Feature Preserving Parameterization for Quadrilateral Mesh Generation Based on Ricci Flow and Cross Field  

作　　者：Na Lei Ping Zhang Xiaopeng Zheng Yiming Zhu Zhongxuan Luo 

机构地区：[1]International School of Information Science and Engineering,Dalian University of Technology,Dalian,116000,China [2]School of Mathematical Sciences,Dalian University of Technology,Dalian,116000,China [3]School of Software Technology,Dalian University of Technology,Dalian,116000,China

出　　处：《Computer Modeling in Engineering & Sciences》2023年第10期843-857,共15页工程与科学中的计算机建模（英文）

基　　金：supported by NSFC Nos.61907005,61720106005,61936002,62272080.

摘　　要：We propose a newmethod to generate surface quadrilateralmesh by calculating a globally defined parameterization with feature constraints.In the field of quadrilateral generation with features,the cross field methods are wellknown because of their superior performance in feature preservation.The methods based on metrics are popular due to their sound theoretical basis,especially the Ricci flow algorithm.The cross field methods’major part,the Poisson equation,is challenging to solve in three dimensions directly.When it comes to cases with a large number of elements,the computational costs are expensive while the methods based on metrics are on the contrary.In addition,an appropriate initial value plays a positive role in the solution of the Poisson equation,and this initial value can be obtained from the Ricci flow algorithm.So we combine the methods based on metric with the cross field methods.We use the discrete dynamic Ricci flow algorithm to generate an initial value for the Poisson equation,which speeds up the solution of the equation and ensures the convergence of the computation.Numerical experiments show that our method is effective in generating a quadrilateral mesh for models with features,and the quality of the quadrilateral mesh is reliable.

关 键 词：Quadrilateral mesh feature preserving Ricci flow cross field 

分 类 号：O17[理学—数学]