基于Lagrange-Newton方法的零亏格网格的参数化.pdfVIP

ISSN 1000-9825, CODEN RUXUEW E-mail: jos@ Journal of Software , Vol.18, Supplement, December 2007, pp.8− 17 © 2007 by Journal of Software . All rights reserved. Tel/Fax: +86-10 ∗ 基于 Lagrange-Newton 方法的零亏格网格的参数化 + 李 莹, 杨周旺 , 邓建松 ( 中国科学技术大学 数学系,安徽 合肥 230026) Spherical Parameterization of Genus-Zero Meshes Using the Lagrange-Newton Method + LI Ying, YANG Zhou-Wang , DENG Jian-Song (Department of Mathematics, University of Science and Technology of China, Hefei 230026, China) + Corresponding author: Phn: +86-551-3601009, Fax: +86-551-3601005, E-mail: yangzw@ Li Y, Yang ZW, Deng JS. Spherical parameterization of genus-zero meshes using the Lagrange-Newton method. Journal of Software, 2007,18(Suppl.):8−17. /1000-9825/18/s8.htm Abstract : This paper addresses the problem of spherical parameterization, i.e., mapping a given polygonal surface of genus-zero onto a unit sphere. There exist some methods to deal with the problem in literatures. In this paper, an improved algorithm is constructed for parameterization of genus-zero meshes and aim to obtain high-quality surfaces fitting with PHT-splines. This parameterization consists of minimizing discrete harmonic energy subject to spherical constraints and solving the constrained optimization by the Lagrange-Newton method. Several examples show that parametric surfaces of PHT-splines can be constructed adaptively and efficiently to fit given meshes associated with the parameterization results. Key words: spherical parameterization; genus-zero mesh; discrete harmonic energy; constrained optimization;