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Practical Fabrication of Discrete Chebyshev Nets
Author(s) -
Liu HaoYu,
Liu ZhongYuan,
Zhao ZhengYu,
Liu Ligang,
Fu XiaoMing
Publication year - 2020
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.14123
Subject(s) - chebyshev filter , chebyshev polynomials , bounded function , computer science , bounding overwatch , frame (networking) , set (abstract data type) , algorithm , computational science , topology (electrical circuits) , mathematics , mathematical analysis , artificial intelligence , computer vision , telecommunications , combinatorics , programming language
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.