Direct Spherical Parameterization of 3D Triangular Meshes Using Local Flattening Operations

Abstract

In this paper, we propose a novel spherical parameterization approach for closed, genus-0, two-manifold, 3D triangular meshes. The method exploits a modified version of the Gaussian curvature, associated to the model vertices. Valid spherical embeddings are obtained by locally flattening the mesh in an iterative manner, which makes it possible to convert the initial mesh into a rounded, sphere-like surface that can be directly mapped onto the unit sphere. Our approach shows superior performances with respect to state of the art techniques, with a reduction in terms of angular and area distortions of more than 35% and 19% respectively.