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<h1><a href="http://www.susqu.edu/facstaff/b/brakke/evolver/evolver.htm">
Surface Evolver</a> Documentation</h1>
</center>
<a href="evolver.htm#doc top">Back to top of Surface Evolver documentation.</a>
<a href="index.htm">Index.</a>

<a name="command language"></a><h1>Surface Evolver command language</h1>

The Surface Evolver has an interactive command language. It has
variables, expressions, subroutines, conditionals,iteration constructs,
subroutines and functions with arguments, local variables, and arrays.
But not structures or objects or pointers.
Variables are either floating point, string, or subroutine names.
The Evolver command language continues to grow by accretion, and it
looks like it's headed towards a full programming language.  
<table><tr valign=top><td>
<ul>
<li><a href="#input">Command input</a>
<li><a href="#command separator">Command separator</a>
<li><a href="#compound commands">Compound commands</a>
<li><a href="#command repetition">Command repetition</a>
<li><a href="#command definition">User-defined commands</a>
<li><a href="#procedure definition">User-defined procedures</a>
<li><a href="#function definition">User-defined functions</a>
<li><a href="#assignment">Assignment commands</a>
<li><a href="#permanent assignment">Permanent assignment commands</a>
</ul></td><td><ul>
<li><a href="#local">Local scope</a>
<li><a href="#piping">Redirecting and piping output</a>
<li><a href="#control structures">Control structures</a>
<li><a href="#generators">Element generators</a>
<li><a href="single.htm">Single letter commands</a>
<li><a href="toggle.htm">Toggle commands</a>
<li><a href="#command verbs">General commands</a>
</ul></td></tr></table>
<hr>
<a name="input"></a><h2>Command input</h2>
The Surface Evolver command interpreter reads from an input
stream, which may be from the end of the 
<a href="datafile.htm#read section">datafile</a>, from a
file given on the system <a href="general.htm#options">command line</a>,
 from stdin (the
	terminal), or from a file given in a <a href="#read"><tt>READ</tt></a>
 command.
<p>
       The interactive command prompt is "<tt>Enter command: </tt>". 
<p>
   Commands are read one at a time, parsed, and executed.
By  default, a line is expected to contain a complete command,
so no special end-of-command token is needed.
<p>
   Multi-line commands may be entered by enclosing them in braces 
<tt>{...}</tt>.
   If a line ends while nested in braces or parenthesis, Evolver
   will ask for more input with the prompt "<tt>more&gt;</tt> ".
     It will also ask for more if the
   line ends with certain tokens (such as `+') that cannot legally
   end a command.  Unclosed quotes will also ask for more, and
   embedded newlines will be omitted from the final string.
   Explicit continuation to the next line may
   be indicated by ending a line with a backslash 
 (<a href="syntax.htm#line splicing">linesplicing</a>).
   You may want to use the 
<a href="#read"><tt>read</tt></a> command to read long commands
   from a file, since there is no command line editing.
<p>
   <a name="history list"></a>
   Successfully parsed commands are saved in a history list, up to
   100 commands.
   They may be accessed with  <tt>!!</tt> for the last command or 
   <tt>!</tt><em>string</em> for the latest command with matching initial string.
   <tt>!</tt><em>n</em> will repeat a command by history list number.
   The command will be echoed.  The saved history list may be printed
   with the <a href="#history"><tt>history</tt></a> command.
<p>
   Some 
<a href="single.htm">single-letter commands</a>
 require interactive input.  For those,
   there are equivalent commands that take input
   information as part of the command.  This is so commands may be
   read from a script without having to put input data on additional
   lines after the command, although that can still be done for the
   single-letter versions.
<p>
             General note: Some commands will prompt you
             for a value.  A null response (just <tt>RETURN</tt>)
             will leave the old value unchanged and return you
             to the command prompt.  On
             options where a zero value is significant, the
             zero must be explicitly entered. Commands that need
	     a real value will accept an arbitrary expression.
<p>
             Many commands that change the surface or
             change the model
              will cause energies and volumes to be recalculated.
	      If you suspect a command has not done this, the
     <a href="#recalc"><tt>recalc</tt></a> command will recalculate everything.
	      It will also update any automatic display.
<p>
   In the command syntax descriptions,
   keywords are shown in upper case, although case is irrelevant in
   actual commands, except for single-letter commands. 
<hr>
<a name="command separator"></a><h2>Command separator</h2>

      Several commands on the same line or within a 
<a href="#compound commands">compound
      command</a> must be separated by a semicolon.
      A semicolon is not needed after the last command,
      but won't hurt.
       Do not use a semicolon after the first command
      in an <tt>IF THEN ELSE</tt> command. Do use a semicolon to separate
a compound command from the next. Example:
<pre>
      g 10; r; g 10; u  
      myc := { print 5;
               g 10;
               if qwer &lt; foo then print 3 else { print 2; print 4; };
               aa := 23
             }
</pre>
<hr>
<a name="compound commands"></a><h2>Compound commands</h2>
 
