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<!DOCTYPE HTML>
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<title>Surface Evolver tutorial</title>
<link rel="stylesheet" type="text/css" href="evdoc-style.css" />
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" >
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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="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>
<br>
<a href="evolver.htm#doc-top">Back to top of Evolver documentation.</a>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<a href="index.htm">Index.</a>
</body>
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