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 the paper, we construct an improved algorithm 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. We also present several examples which show that parametric surfaces of PHT-splines can be constructed adoptively and efficiently to fit given meshes associated with our parameterization results.