An Algorithm for Discrete Constant Mean Curvature Surfaces

Bernd Oberknapp and Konrad Polthier
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Bernd Oberknapp: Universität Bonn, Mathematisches Institut
Konrad Polthier: Technische Universität Berlin, Fachbereich Mathematik

A chapter in Visualization and Mathematics, 1997, pp 141-161 from Springer

Abstract: Summary 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 i : 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.

Keywords: Minimal Surface; Curvature Surface; Period Problem; Discrete Surface; Dirichlet Energy (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-59195-2_10

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DOI: 10.1007/978-3-642-59195-2_10

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