Designing approximation minimal parametric surfaces with geodesics

Geodesic is an important curve in practical application, especially in shoe design and garment design. In practical applications, we not only hope the shoe and garment surfaces possess characteristic curves, but also we hope minimal cost of material to build surfaces. In this paper, we combine the g...

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Bibliographic Details
Published in:Applied mathematical modelling 2013-05, Vol.37 (9), p.6415-6424
Main Authors: Li, Cai-Yun, Wang, Ren-Hong, Zhu, Chun-Gang
Format: Article
Language:English
Subjects:
Approximation
Design engineering
Dirichlet function
Dirichlet problem
Garments
Geodesic
Linear systems
Mathematical analysis
Mathematical models
Minimal surface
Minimal surfaces
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Summary:Geodesic is an important curve in practical application, especially in shoe design and garment design. In practical applications, we not only hope the shoe and garment surfaces possess characteristic curves, but also we hope minimal cost of material to build surfaces. In this paper, we combine the geodesic and minimal surface. We study the approximation minimal surface with geodesics by using Dirichlet function. The extremal of such a function can be easily computed as the solutions of linear systems, which avoid the high nonlinearity of the area function. They are not extremal of the area function but they are a fine approximation in some cases.
ISSN:0307-904X
DOI:10.1016/j.apm.2013.01.035