Chebyshev Nets from Commuting PolyVector Fields

Albert Chern
TU Berlin
Amir Vaxman
Utrecht University

We propose a method for computing global Chebyshev nets on triangular meshes. We formulate the corresponding global parameterization problem in terms of commuting PolyVector fields, and design an efficient optimization method to solve it. We compute, for the first time, Chebyshev nets with automatically-placed singularities, and demonstrate the realizability of our approach using real material.

A.O. Sageman-Furnas and A. Chern were supported by the DFG Collaborative Research Center TRR 109 Discretization in Geometry and Dynamics. M. Ben-Chen acknowledges funding from the European Research Council (ERC starting grant No. 714776 OPREP). Additional support was provided by SideFX software.