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浙江大学学报（理学版）
Journal of Zhejiang University (Science Edition)  2023, Vol. 50 Issue (6): 820-828    DOI: 10.3785/j.issn.1008-9497.2023.06.017
CSIAM-GDC 2023     
Fitting and fairing quad-meshes by matrix weighted NURBS surfaces
Guoxin DONG,Xunnian YANG()
School of Mathematical Sciences，Zhejiang University，Hangzhou 310058，China
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Abstract  

This paper proposes to employ matrix weighted NURBS surfaces to fit and fair quad meshes. For a quadrilateral mesh with given or estimated unit normals at vertices, a matrix weighted NURBS surface can be constructed by choosing the mesh vertices as control points and employing normals at each vertex for computing matrix weights. Compared with traditional NURBS surfaces, matrix weighted NURBS surfaces have quasi-cylindrical accuracy. When the input data is uniformly sampled from a smooth surface, the constructed matrix weighted NURBS surface has good smoothness and fits the mesh model well; if the input grid data contain noise, a fair fitting surface that approximates the original grid well can still be obtained by resampling control vertices on current fitting surfaces and re-calculating vertex normals based on the new quad meshes iteratively.

Key words： matrix weighted NURBS      surface fitting      fairing     
Received: 21 June 2023      Published: 30 November 2023
CLC:  TP 391  
Corresponding Authors: Xunnian YANG     E-mail: yxn@zju.edu.cn
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Guoxin DONG
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Cite this article:

Guoxin DONG,Xunnian YANG. Fitting and fairing quad-meshes by matrix weighted NURBS surfaces. Journal of Zhejiang University (Science Edition), 2023, 50(6): 820-828.

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https://www.zjujournals.com/sci/EN/Y2023/V50/I6/820


矩阵权NURBS曲面的拟合与光顺

介绍了利用矩阵权非均匀有理 B-spline（non-uniform rational B-spline，NURBS）曲面拟合与光顺带法向的网格数据。通过输入带法向的规则四边形网格，以网格的顶点为曲面的控制顶点，用法向信息计算每个控制顶点对应的矩阵权，构造矩阵权NURBS曲面。与传统NURBS曲面相比，矩阵权NURBS曲面具有拟柱面精度，当数据均匀采样自光滑曲面时，构造的矩阵权NURBS曲面具有较好的光顺性且能很好地拟合网格模型；当输入的网格数据掺杂噪声时，通过迭代在已有的矩阵权NURBS曲面上重新采样顶点和计算法向量构造新的矩阵权NURBS曲面，最后得到具有较好光顺性且仍能逼近原始网格数据的拟合曲面。


关键词： 矩阵权NURBS,  曲面拟合,  光顺 
Fig.1 The matrix weighted NURBS surface is used to fit the mesh sampled from a cylinderNote The number pair （i， j） represents the degree of the B-spline basis function in the parameter u and v directions respectively. （a） and （b） are bicubic matrix weighted NURBS surfaces fitted to cylindrical meshes with and without noise， respectively； （c） and （d） are the fitting results of matrix weighted NURBS surfaces with bi-degree five or bi-degree seven， respectively.
Fig.2 The matrix weighted NURBS surface
Fig.3 Fitting and fairing a noise plane
Fig.4 Fitting and fairing an ear mesh model by matrix weighted NURBS surfaces
Fig.5 Fitting and fairing a head model by matrix weighted NURBS surfaces
Fig.6 Fitting and fairing a tooth model by matrix weighted NURBS surface
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