基于径向基函数的网格光滑变形  

Smooth mesh deformation based on radial basis function

作　　者：廖海岳 陈仁杰 LIAO Haiyue;CHEN Renjie(School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]中国科学技术大学数学科学学院,合肥230026

出　　处：《中国科技论文》2023年第7期735-740,共6页China Sciencepaper

基　　金：国家自然科学基金资助项目(62072422);安徽省自然科学基金资助项目(2008085MF195)。

摘　　要：三角网格编辑中,高扭曲面片通常集中分布于控制点附近,且控制点附近三角面片的几何扭曲程度随其与控制点间距离的增大而降低。针对这一现象,结合网格变形中控制点分布通常具有的稀疏性,提出一种无需引入额外能量项的光滑变形算法。该算法结合以控制点为中心的径向基函数(radial basis function,RBF),设计了一种加权能量积分。实验结果显示,对比现有算法,使用本文算法优化所得曲面上的扭曲更趋于均匀分布,控制点附近集中出现高扭曲面片的现象得到有效缓解;该算法能够有效提高变形后网格在控制点附近的质量,同时算法的局部性亦可保证计算量与控制点数量相当;与已有能量光顺算法相比,该算法更简单,且计算复杂度更低;相较于不做光顺处理的结果,全局扭曲能量的下降不受光顺处理的影响。Control vertices are embbeded in high-distortion patches,of which distortion abates as the distance increases in mesh editing.In our study of this phenomenon,a smooth editing approach without introducing an additional energy regulation term is presented in view of the sparseness of control vertices over the mesh.We purposed a novel energy integration weighted by control-vertex centered radial basis function(RBF).Experimental results show that the distortion on the optimized surface using the presented method tends to be more evenly distributed.In contrast to the existing methods,our method substaintially alleviates distortions surrouding control vertices.Results manifest that our approach can effectively improve the quality of the region near control points.The control-vertex centered local weighting also ensures that the cost of calculation is comparative to the number of control points.Compared with the state-of art energy smoothing method,our approach barely induces extra time consumption in each Newton iteration,and is straightforward to implement with reliable stability.Meanwhile,the smoothing process won’t hinder the original energy descending.

关 键 词：几何优化 网格编辑 能量光顺 局部权重 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]