Explicit form of parametric polynomial minimal surfaces with arbitrary degree

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摘要

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.

论文关键词:Minimal surface,Parametric polynomial minimal surface,Enneper surface,Conjugate minimal surface

论文评审过程:Available online 10 March 2015.

论文官网地址:https://doi.org/10.1016/j.amc.2015.02.065