      Curly braces group a list of commands into one command.  The 
      commands are separated by semicolons.  A semicolon is needed
      after a compound command within a compound command to separate
      it from following commands (note this is different from the C language).  
      Do not use a semicolon after the first command
	    in an IF THEN ELSE command.   An empty compound command <tt>{}</tt>
		   is legal.
Examples:
<pre>
  if ( foo &gt; 4 ) then { g;g;u; } else print 4;
  while ( xx &lt; 2 ) do { g; xx := xx + 1 }
  aa := { g 5; 
          foreach vertex vv do {
              printf "id: %g  coord: %f %f %f\n",id,x,y,z;
              count := count + 1;
              };  // note semicolon here!
          printf "done.\n"
        }
</pre>

<hr>
<a name="command repetition"></a><h2>Command repetition</h2>

      Certain types of commands can be repeated a number of times by following
      the command with an integer.  Be sure
      to leave a space between a single-letter command and the expression
      lest your command be interpreted as one identifier.
      To avoid several types of confusion, only certain types
      of commands are repeatable:
<ul>
    <li> 
<a href="single.htm">Single letter commands</a>
 that don't have optional arguments
		(<tt>K,k,l,t,j,m,n,p,w,y,P,M,G</tt> have optional arguments),
<li> <a href="#compound commands">Compound commands</a> in braces,
<li> <a href="#command definition">User-defined command</a> names.
<li> <a href="single.htm#redefinition">Redefined single-letter commands</a>.
</ul>
Examples:
<pre>   g 10
   U 2
   { g 20; u; V; u } 20
   myc := { g 20; V }; myc 10
</pre>

<hr>
<a name="assignment"></a><h2>Assignment commands</h2>

The assignment operator <tt>:=</tt> can be used to assign values
to various entities.
Note that '<tt>:=</tt>' is used for assignment, not '<tt>=</tt>'.
The C-style arithmetic assignments <tt>+=</tt>, <tt>-=</tt>, <tt>*=</tt>, and
<tt>/=</tt> work.  For example, <tt>val += 2</tt> is equivalent to
<tt>val := val + 2</tt>.  These also work in other assignment situations where I
thought they made sense, such as attribute assignment.  Possible assignments:

<ul>
<li> <a href="#command definition">User-defined commands</a>, Ex: <tt> gogo := {g 100; r; g 100}</tt> 
<li> <a href="#variable assignment">User-defined variables</a>, Ex: <tt> foo := 2.3</tt>
<li> Writable <a href="syntax.htm#internal variables">internal variables</a>, Ex: <tt>scale := 0.1</tt>
<li> <a href="quants.htm#named quantities">Named quantity</a> 
<a href="quants.htm#quantity modulus">modulus</a>, 
<a href="quants.htm#quantity target">target</a>, and 
<a href="quants.htm#quantity volconst">volconst</a>. Syntax:
<pre>   <em>quantityname</em>.modulus := <em>expr</em>
   <em>quantityname</em>.target := <em>expr</em>
   <em>quantityname</em>.volconst := <em>expr</em> </pre>
<li> <a href="quants.htm#method instances">Method instance</a> modulus.
Syntax:
<pre>   <em>instancename</em>.modulus := <em>expr</em>
</pre>
</ul>

<hr>
<a name="permanent assignment"></a><h2>Permanent assignment commands</h2>
The permanent assignment operator <tt>::=</tt> can be used to make assignments
to variables and commands that are not forgotten when a new datafile is
loaded.  Such a command may only make reference to permanent variables,
permanent commands, and internal variables.  See 
<a href="#permload">permload</a> command for an example of use.

<hr>
<a name="command definition"></a><h2>User-defined commands</h2>
Users may define their own commands with the syntax
<pre>
   <a href="syntax.htm#identifiers"><em>identifier</em></a> <tt>:=</tt> <em>command</em>
</pre>
The shortest complete command on the right side is used.
      Thus "<tt>gg := g 10; u</tt>" would give <tt>gg</tt> the same
      value as "<tt>gg := g 10</tt>".  
It is wise and strongly advised to use braces to 
      enclose the command on the right side so the parser can tell 
      it's a command and not an expression. Also multiline commands 
      then don't need linesplicing. 
Do not try to redefine single-letter
commands this way; use  <a href="single.htm#redefinition"><tt>:::=</tt></a>.
Example:
<pre>
   gg := {g 10; u}
</pre>

<hr>
<a name="procedure definition"></a><h2>User-defined procedures</h2>
Users may define their own procedures with arguments 
with the syntax
<pre>
   procedure <a href="syntax.htm#identifiers"><em>identifier</em></a> ( <em>type arg1</em>, <em>type arg2</em>, ... )
   { <em>commands</em> }
</pre>
Right now the implemented types for arguments are 
<tt>real</tt> and <tt>integer</tt>.  The argument list can be empty.
 Example:
<pre>
   procedure proc1 ( real ht, real wd )
   { 
     prod := ht*wd;   // this would make prod a global variable
     return; 
   }
</pre>
Note that the procedure arguments act as <a href="#local">local</a>
 variables, i.e. their scope
is the procedure body, and they have stack storage so procedures may be
recursive.
Procedure prototypes may be used to declare procedures before their bodies
are defined with the same syntax, just replacing the body of the procedure
with a semicolon. Prototype syntax:
<pre>
   procedure <a href="syntax.htm#identifiers"><em>identifier</em></a> ( <em>type arg1</em>, <em>type arg2</em>, ... );
</pre>
Note that a procedure is used as a command, and a function is used in
a numerical expression.

