Interactive Editing of Discrete Chebyshev Nets
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Date
2022
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
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}
}