Practical Spherical Embedding of Manifold Triangle Meshes

Gotsman et al. (SIGGRAPH 2003) presented the first method to generate a provably bijective parameterization of a closed genus-0 manifold mesh to the unit sphere. This involves the solution of a large system of non-linear equations. However, they did not show how to solve these equations efficiently, so, while theoretically sound, the method has remained impractical to date. We show why simple iterative methods to solve the equations are bound to fail, and provide an efficient numerical scheme which succeeds. Our method uses a number of optimization methods combined with an algebraic multigrid technique. With these, we are able to spherically parameterize meshes containing up to a hundred thousand vertices in a matter of minutes.

• Type: Conference
• Year: 2005
• Where: SMI
• Authors: Shadi Saba, Irad Yavneh, Craig Gotsman, Alla Sheffer
• Keywords: Efficient Numerical Scheme, Non-linear Equations, Simple Iterative Methods, SMI 2005