<hr>
<a name="function definition"></a><h2>User-defined functions</h2>
Users may define their own functions that have arguments and
return values with the syntax
<pre>
   function <em>type</em> <a href="syntax.htm#identifiers"><em>identifier</em></a> ( <em>type arg1</em>, <em>type arg2</em>, ... )
   { <em>commands</em> }
</pre>
Right now the implemented types for return value and arguments are 
<tt>real</tt> and <tt>integer</tt>.  The argument list can be empty.
The return value is given in a
<tt>return</tt> <em>expr</em> statement.  Example:
<pre>
   function real func1 ( real ht, real wd )
   { local prod;
     prod := ht*wd;
     return prod;
   }
</pre>
Note that the function arguments act as <a href="#local">local</a>
 variables, i.e. their scope
is the function body, and they have stack storage so functions may be
recursive.
Function prototypes may be used to declare functions before their bodies
are defined with the same syntax, just replacing the body of the function
with a semicolon. Prototype syntax:
<pre>
   function <em>type</em> <a href="syntax.htm#identifiers"><em>identifier</em></a> ( <em>type arg1</em>, <em>type arg2</em>, ... );
</pre>
Note that a procedure is used as a command, and a function is used in
a numerical expression.

<hr>
<a name="variable assignment"></a><h2>Variable assignment</h2>
Values can be assigned to variables.  Values can be numeric or string.
The variable names must be
two or more letters, in order they not be confused with single-letter
commands.  
Syntax:
<pre>
   <a href="syntax.htm#identifiers"><em>identifier</em></a> <tt>:=</tt> <a href="syntax.htm#expressions"><em>expr</em></a>
   <a href="syntax.htm#identifiers"><em>identifier</em></a> <tt>:=</tt> <a href="syntax.htm#stringexpr"><em>stringexpr</em></a>
</pre>
 If the variable does not exist, it will be created.  These are
      the same class of variables as the adjustable parameters in
      the datafile, hence are all of global scope and may also be
      inspected and changed with the '<a href="single.htm#A"><tt>A</tt></a>'
 command.
      Examples:
<pre>
   maxlen := max(edge,length)
   newname := sprintf "file%03g",counter 
</pre>

<hr>
<a name="local"></a><h2>Local scope</h2>

The scope of a variable name may be restricted to a compound command block
by declaring the name to be local.  Example:
<pre>
   do_stuff := { 
     local inx;
     for ( inx := 1 ; inx &lt; 5 ; inx += 1 )
     { local jnx;
       jnx := inx*2;
       print jnx;
     };
   }
</pre>
Using local variables is good for avoiding pollution of global namespace
and for writing recursive functions (storage space for locals is allocated
on the runtime stack).
Note that the local declaration is a scope declaration, not a type
declaration.  Also, it cannot be combined with initialization of the
variable (yet), and there is one name per declaration.
Function arguments also act as local variables.
<hr>
<a name="redirection"></a>
<a name="piping"></a><h2>Redirecting and piping command output</h2>

The output of a command can be redirected to a file with the
unix-style append symbol '&gt;&gt;'.  This appends output to
the file; it does not erase any existing file. Syntax:
<pre>
   <em>command</em> &gt;&gt; <a href="syntax.htm#stringexpr"><em>stringexpr</em></a>
</pre>

The output of a command can be redirected to a file with the
 symbol '&gt;&gt;&gt;'.  This overwrites an existing file. 
Syntax:
<pre>
   <em>command</em> &gt;&gt;&gt; <a href="syntax.htm#stringexpr"><em>stringexpr</em></a>
</pre>
 Redirection with `<tt>&gt;</tt>' is not available due to
     the use of `<tt>&gt;</tt>' as an comparison operator.  

The output of a command can be piped to a system  command using
the unix-style pipe symbol `<tt>|</tt>'. Syntax:
<pre>
   <em>command</em> | <a href="syntax.htm#stringexpr"><em>stringexpr</em></a>
</pre>
  The <em>stringexpr</em> is interpreted as a system command.
  <p>

