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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>
<a href="index.htm">Index.</a>
<a id="tutorial"></a>
<h1>Surface Evolver Tutorial</h1>
To get started using the Surface Evolver, read the Basic Concepts
section for a quick introduction, then try the examples.
Many more examples can be found at the
<a href="http://www.susqu.edu/facstaff/b/brakke/evolver/examples/examples.htm">
Evolver Examples Web Page</a>
<ul>
<li> <a href="#basic-concepts">Basic concepts</a>
<li> <a href="cube.htm">Cube example</a>
<li> <a href="mound.htm">Mound example</a>
<li> <a href="catenoid.htm">Catenoid example</a>
<li> <a href="twointor.htm">Torus model example (Kelvin's foam)</a>
<li> <a href="ringblob.htm">Spinning ring example</a>
<li> <a href="column.htm">Liquid column example</a>
</ul>
<hr>
<a id="basic-concepts"></a>
<h1> Basic Concepts </h1>
The basic geometric elements used to represent a surface
are vertices, edges, facets, and bodies.
Vertices are points in space.
Edges are straight line segments joining pairs of vertices.
Facets are flat triangles bounded by three edges. A surface
is a union of facets. (Actually, there is no separate surface
entity in the program; all facets belong to one
logical surface.) A body is defined by giving its bounding
facets. <P>
The term "surface", when used to refer to the entity upon
which the Evolver operates, refers to all the geometric
elements plus auxiliary data such as constraints, boundaries,
and forces. <P>
There are no limitations on how
many edges may share a vertex nor on how many facets may
share an edge. Thus arbitrary topologies are possible,
including the triple junctions of surfaces characteristic
of soap films. <P>
Edges and facets are oriented for bookkeeping purposes,
but there are no restrictions on the orientation of
neighboring facets. Unoriented surfaces are thus possible. <P>
A surface is deemed to have a total energy, arising
from surface tension, gravitational energy, and possibly
other sources. It is this energy which the Evolver
minimizes. <P>
No particular units of measurement are used. The program
only deals with numerical values. If you wish to relate
the program values to the real world, then all values
should be within one consistent system, such as cgs or mks. <P>
The initial surface is specified in a text file (hereafter
referred to as the datafile) that may be created with any
standard text editor.
(The <code>.fe</code> extension I always use for datafiles stands for
facet-edge, which refers to the internal data structure
used to represent the surface. You may use any name
you wish for a datafile.) <P>
The basic operation of the Evolver is to read in a
datafile and take commands from the user. The main
command prompt is
<pre>
Enter command:
</pre>
The most common commands are one letter (case is significant
for these), sometimes
with a numerical parameter. The most frequently used commands
are:
<pre>
g n do n iterations ('g' is for 'go')
r refine the triangulation of surface
P graphics output (option 8 for geomview, option 3 for PostScript)
s show surface on screen (Evolver's own simple graphics)
q quit
</pre>
There is also a more elaborate command language (in which case is
not significant).
Commands must be followed with the ENTER key; Evolver only reads
complete lines. <P>
An iteration is one evolution step. The motion for
the step is calculated as follows: First, the force
on each vertex is calculated from the gradient of the
total energy of the surface as a function of the position
of that vertex. The force gives the direction of motion.
Second, the force is made to conform to whatever
constraints are applicable. Third, the actual
motion is found by multiplying the force by a global
scale factor. <P>
<hr>
<a href="cube.htm">Next: Cube example.</a> <br>
<a href="#tutorial">Back to top of tutorial.</a>
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<a href="evolver.htm#doc-top">Back to top of Evolver documentation.</a>
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