Qiu, Di and Lam, Ka-Chun and Lui, Lok-Ming (2019) Computing Quasi-Conformal Folds. SIAM Journal on Imaging Sciences, 12 (3). pp. 1392-1424. ISSN 1936-4954. doi:10.1137/18m1220042. https://resolver.caltech.edu/CaltechAUTHORS:20191017-145048101
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Abstract
Computing surface folding maps has numerous applications ranging from computer graphics to material design. In this work we propose a novel way of computing surface folding maps via solving a linear PDE. This framework is a generalization of the existing computational quasi-conformal geometry and allows precise control of the geometry of folding. This property comes from a crucial quantity that occurs as the coefficient of the equation, namely, the alternating Beltrami coefficient. This approach also enables us to solve an inverse problem of parametrizing the folded surface given only partial data with known folding topology. Various interesting applications such as fold sculpting on 3 dimensional models, study of Miura-ori patterns, and self-occlusion reasoning are demonstrated to show the effectiveness of our method.
| Item Type: | Article | |||||||||
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| Alternate Title: | Computing quasiconformal folds | |||||||||
| Additional Information: | © 2019 Society for Industrial and Applied Mathematics. Received by the editors October 10, 2018; accepted for publication (in revised form) May 2, 2019; published electronically August 13, 2019. Funding: The work of the authors was supported by the Hong Kong Research Grants Council GRF project 2130549. The first author would like to thank Mr. Leung Liu Yusan and Dr. Emil Saucan for some useful help and discussions in the early stage of this work. The examples' meshes are generated by the software Triangle [20]. | |||||||||
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| Subject Keywords: | Beltrami equation, quasi-conformal geometry, mathematical origami, fold modeling | |||||||||
| Issue or Number: | 3 | |||||||||
| Classification Code: | AMS subject classifications: 65D18, 68U05, 65D17 | |||||||||
| DOI: | 10.1137/18m1220042 | |||||||||
| Record Number: | CaltechAUTHORS:20191017-145048101 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20191017-145048101 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 99338 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 19 Oct 2019 04:42 | |||||||||
| Last Modified: | 16 Nov 2021 17:45 |
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