      Examples:
<pre>
   list facets | "more"
   list vertices | "tee vlist" ; g 10 | "tee g.out"
   { {g 10; u } 20 } &gt;&gt; "logfile"
   {foreach facet do print area} | "cat &gt; areafile"
</pre>
<hr>
<a name="control structures"></a><h2>Control structures</h2>
The following control structures are available in the Evolver commmand
language:
<ul>
<li><a href="#if then else">if ... then ... else</a>
<li><a href="#do">do ... while ....</a>
<li><a href="#while">while .... do ...</a>
<li><a href="#for">for</a>
<li><a href="#foreach">foreach</a>
<li><a href="#break">break</a>
<li><a href="#continue">continue</a>
<li><a href="#return">return</a>
</ul>
<hr>
<a name="if"></a><a name="then"></a><a name="else"></a>
<a name="if then else"></a><h2>IF ... THEN ... ELSE</h2>
Commands may be conditionally executed by the syntax
<pre>
   IF <em>expr</em> THEN <em>command</em> 

   IF <em>expr</em> THEN <em>command</em> ELSE <em>command</em>
</pre>
   <a href="syntax.htm#expressions"><em>expr</em></a>
 is true if nonzero.  Parentheses around <em>expr</em>
   are not needed, but do not hurt.
      Do not use a semicolon to end the first command.
      Example:
<pre>
   if max(edges,length) &gt; 0.02 then {r; g 100} else g 4 
</pre>

<hr>
<a name="while"></a><h2>WHILE ... DO ... </h2>
Command syntax for pretest iteration loop. Syntax:
<pre>
  WHILE <em>expr</em> DO <em>command</em>
</pre>
   <a href="syntax.htm#expressions"><em>expr</em></a>
   is true if nonzero.  Parentheses around <em>expr</em>
   are not needed, but do not hurt.
    Example:
<pre>
   count := 0
   while count &lt; 10 do { g 10; u; print total_energy; count := count + 1 }
</pre>

<hr>
<a name="do"></a><h2>DO ... WHILE ...</h2>
Command syntax for posttest iteration loop. Syntax:
<pre>
   DO <em>command</em> WHILE <em>expr</em>
</pre>
   <a href="syntax.htm#expressions"><em>expr</em></a>
   is true if nonzero.  Parentheses around <em>expr</em>
   are not needed, but do not hurt.
    Example:
<pre>
   do { oldenergy := total_energy; g 10 } 
   while (oldenergy-total_energy &lt; 1e-6)
</pre>


<hr>
<a name="for"></a><h2>FOR</h2>
This is the Evolver's version of the C language "for" construct. Syntax:
<pre>
  FOR ( <em>command1</em> ; <em>expr</em> ; <em>commmand2</em> ) <em>command3</em>
</pre>
The first
command is the initialization command; note that it is a single command,
rather than an expression as in C.  If you want multiple commands in the
initialization, use a compound command enclosed in curly braces. The
middle expression is evaluated at the start of each loop iteration; if its
value is true (i.e. nonzero) then the loop is executed; otherwise the
flow of control passes to the command after command3. The command2 is
executed at the end of each loop iteration; again, it is a single command.
The body of the loop is the single command command3, often a compound]
command.  Note: Command3 should end with a semicolon, unless it is
the if clause of an if-then statement. Examples:
<pre>
   for ( inx := 1 ; inx &lt; 3 ; inx += 1 )
      print facet[inx].area;
   for ( {inx := 1; factorial := 1; } ; inx &lt; 7 ; inx += 1 )
   { factorial *= inx;
     printf "factorial %d is %d\n",inx,factorial;
   };
</pre>


<hr>
<a name="foreach"></a><h2>FOREACH</h2>

Repeat a command for each element produced by an element generator.
Syntax:
<pre>FOREACH <a href="commands.htm#generators"><em>generator</em></a> DO <em>command</em>  
</pre>Examples:
<pre>
 foreach vertex do print x^2 + y^2 + z^2

 foreach edge ee where ee.dihedral &gt; .4 do {
   printf "id %g\n",id; 
   foreach ee.vertex do printf " %g %g %g\n",x,y,z; 
 }
</pre>
<hr>
<a name="break"></a><h2>BREAK</h2>
Command syntax for exiting loops. 
Syntax:
<pre>
   BREAK

   BREAK <em>n</em>
</pre>
The first form exits the innermost current loop.  The second form
exits <em>n</em> loops.  Note: Commands with
repetition counts do not qualify as loops.
Example:
<pre>
   foreach vertex do { print x; if y &lt; 0 then break; print z }
</pre>

<hr>
<a name="continue"></a><h2>CONTINUE</h2>

Command syntax for skipping the rest of the body of the current loop, 
    and going to the next iteration of the loop.
<pre>
   CONTINUE

   CONTINUE <em>n</em>
</pre> 
    The second form exits the innermost <em>n</em>-1 loops, 
    and skips to the loop control of the <em>n</em>th innermost loop.
    Note: Commands with
    repetition counts do not qualify as loops.
Example:
<pre>
   foreach vertex vv do {
       foreach vv.edge do {
         print length; if length &lt; .4 then continue 2; 
       }
   }
 </pre>
<hr>
<a name="return"></a><h2>RETURN</h2>
Command syntax for exiting the current command.  This is essentially
a return from a subroutine.  If the current command is a user-defined
command called  by another command, the parent command continues.
Example:
<pre>  if ( acc &lt; 1.e-10 ) then return;
</pre>

