Minimal quasi-Bézier surface

The quasi-Bézier surface is a kind of commonly used surfaces in CAGD/CAD systems. In this paper, we study how to find the quasi-Bézier surface of minimal area among all the quasi-Bézier surfaces with prescribed borders, i.e., the Plateau-quasi-Bézier problem. The prescribed borders can not only be p...

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Bibliographic Details
Published inApplied mathematical modelling Vol. 36; no. 12; pp. 5751 - 5757
Main Authors Hao, Yong-Xia, Wang, Ren-Hong, Li, Chong-Jun
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2012
Subjects
Borders
Catenaries
Computer aided design
Dirichlet functional
Harmonic surface
Harmonics
Mathematical models
Minimal surface
Modelling
Quasi-Bézier surface
Harmonic surface
Quasi-Bézier surface
Minimal surface
Dirichlet functional
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Summary:The quasi-Bézier surface is a kind of commonly used surfaces in CAGD/CAD systems. In this paper, we study how to find the quasi-Bézier surface of minimal area among all the quasi-Bézier surfaces with prescribed borders, i.e., the Plateau-quasi-Bézier problem. The prescribed borders can not only be polynomial curves, but also catenaries and circular arcs. Moreover, the harmonic and biharmonic quasi-Bézier surfaces are investigated.
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ISSN:0307-904X
DOI:10.1016/j.apm.2012.01.040