Multi-sided Coons patches based on generalized barycentric coordinates

doi:10.3785/j.issn.1008-973X.2024.02.007

Journal of ZheJiang University (Engineering Science)

2024, Vol. 58

Issue (2): 288-293 DOI: 10.3785/j.issn.1008-973X.2024.02.007

Multi-sided Coons patches based on generalized barycentric coordinates

Chuanjiang LUO(

),Yajuan LI,Chongyang DENG*(

)

School of Science, Hangzhou Dianzi University, Hangzhou 310018, China

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Abstract

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.

Key words： Coons patch generalized barycentric coordinate polygonal domain hole-filling

Received: 15 July 2023 Published: 23 January 2024

CLC:

TP 391

Fund: 国家自然科学基金资助项目(61872121)

Corresponding Authors: Chongyang DENG E-mail: lcj1201@hdu.edu.cn;dcy@hdu.edu.cn

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Cite this article:

Chuanjiang LUO,Yajuan LI,Chongyang DENG. Multi-sided Coons patches based on generalized barycentric coordinates. Journal of ZheJiang University (Engineering Science), 2024, 58(2): 288-293.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2024.02.007 OR https://www.zjujournals.com/eng/Y2024/V58/I2/288

基于广义重心坐标的多边形域Coons面片

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.

关键词： Coons面片, 广义重心坐标, 多边形域, 补洞

Fig.1 Boundary curves and corner points of quadrilateral patches

Fig.2 Construction of bilinear Coons patch

Fig.3 Pentagon domain and triangles defining Wachspress coordinates

Fig.4 Contour lines of Wachspress coordinate

Fig.5 Correspondence between boundary curves of quadrilateral patches

Fig.6 Correspondence between boundary curves of multi-sided patches

Fig.7 “Fill the holes” with MGC patches

Fig.8 “Fill the holes” with MC patches

Fig.9 Gaussian curvature diagram

Tab.1 Comparison of average calculation time between two methods under different models


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