Computing Discrete Minimal Surfaces and Their Conjugates

Ulrich Pinkall and Konrad Polthier


We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of fixed or free boundary curves in R3, S3 and H3. The algorithm makes no restriction on the genus and can handle singular triangulations. For a discrete harmonic map a conjugation process is presented leading in case of minimal surfaces additionally to instable solutions of the free boundary value problem for minimal surfaces. Symmetry properties of boundary curves are respected during conjugation.
Appeared in: Experimental Mathematics 2 (1993) 15-36

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