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Explicit form of parametric polynomial minimal surfaces with arbitrary degree

Author

Listed:
  • Xu, Gang
  • Zhu, Yaguang
  • Wang, Guozhao
  • Galligo, André
  • Zhang, Li
  • Hui, Kin-chuen

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.

Suggested Citation

  • Xu, Gang & Zhu, Yaguang & Wang, Guozhao & Galligo, André & Zhang, Li & Hui, Kin-chuen, 2015. "Explicit form of parametric polynomial minimal surfaces with arbitrary degree," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 124-131.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:124-131
    DOI: 10.1016/j.amc.2015.02.065
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    Cited by:

    1. Li, Yibao & Guo, Shimin, 2017. "Triply periodic minimal surface using a modified Allen–Cahn equation," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 84-94.

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