Interactive Editing of Discrete Chebyshev Nets

Abstract

AbstractWe propose an interactive method to edit a discrete Chebyshev net, which is a quad mesh with edges of the same length. To ensure that the edited mesh is always a discrete Chebyshev net, the maximum difference of all edge lengths should be zero during the editing process. Hence, we formulate an objective function using ℓp‐norm (p > 2) to force the maximum length deviation to approach zero in practice. To optimize the nonlinear and non‐convex objective function interactively and efficiently, we develop a novel second‐order solver. The core of the solver is to construct a new convex majorizer for our objective function to achieve fast convergence. We present two acceleration strategies to further reduce the optimization time, including adaptive p change and adaptive variables reduction. A large number of experiments demonstrate the capability and feasibility of our method for interactively editing complex discrete Chebyshev nets.