矩阵权NURBS曲面的拟合与光顺  

Fitting and fairing quad-meshes by matrix weighted NURBS surfaces

作　　者：董国鑫 杨勋年[1] DONG Guoxin;YANG Xunnian(School of Mathematical Sciences,Zhejiang University,Hangzhou 310058,China)

机构地区：[1]浙江大学数学科学学院,浙江杭州310058

出　　处：《浙江大学学报（理学版）》2023年第6期820-827,共8页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(12171429).

摘　　要：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。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 recalculating vertex normals based on the new quad meshes iteratively.

关 键 词：矩阵权NURBS 曲面拟合 光顺 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]