Explicit form of parametric polynomial minimal surfaces with arbitrary degree
Explicit form of parametric polynomial minimal surfaces with arbitrary degree
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任意次数参数多项式最小曲面的显式形式
DOI：
10.1016/j.amc.2015.02.065
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发表时间：
2015
影响因子：
4
通讯作者：
Hui Kin-chuen
中科院分区：
文献类型：
--
作者：
徐岗;Zhu Yaguang;Wang Guozhao;Galligo Andre;Zhang Li;Hui Kin-chuen
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= 4 k-1, n= 4 k, n= 4 k+ 1 and n= 4 k+ 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.
