(appeared in: Visualization and Mathematics , H.C. Hege and K. Polthier)
Bernd Oberknapp and Konrad Polthier
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.
Full Preprint: An Algorithm for Discrete Constant Mean Curvature Surfaces (.pdf 827KB, .ps.gz 3.8MB)