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<!DOCTYPE HTML>
<HEAD><TITLE>Surface Evolver Documentation - Introduction</title>
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<h1 class="center">
<a href="http://www.susqu.edu/brakke/evolver/evolver.htm" class="comic">
Surface Evolver</a> Documentation</h1>

<a href="evolver.htm#doc-top">Back to top of Surface Evolver documentation.</a>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<a href="index.htm">Index.</a>

<a   id="overview"></a>
<h1>Surface Evolver Overview</h1>

<h2>General description</h2>

       The Surface Evolver is an interactive program for the study of
       surfaces shaped by surface tension and other 
<a href="energies.htm">energies</a>, and subject
to various <a href="constrnt.htm">constraints</a>.  A
       surface is implemented as a simplicial complex, that is, a union
       of triangles.  The user defines an initial surface in a datafile.  The
       Evolver evolves the surface toward minimal energy by a gradient
       descent method.   The aim can be to find a minimal energy surface,
or to model
       the process of evolution by mean curvature, which was studied
       in <a href="biblio.htm#refB1">[B1]</a> for surface tension energy in the context of varifolds
       and geometric measure theory.  The energy in the Evolver can be
       a combination of
       surface tension, gravitational energy, squared mean curvature,
       user-defined surface integrals, or knot energies.  The Evolver can handle
       arbitrary topology (as seen in real soap bubble clusters),
       volume constraints, boundary constraints, boundary contact
       angles, prescribed mean curvature, crystalline integrands,
       gravity, and constraints expressed as surface integrals.  The
       surface can be in an ambient space of arbitrary dimension, which
       can have a Riemannian metric, and the ambient space can be a
       quotient space under a group action.  The user can interactively
       modify the surface to change its properties or to keep the
       evolution well-behaved.  The Evolver was written for one and two
       dimensional surfaces, but it can do higher dimensional surfaces
       with some restrictions on the features available.  Graphical
       output is available as screen graphics and in several file
       formats, including PostScript.
<p>
       The Surface Evolver program is freely 
       <a href="install.htm">available</a>
       and is in use by a number of researchers.  Some of the
       applications of the Evolver so far include modelling the shape
       of fuel in rocket tanks in low gravity 
       <a href="biblio.htm#refTe">[Te]</a>, calculating areas
       for the Opaque Cube Problem <a href="biblio.htm#refB4">[B4]</a>, 
       computing capillary surfaces
       in cubes <a href="biblio.htm#refMH">[MH]</a> and in exotic containers 
       <a href="biblio.htm#refC">[C]</a>, simulating grain
       growth <a href="biblio.htm#refFT">[FT]</a><a href="biblio.htm#refWM">
       [WM]</a>, studying grain boundaries pinned by
       inclusions, finding  partitions of space more efficient
       than Kelvin's tetrakaidecahedra <a href="biblio.htm#refWP">[WP]</a>
       <a href="biblio.htm#refKS1">[KS1]</a>, 
       foam rheology <a href="biblio.htm#refKR1">[KR1]</a>
       <a href="biblio.htm#refKR2">[KR2]</a>,
       sphere eversion <a href="biblio.htm#refFS">[FS]</a>,
       modelling the shape of molten solder on
       microcircuits <a href="biblio.htm#refRSB">[RSB]</a>, 
       studying polymer chain packing, modelling
       cell membranes <a href="biblio.htm#refMB">[MB]</a>, 
       and classifying minimal surface  singularities. 
<p>
       The strength of the Surface Evolver program is in the breadth
       of problems it handles, rather than optimal treatment of some
       specific problem.  It is under continuing development, and 
       users are invited to suggest new features.
<p>
   This manual contains full operational details.
   A journal article description of the Evolver 
   appeared in <a href="biblio.htm#refB2">[B2]</a>.
<p>
<h2>Portability</h2>
       The Evolver is written in portable C and has been run
       on several systems, including Microsoft Windows, Macintosh, Linux, and unix.
       It is meant to be easily portable to any
       system that has C.
<p>
<h2>Acknowledgements</h2>
       The Evolver was written as part of the Geometry Supercomputing
       Project (later 
<a href="http://www.geom.umn.edu">The Geometry Center</a>, now defunct),
       sponsored by the National Science Foundation, the Department
       of Energy, Minnesota Technology, Inc., and the University of
       Minnesota. The program is available free of charge.  
<p>
<hr>
<a href="evolver.htm#doc-top">Back to top of Surface Evolver documentation.</a>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<a href="index.htm">Index.</a>
<hr>
<a href="http://www.susqu.edu/facstaff/b/brakke/">
Author's home page.</a>
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