<hr>
<a name="where"></a>
<a name="indexed elements"></a>
<a name="generators"></a><h2>Element generators</h2>

One feature different from ordinary C is the presence of generators
of sets of geometric elements.  These occur wherever an element type
(vertices, edges, facets, bodies, singular or plural) appears in a
command.  Attributes of the iteration element may be used later in the
command.  The general form of a generator is 
<pre>
  <em>elementgen name where expr</em>
</pre>
<em>elementgen</em> may be
<ul><li> a multiple element generator, which can be
<ul><li> an element type, <tt>vertex, edge, facet, or body</tt>,
which generates all elements of that type in the surface.  But new
elements created during a loop will not be generated, so
"<tt>refine edges</tt>" will refine all existing edges just once.
<li> a single element subelement. The implemented subelements are:
<ul> <li> of a vertex: edge, facet (in no particular order)
<li> of an edge: vertex (in tail, head order), facet (in geometric order)
<li> of a facet: vertex, edge, body (all in order around the facet)
<li> of a body: facet (in no particular order)
</ul> </ul>
<li> a single element, which can be
<ul>
<li> an element name of an active generator
<li> an indexed element type, <tt>vertex, edge, facet, or body</tt>.
Indexing starts at 1.
The index may be negative, in which case the generated element has
negative orientation. 
<li> an indexed subelement of an element (error if no element of
that index). Indexing starts at 1.  The indexing is the same as the
order produced by the <a href="#foreach">foreach</a> generator.  Indexed
subelements of an edge or facet follow the orientation of the edge or facet.
</ul>
</ul>
<em>name</em> is an optional <a href="syntax.htm#identifiers">identifier</a>
which can be used in the body of a loop to refer to the generated element.
<a href="syntax.htm#expressions"><em>expr</em></a> is interpreted as
a boolean expression, 0 for false, nonzero for true. Only elements
for which <em>expr</em> is true are generated.  The <em>where expr</em>
clause is optional.  The innermost generator generates a default element,
which can have its 
<a href="elements.htm#attributes">attributes</a> 
referred to just by attribute name.
But be sure to remember that
in a nested iteration, an unqualified element type generates all elements
of that type, not just those associated with the parent element. 
Examples:
<pre>
   list facet where color == red

