基于Lagrange-Newton 方法的零亏格网格的参数化

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.

Spherical Parameterization of Genus-Zero Meshes Using the Lagrange-Newton Method

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.