A Low Distortion Mesh Parameterization Mapping Method Based on Proxy Function and Combined Newton

作     者：Cai, Xingquan Feng, Dingwei Cai, Mohan Sun, Chen Sun, Haiyan 

作者机构：North China Univ Technol Sch Informat Sci & Technol Beijing 100144 Peoples R China 

出 版 物：《INTERNATIONAL JOURNAL OF PATTERN RECOGNITION AND ARTIFICIAL INTELLIGENCE》 (国际图形识别与人工智能杂志)

年 卷 期：2022年第36卷第2期

核心收录：

学科分类：08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：National Natural Science Foundation of China Beijing Social Science Foundation [19YTC043, 20YTB011] Yuyou Talent Program in the North China University of Technology [YY19XN132] 

主　　题：Mesh parameterization mapping distortion distortion metric function optimal coordinate points 

摘      要：To address the issues of low efficiencies and serious mapping distortions in current mesh parameterization methods, we present a low distortion mesh parameterization mapping method based on proxy function and combined Newton s method in this paper. First, the proposed method calculates visual blind areas and distortion prone areas of a 3D mesh model, and generates a model slit. Afterwards, the method performs the Tutte mapping on the cut three-dimensional mesh model, measures the mapping distortion of the model, and outputs a distortion metric function and distortion values. Finally, the method sets iteration parameters, establishes a reference mesh, and finds the optimal coordinate points to get a convergent mesh model. When calculating mapping distortions, Dirichlet energy function is used to measure the isometric mapping distortion, and MIPS energy function is used to measure the conformal mapping distortion. To find the minimum value of the mapping distortion metric function, we use an optimal solution method combining proxy functions and combined Newton s method. The experimental data show that the proposed method has high execution efficiency, fast descending speed of mapping distortion energy and stable optimal value convergence quality. When a texture mapping is performed, the texture is evenly colored, close laid and uniformly lined, which meets the standards in practical applications.