Interactive Editing of Discrete Chebyshev Nets

Abstract
We 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.
Description

CCS Concepts: Computing methodologies --> Shape modeling

        
@article{
10.1111:cgf.14462
, journal = {Computer Graphics Forum}, title = {{
Interactive Editing of Discrete Chebyshev Nets
}}, author = {
Li, Rui-Zeng
and
Guo, Jia-Peng
and
Wang, Qi
and
Chai, Shuangming
and
Liu, Ligang
and
Fu, Xiao-Ming
}, year = {
2022
}, publisher = {
The Eurographics Association and John Wiley & Sons Ltd.
}, ISSN = {
1467-8659
}, DOI = {
10.1111/cgf.14462
} }
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