An Algorithm for Discrete Constant Mean Curvature Surfaces

(appeared in: Visualization and Mathematics , H.C. Hege and K. Polthier)

Bernd Oberknapp and Konrad Polthier

Abstract

We present a new algorithm for computing discrete constant mean curvature surfaces in R³. It is based on the definition of a discrete version of the conjugate surface construction for CMC surfaces. Here we solve a Plateau problem for a discrete minimal surface in S³ by computing a sequence of discrete harmonic maps F : S³ --> S³. The definition of a discrete conjugation allows to transform this sequence to a sequence of conjugate discrete maps which converges to a discrete CMC surface in R³. The algorithm is applicable to free boundary value problems for CMC surfaces and led to the recent discovery of new compact CMC surfaces.

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