Direct Spherical Parameterization Based on Surface Curvature

In this paper we propose a novel spherical parameterization for closed, genus-0, two-manifold, 3D triangular meshes. The key point of our method concerns the Gaussian curvature criterion involved, which makes it possible to detect iteratively salient mesh vertices and to locally flatten them, until a sphere-like surface, adapted to a direct spherical parameterization is obtained. The experimental evaluation, carried out on a set of 3D models of various shapes and complexities, shows that the proposed method makes it possible to reduce both angle and area distortions with more than 78% and 40% respectively.