| 摘要: |
| 考虑零亏格网格的球面参数化问题,即将给定的零亏格多边形曲面一一映射到单位球面上.已有一些方法解决该问题.针对应用PHT 样条进行曲面拟合的需要,对于给定的零亏格网格,提供了一个改进的算法.这种参数化方法主要包含两部分:一是限制在球面约束条件下,极小化离散调和能量;二是使用Lagrange-Newton 方法求解带约束的优化问题.几个例子演示了参数化的结果,并且说明了应用该参数化结果,能够用PHT 样条曲面更好地拟合给定网格曲面. |
| 关键词: 球面参数化 零亏格网格 离散调和能量 带约束的优化问题 Lagrange-Newton 方法 |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant Nos.60533060, 60473132, 10626049, 10701069 (国家自然科学基金); the National Basic Research Program of China under Grant No.2004CB318000 (国家重点基础研究发展计划(973)); the Natural Science Foundation of Anhui Province of China under Grant No.070416230 (安徽省自然科学基金) |
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| Spherical Parameterization of Genus-Zero Meshes Using the Lagrange-Newton Method |
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LI Ying,YANG Zhou-Wang,DENG Jian-Song
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| 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 Lagrange-Newton method |
