基于广义重心坐标的多边形域Coons面片  

Multi-sided Coons patches based on generalized barycentric coordinates

作　　者：罗川疆 李亚娟[1] 邓重阳[1] LUO Chuanjiang;LI Yajuan;DENG Chongyang(School of Science,Hangzhou Dianzi University,Hangzhou 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《浙江大学学报（工学版）》2024年第2期288-293,共6页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金资助项目(61872121)。

摘　　要：为了提高曲面“补洞”效率,提出多边形域Coons面片,继承了构造双线性Coons面片的布尔和方法,是双线性Coons曲面在凸多边形域上的直接推广.利用双线性坐标改写双线性Coons面片,将参数域推广到凸多边形域,用凸多边形域上的广义重心坐标代替矩形域上的双线性坐标,构造多边形域Coons面片.理论推导和数值算例表明,所提的多边形域Coons面片具有边界插值性,构造简单,计算高效,能够部分解决“补洞”问题.The concept of multi-sided Coons patches was introduced to enhance the efficiency of surface‘hole-filling’,which leverage the Boolean sum methodology of bilinear Coons patches and serve as a direct extension of bilinear Coons patches within the polygonal domain.The bilinear Coons patches were reformulated by using bilinear coordinates.The parameter domain was expanded to encompass a convex polygonal domain.The bilinear coordinates on the rectangular domain were replaced by generalized barycentric coordinates on the convex polygonal domain,thereby facilitating the construction of the multi-sided Coons patches.Theoretical derivations and numerical examples demonstrate that the proposed multi-sided Coons patches possess boundary interpolation properties,offer straightforward construction methodologies,exhibit high computational efficiency,and provide a partial resolution to the hole-filling problem.

关 键 词：Coons面片 广义重心坐标 多边形域 补洞 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]