   foreach edge ee where ee.length &lt; .3 do list ee.vertex

   print facet[2].edge[1].vertex[2].id

   foreach facet ff do { printf "facet %g:\n"; list ff.edge }

   print max(edge where on_constraint 1, length)
</pre>


<hr>
<a name="command verbs"></a>         <h2>General commands</h2>
Many commands in the Evolver <a href="#command language">command language</a>
have a sentence-like structure and start with a verb.  
<table border>
<tr valign=top><td><ul>
<li><a href="#abort">ABORT</a>
<li><a href="#addload">ADDLOAD</a>
<li><a href="#areaweed">AREAWEED</a>
<li><a href="#binary_off_file">BINARY_OFF_FILE</a>
<li><a href="#binary_printf">BINARY_PRINTF</a>
<li><a href="#body_metis">BODY_METIS</a>
<li><a href="#breakpoint">BREAKPOINT</a>
<li><a href="#chdir">CHDIR</a>
<li><a href="#close_show">CLOSE_SHOW</a>
<li><a href="#define">DEFINE</a>
<li><a href="#delete">DELETE</a>
<li><a href="#delete_text">DELETE_TEXT</a>
<li><a href="#dirichlet">DIRICHLET</a>
<li><a href="#dirichlet_seek">DIRICHLET_SEEK</a>
<li><a href="#display_text">DISPLAY_TEXT</a>
<li><a href="#dissolve">DISSOLVE</a>
<li><a href="#dump">DUMP</a>
<li><a href="#dump_memlist">DUMP_MEMLIST</a>
<li><a href="#edge_merge">EDGE_MERGE</a>
<li><a href="#edgeswap">EDGESWAP</a>
<li><a href="#edgeweed">EDGEWEED</a>
<li><a href="#equiangulate">EQUIANGULATE</a>
<li><a href="#eigenprobe">EIGENPROBE</a>
<li><a href="#errprintf">ERRPRINTF</a>
<li><a href="#exec">EXEC</a>
<li><a href="#exprint">EXPRINT</a>
<li><a href="#facet_merge">FACET_MERGE</a>
<li><a href="#fix">FIX</a>
<li><a href="#flush_counts">FLUSH_COUNTS</a>
<li><a href="#free_discards">FREE_DISCARDS</a>
<li><a href="#geompipe">GEOMPIPE</a>
<li><a href="#geomview command">GEOMVIEW</a>
<li><a href="#help">HELP</a>
<li><a href="#hessian command">HESSIAN</a>
<li><a href="#hessian_menu">HESSIAN_MENU</a>
<li><a href="#hessian_seek">HESSIAN_SEEK</a>
<li><a href="#histogram">HISTOGRAM</a>
<li><a href="#history">HISTORY</a>
<li><a href="#kmetis">KMETIS</a>
<li><a href="#lagrange">LAGRANGE</a>
<li><a href="#lanczos">LANCZOS</a>
</ul></td><td><ul>
<li><a href="#linear">LINEAR</a>
<li><a href="#list">LIST</a>
<li><a href="#list attributes">LIST ATTRIBUTES</a>
<li><a href="#list bottominfo">LIST BOTTOMINFO</a>
<li><a href="#list procedures">LIST PROCEDURES</a>
<li><a href="#list topinfo">LIST TOPINFO</a>
<li><a href="#load">LOAD</a>
<li><a href="#longj">LONGJ</a>
<li><a href="#matrix_inverse">MATRIX_INVERSE</a>
<li><a href="#matrix_multiply">MATRIX_MULTIPLY</a>
<li><a href="#metis">METIS</a>
<li><a href="#move">MOVE</a>
<li><a href="#new_vertex">NEW_VERTEX</a>
<li><a href="#new_edge">NEW_EDGE</a>
<li><a href="#new_facet">NEW_FACET</a>
<li><a href="#new_body">NEW_BODY</a>
<li><a href="#notch">NOTCH</a>
<li><a href="#ometis">OMETIS</a>
<li><a href="#ooglfile">OOGLFILE</a>
<li><a href="#optimize">OPTIMIZE</a>
<li><a href="#pause">PAUSE</a>
<li><a href="#permload">PERMLOAD</a>
<li><a href="#pop">POP</a>
<li><a href="#pop_edge_to_tri">POP_EDGE_TO_TRI</a>
<li><a href="#pop_quad_to_quad">POP_QUAD_TO_QUAD</a>
<li><a href="#pop_tri_to_edge">POP_TRI_TO_EDGE</a>
<li><a href="#postscript command">POSTSCRIPT</a>
<li><a href="#print">PRINT</a>
<li><a href="#printf">PRINTF</a>
<li><a href="#quadratic">QUADRATIC </a>
</ul></td><td><ul>
<li><a href="#quit">QUIT</a>
<li><a href="#rawestv">RAWESTV</a>
<li><a href="#rawest_vertex_average">RAWEST_VERTEX_AVERAGE</a>
<li><a href="#rawv">RAWV</a>
<li><a href="#raw_vertex_average">RAW_VERTEX_AVERAGE</a>
<li><a href="#read">READ</a>
<li><a href="#rebody">REBODY</a>
<li><a href="#recalc">RECALC</a>
<li><a href="#refine">REFINE</a>
<li><a href="#reset_counts">RESET_COUNTS</a>
<li><a href="#reverse_orientation">REVERSE_ORIENTATION</a>
<li><a href="#ritz">RITZ</a>
<li><a href="#renumber_all">RENUMBER_ALL</a>
<li><a href="#reorder_storage">REORDER_STORAGE</a>
<li><a href="#saddle">SADDLE</a>
<li><a href="#set">SET</a>
<li><a href="#shell">SHELL</a>
<li><a href="#show">SHOW</a>
<li><a href="#show_expr">SHOW_EXPR</a>
<li><a href="#showq">SHOWQ</a>
<li><a href="#simplex_to_fe">SIMPLEX_TO_FE</a>
<li><a href="#sobolev">SOBOLEV</a>
<li><a href="#sprintf">SPRINTF</a>
<li><a href="#subcommand">SUBCOMMAND</a>
<li><a href="#system">SYSTEM</a>
<li><a href="#t1_edgeswap">T1_EDGESWAP</a>
<li><a href="#unfix">UNFIX</a>
<li><a href="#unset">UNSET</a>
<li><a href="#vertex_average">VERTEX_AVERAGE</a>
<li><a href="#vertex_merge">VERTEX_MERGE</a>
<li><a href="#whereami">WHEREAMI</a>
<li><a href="#wrap_vertex">WRAP_VERTEX</a>
<li><a href="#zoom">ZOOM</a>
</ul></td></tr></table>

<hr>
<a name="abort"></a><h2>ABORT</h2>
<a href="#command language">Main prompt command</a>.
Causes immediate termination of the executing command
and returns to the command prompt.  Meant for stopping
execution of a command when an error condition is found.
There will be an error message output, giving the file
and line number where the abort occurred, but
it is still wise to have a script or procedure or function
 print an error message using 
<a href="commands.htm#errprintf"><tt>errprintf</tt>
before doing the <tt>abort</tt> command, so the 
user knows why.


<hr>
<a name="addload"></a><h2>ADDLOAD</h2>
<a href="#command language">Main prompt command</a>.

