MIRELA BEN-CHEN, Israel Institute of Technology, Israel
Chebyshev Nets on Discrete Surfaces
From gridshells to fruit packaging, quad meshes with uniform edge lengths are often needed in surface modeling. The analogous smooth mathematical structure is called a Chebyshev net.
In this talk I will present a new method to compute a Chebyshev net approximating an input triangle mesh. The net is allowed to have point singularities, which end up as irregular vertices in the resulting quad mesh. We formulate the problem using global parameterization with commuting (Poly)vector fields (as opposed to the commonly used curl-free fields), and design and solve efficiently the corresponding optimization problem. We compute, for the first time, Chebyshev nets with automatically-placed point singularities, and demonstrate the realizability of our approach using real material.
Joint work with Andrew O. Sageman-Furnas, Albert Chern and Amir Vaxman.