Practical Fabrication of Discrete Chebyshev Nets

We propose a computational and practical technique to allow home users to fabricate discrete Chebyshev nets for various 3D models. The success of our method relies on two key components. The first one is a novel and simple method to approximate discrete integrable, unit‐length, and angle‐bounded fra...

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Bibliographic Details
Published in:Computer graphics forum 2020-10, Vol.39 (7), p.13-26
Main Authors: Liu, Hao‐Yu, Liu, Zhong‐Yuan, Zhao, Zheng‐Yu, Liu, Ligang, Fu, Xiao‐Ming
Format: Article
Language:English
Subjects:
Algorithms
Approximation
CCS Concepts
Chebyshev approximation
Computing methodologies → Shape modeling
Fields (physics)
Specifications
Three dimensional models
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Summary:We propose a computational and practical technique to allow home users to fabricate discrete Chebyshev nets for various 3D models. The success of our method relies on two key components. The first one is a novel and simple method to approximate discrete integrable, unit‐length, and angle‐bounded frame fields, used to model discrete Chebyshev nets. Central to our field generation process is an alternating algorithm that takes turns executing one pass to enforce integrability and another pass to approach unit length while bounding angles. The second is a practical fabrication specification. The discrete Chebyshev net is first partitioned into a set of patches to facilitate manufacturing. Then, each patch is assigned a specification on pulling, bend, and fold to fit the nets. We demonstrate the capability and feasibility of our method in various complex models.
ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.14123