## 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 R^{3}. 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 S^{3} by computing a sequence
of discrete harmonic maps F : S^{3} --> S^{3}. 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 R^{3}.
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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