Loads a new datafile without deleting the current surface,
permitting the simultaneous loading of multiple copies of the
same datafile or different datafiles.  Syntax:
<pre>
   ADDLOAD <em>string</em>
</pre>
where <em>string</em> is either a sting literal in double quotes,
or a string variable name such as 
<a href="syntax.htm#datafilename"><tt>datafilename</tt></a>.
Elements in the new datafile are re-numbered to not conflict with
existing elements.  This is actually the same as the default
behavior of Evolver when loading a single datafile.  Thus the
<a href="general.htm#options"> -i 
command line option</a> or the 
<a href="datafile.htm#keep_originals"><tt>keep_originals</tt></a> keyword is
 not obeyed for the new datafile.  The 
<a href="datafile.htm#read section"><tt>read</tt></a> section of the new
datafile is not executed; this permits a datafile to use the <tt>addload</tt>
commnand in its <tt>read</tt> section to load more copies of itself.
The loading script is responsible for all  initialization that would
ordinarily be done in the <tt>read</tt> section of the new datafile.
Declarations in the top section of the new datafile will overwrite
any existing declarations.  This is usually not a problem when
loading multiple copies of the same datafile, but requires attention
when loading different datafiles.  For example, numbered constraints
are a bad idea; use named constraints instead.  See the sample
datafile <a href="addload_example.fe">addload_example.fe</a> for
an example of how to load and distinguish between multiple copies
of the same surface.






<hr>
<a name="areaweed"></a><h2>AREAWEED</h2>
<a href="#command language">Main prompt command</a>.

For deleting facets with less than a given area. Syntax:
<pre>   AREAWEED <em>expr</em></pre>
 Same as '<a href="single.htm#w">w</a>' command, 
  except does not need interactive response.
 Also same as "<tt>delete facets where area &lt;  <em>expr</em></tt>".
Examples:
<pre>   areaweed 0.001
   areaweed 2*min(facet,area)
</pre>


<hr>
<a name="binary_off_file"></a><h2>BINARY_OFF_FILE</h2>
<a href="#command language">Main prompt command</a>.
Produces one frame file for my 
<a href="http://www.susqu.edu/brakke/evmovie/evmovie-doc.html">evmovie</a>
3D movie program. Syntax:
<pre> BINARY_OFF_FILE <em>string</em>
</pre>
where <em>string</em> is the name of the output file, either a 
double-quoted string, a string variable, or a string-generating
expression (typically using <a href="#sprintf">sprintf</a>).


<hr>
<a name="binary_printf"></a><h2>BINARY_PRINTF</h2>
<a href="#command language">Main prompt command</a>.
For printing formatted binary output to files.  Syntax:
<pre>BINARY_PRINTF <em>string,expr,expr,...</em>
</pre>
  Prints to standard output using a binary interpretation
  of the standard C formats:  
<ul>
<li> %c one byte
<li> %d two byte integer
<li> %ld four byte integer
<li> %f four byte float
<li> %lf eight byte float
<li> %s  string, without the trailing null
<li> non-format characters are copied verbatim as single bytes.
</ul>
  The byte order for numbers can be set with the 
  <a href="toggle.htm#big_endian">big_endian</a> or
  <a href="toggle.htm#little_endian">little_endian</a> toggles. 
  NOTE: Either big_endian or little_endian must be set for binary_printf
   to work!
  The format string can be a string variable or a quoted string.
  There is a limit of 1000 characters on the format string, otherwise
  there is no limit on the number of arguments.  Meant to be use
  with redirection to a file. In Microsoft Windows, the output file type is 
   temporarily changed from TEXT to BINARY
 so newline bytes don't get converted.
 Example:
<pre>
  binary_printf "%ld%ld%ld",vertex_count,edge_count,facet_count &gt;&gt;"out.bin"
</pre>

<hr>
<a name="body_metis"></a>
<h2>BODY_METIS</h2>
<a href="#command language">Main prompt command</a>.
Partitions the set of bodies into n parts using the 
<a href="http://www.cs.umn.edu/~karypis/metis/metis/index.html">METIS</a>
library of Karypis and Kumar, if this library has been compiled into
the Evolver.  
The partition number of each body is left in its extra attribute
bpart (which will be created if it does not already exist).
BODY_METIS works only in the soapfilm model; for the string model,
partition facets using <a href="#metis">metis</a> or
<a href="#kmetis">kmetis</a>.
 BODY_METIS uses the PMETIS algorithm.  
Meant for experiments in partitioning the surface for
multiprocessors. 
Syntax: <pre> <tt>BODY_METIS</tt> <i>n</i>
</pre>
Example: <pre>
  body_metis 50;  // supposing we have thousands of bodies, say
  for each body bb do set bb.facet frontcolor (bb.bpart imod 15)+1;
</pre>

<hr>
<a name="breakpoint"></a><h2>BREAKPOINT</h2>
<a href="#command language">Main prompt command</a>.
The user may set a breakpoint in an already loaded script
with the "set breakpoint" command.  The syntax is
<pre>
  BREAKPOINT <em>scriptname</em> <em>linenumber</em>
</pre>
where <em>scriptname</em> is the name of the function or
procedure and <em>linenumber</em> is the line number in
the file where the breakpoint is to be set. There must be
executable code on the line, or you will get an error.
<em>linenumber</em> may be an expression.
<p>
Breakpoints may be unset individually with
<pre>
  UNSET BREAKPOINT <em>scriptname</em> <em>linenumber</em>
</pre>
or as a group with
<pre>
  UNSET BREAKPOINTS
</pre>
When a breakpoint is reached, Evolver will enter into a subcommand prompt,
at which the user may enter any Evolver commands (although some commands,
such as <tt>load</tt> would be very unwise).
To exit from the
subcommand prompt, use <tt>q</tt> or <tt>exit</tt> or <tt>quit</tt>.

