2023/07/21 by Shu-Yung Liu, Liu, Shu-Yung, Mei-Heng Yueh +1 · 2 citations
Engineering · #33F05 #3D Shape Modeling and Analysis #52C35 #65D18 #65E10 #68U05 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Manufacturing Process and Optimization #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2307.11363
openalex publication_date 2023/07/21 · openalex created_date 2023/07/25 · openalex updated_date 2026/07/28
An area-preserving parameterization is a bijective mapping that maps a surface onto a specified domain and preserves the local area. This paper formulates the computation of disk area-preserving parameterization as an authalic energy minimization (AEM) problem and proposes a novel preconditioned nonlinear conjugate gradient method for the AEM with guaranteed theoretical convergence. Numerical experiments indicate that our new approach has significantly improved area-preserving accuracy and computational efficiency compared to another state-of-the-art algorithm. Furthermore, we present an application of surface registration to illustrate the practical utility of area-preserving mappings as parameterizations of surfaces.