We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of fixed or free boundary curves in $\R^3$, $\Sph ^3$ and $\H^3$. The algorithm makes no restriction on the genus and can handle singular triangulations.
Additionally, we present an algorithm that, starting from a discrete harmonic map, gives a conjugate harmonic map. This can be applied to the identity map on a minimal surface to produce its conjugate minimal surface, a procedure that often yields unstable solutions to a free boundary value problem for minimal surfaces. Symmetry properties of boundary curves are respected during conjugation.
%0 Journal Article
%1 pinkall1993computing
%A Pinkall, U.
%A Polthier, K.
%D 1993
%I Taylor & Francis
%J Experimental mathematics
%K dirichlet.energy
%N 1
%P 15--36
%R 10.1080/10586458.1993.10504266
%T Computing discrete minimal surfaces and their conjugates
%V 2
%X We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of fixed or free boundary curves in $\R^3$, $\Sph ^3$ and $\H^3$. The algorithm makes no restriction on the genus and can handle singular triangulations.
Additionally, we present an algorithm that, starting from a discrete harmonic map, gives a conjugate harmonic map. This can be applied to the identity map on a minimal surface to produce its conjugate minimal surface, a procedure that often yields unstable solutions to a free boundary value problem for minimal surfaces. Symmetry properties of boundary curves are respected during conjugation.
@article{pinkall1993computing,
abstract = {We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of fixed or free boundary curves in $\R^3$, $\Sph ^3$ and $\H^3$. The algorithm makes no restriction on the genus and can handle singular triangulations.
Additionally, we present an algorithm that, starting from a discrete harmonic map, gives a conjugate harmonic map. This can be applied to the identity map on a minimal surface to produce its conjugate minimal surface, a procedure that often yields unstable solutions to a free boundary value problem for minimal surfaces. Symmetry properties of boundary curves are respected during conjugation.},
added-at = {2012-12-30T00:34:20.000+0100},
author = {Pinkall, U. and Polthier, K.},
biburl = {https://www.bibsonomy.org/bibtex/2dc1ef500fa94335a460369361ec63ed7/ytyoun},
doi = {10.1080/10586458.1993.10504266},
interhash = {2abcea7ff045db8bff287acd0f105376},
intrahash = {dc1ef500fa94335a460369361ec63ed7},
journal = {Experimental mathematics},
keywords = {dirichlet.energy},
number = 1,
pages = {15--36},
publisher = {Taylor \& Francis},
timestamp = {2012-12-30T00:34:20.000+0100},
title = {Computing discrete minimal surfaces and their conjugates},
volume = 2,
year = 1993
}