement, and the calculation results show the feasibility of the algorithm.

关 键 词：测地线 三角域 COONS曲面 重构 

分 类 号：O241[理学—计算数学]