Parameterization for fitting triangular mesh

作     者：LIN Hongwei**, WANG Guojin, LIU Ligang and BAO Hujun(State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China) 

作者机构：[a]State Key Laboratory of CAD &CG Zhejiang University Hangzhou China 

出 版 物：《Progress in Natural Science:Materials International》 (自然科学进展·国际材料(英文))

年 卷 期：2006年第16卷第11期

页      面：1214-1221页

核心收录：

学科分类：08[工学] 080203[工学-机械设计及理论] 0802[工学-机械工程] 

基　　金：Supported bythe Major State Basic Research Development Programof China (Grant No .2004CB719400)  and National Natural Science Founda-tion of China (Grant Nos .60503057  60333010  60021201) 

主　　题：parameterization regular parametric curve grid mesh fitting reverse engineering. 

摘      要：In recent years, with the development of 3D data acquisition equipments, the study on reverse engineering has become more and more important. However, the existing methods for parameterization can hardly ensure that the parametric domain is rectangular, and the parametric curve grid is regular. In order to overcome these limitations, we present a novel method for parameterization of triangular meshes in this paper. The basic idea is twofold: first, because the isotherms in the steady temperature do not intersect with each other, and are distributed uniformly, no singularity (fold-over) exists in the parameterization; second, a 3D harmonic equation is solved by the finite element method to obtain the steady temperature field on a 2D triangular mesh surface with four boundaries. Therefore, our proposed method avoids the embarrassment that it is impossible to solve the 2D quasi-harmonic equation on the 2D triangular mesh without the parametric values at mesh vertices. Furthermore, the isotherms on the temperature field are taken as a set of iso-parametric curves on the triangular mesh surface. The other set of iso-parametric curves can be obtained by connecting the points with the same chord-length on the isotherms sequentially. The obtained parametric curve grid is regular, and distributed uniformly, and can map the triangular mesh surface to the unit square domain with boundaries of mesh surface to boundaries of parametric domain, which ensures that the triangular mesh surface or point cloud can be fitted with the NURBS surface.