Construction of minimal subdivision surface with a given boundary

Authors:
Qing Pan;Guoliang Xu
Affiliations:
College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, China;LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China
Venue:
Computer-Aided Design
Year:
2011

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Abstract

The fascinating characters of minimal surface make it to be widely used in shape design. While the flexibility and high quality of subdivision surface make it a powerful mathematical tool for shape representation. In this paper, we construct minimal subdivision surfaces with given boundaries using the mean curvature flow, a second order geometric partial differential equation. This equation is solved by a finite element method where the finite element space is spanned by the limit functions of an extended Loop's subdivision scheme proposed by Biermann et al. Using this extended Loop's subdivision scheme we can treat a surface with boundary, thereby construct the perfect minimal subdivision surfaces with any topology of the control mesh and any shaped boundaries.