Explicit form of parametric polynomial minimal surfaces with arbitrary degree

Gang Xu, Yaguang Zhu, Guozhao Wang, André Galligo, Li Zhang and Kin-chuen Hui

Applied Mathematics and Computation, 2015, vol. 259, issue C, 124-131

Abstract: In this paper, from the viewpoint of geometric modeling in CAD, we propose an explicit parametric form of a class of polynomial minimal surfaces with arbitrary degree, which includes the classical Enneper surface for the cubic case. The proposed new minimal surface possesses some interesting properties such as symmetry, containing straight lines and self-intersections. According to the shape properties, the proposed minimal surface can be classified into four categories with respect to n=4k-1, n=4k,n=4k+1 and n=4k+2, where n is the degree of the coordinate functions in the parametric form of the minimal surface and k is a positive integer. The explicit parametric form of the corresponding conjugate minimal surface is given and the isometric deformation is also implemented.

Keywords: Minimal surface; Parametric polynomial minimal surface; Enneper surface; Conjugate minimal surface (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:259:y:2015:i:c:p:124-131

DOI: 10.1016/j.amc.2015.02.065

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