In this paper, we are exploring how to construct a discrete minimal surface. We map the conformal curvature lines of a parameterized continuous minimal surface to a unit sphere by the Gauss map. Then, based on a circle patterns we create, the Koebe polyhedron can be obtained. By dualizing the Koebe polyhedron, we are able to get the discrete minimal surface. Moreover, instead of only developing the method theoretically, we also show concrete procedures visually by Mathematica for Enneper with arbitrary domain. This is an expository project mainly based on the paper "Minimal surface from circle patterns: geometry from combinatorics" by Alexander I. Bobenko, Tim Hoffmann and Boris A. Springborn.
|Advisor:||Weyhuapt, Adam G.|
|Commitee:||Lu, Chunqing, Parish, James L.|
|School:||Southern Illinois University at Edwardsville|
|Department:||Mathematics and Statistics|
|School Location:||United States -- Illinois|
|Source:||MAI 52/02M(E), Masters Abstracts International|
|Keywords:||Catenoid, Cell decomposition, Christoffel dual, Discrete christoffel dual, Discrete minimal surface, Enneper, Gauss map, Koebe polyhedron, Minimal surface|
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