<hr>
<a name="chdir"></a><h2>CHDIR</h2>
<a href="#command language">Main prompt command</a>.
 Changes the current directory, used for searching for files
 before EVOLVERPATH is used. Syntax:
<pre>   CHDIR <em>stringexpr</em></pre>
In MS-Windows, use a front slash '/'
or a double backslash '\\' instead of a single backslash as
the path character. 
Example:
<pre>  chdir "/usr/smith/project" 
</pre>

<hr>
<a name="show_off"></a>
<a name="close_show"></a><h2>CLOSE_SHOW</h2>

<a href="#command language">Main prompt command</a>.
   Closes the native graphics window started by the 
   `<a href="single.htm#s">s</a>' or
   <a href="commands.htm#show">SHOW</a> commands.  Does not affect geomview
 version. Synonym: show_off.

<hr>
<a name="define"></a><h2>DEFINE</h2>
<a href="#command language">Main prompt command</a>.
For runtime defining of 
<a href="syntax.htm#variables">variables</a>,
<a href="syntax.htm#arrays">arrays</a>,
<a href="constrnt.htm#level set constraints">level set constraints</a>,
<a href="constrnt.htm#boundaries">boundaries</a>,
<a href="quants.htm#named quantities">named quantities</a>,
<a href="quants.htm#named methods">named method instances</a>, and
<a href="elements.htm#extra attributes">extra attributes</a > of elements. 
The syntax for defining single variables is 
<pre>    DEFINE <em>variable</em> <em>type</em> </pre>
where <em>type</em> is <tt>REAL</tt>, <tt>INTEGER</tt>, or <tt>STRING</tt>.  
Note that this
way of declaring a variable does not take an initial value; thus it is
a way of making sure a variable is defined without overwriting an existing
value of the variable.
The syntax for defining
<a href="syntax.htm#arrays">arrays</a>
 and
<a href="datafile.htm#extra decl">extra attributes</a>
 is the same as in
the top of the datafile;
for
<a href="datafile.htm#constraint decl">constraints</a>,
<a href="datafile.htm#boundary decl">boundaries</a>,
<a href="datafile.htm#named quantity decl">named quantities</a>, and
<a href="datafile.htm#method instance decl">method instances</a>,
it is the same as in the top of the datafile except
the word "define" comes first.   Multi-line definitions should be
enclosed in brackets and terminated with a semicolon.  Or they can
be enclosed in quotes and fed to the <a href="commands.htm#exec">exec</a>
command.  Of course, using exec means the parser doesn't know about the
define until the exec is executed, so you cannot use the defined item
in commands until then.  It is legal to re-define an existing array or
array extra attribute with different dimensions (but the same number
of dimensions); data will be preserved
as best as possible in the resized array.
An array may be given the dimension 0 to free its memory allocation.
 Examples:
<pre>
  define fudge_factor real
  define pqlist real[imax][jmax]
  define edge attribute charlie real 
  define vertex attribute oldx real[3] 
  define facet attribute knots real[5][5][5] 
  { define constraint frontcon formula z = 0
    energy:
    e1: -y/2
    e2:  x/2
    e3:  0; }
  exec "define boundary newboundary parameters 1
    x: sin(p1)
    y: cos(p1)
    z: 3"
  exec "define quantity qarea info_only method facet_area global"
</pre>


<hr>
<a name="delete"></a><h2>DELETE</h2>
<a href="#command language">Main prompt command</a>.
For collapsing edges or facets. Syntax:
<pre>
   DELETE  <em><a href="#generators">generator</a></em>
</pre>
   Deletes edges by shrinking the edge to zero length
   (as in the tiny edge weed command t) and facets by eliminating
   one edge of the facet.  Facet edges will be tried for elimination
   in shortest to longest order.  Edges will not be deleted if both
   endpoints are 
<a href="elements.htm#fixed vertex">fixed</a>, 
or both endpoints have different 
<a href="constrnt.htm#level set constraints">constraints</a>
   or <a href="constrnt.htm#parametric boundaries">boundaries</a>
 from the edge.  DELETE will also fail if it would create two edges
  with the same endpoints, unless the <a href="toggle.htm#force_deletion">
  force_deletion</a> toggle is on; also see 
 <a href="toggle.htm#star_finagling">star_finagling</a>. DELETE maintains the continuity and
   connectedness of the surface, as opposed to <a href="#dissolve">
   DISSOLVE</a>.

  Example:
<pre>
      delete facets where area &lt; 0.0001
</pre>

<hr>
<a name="delete_text"></a><h2>DELETE_TEXT</h2>
Command to delete a text string from the graphics display.
Syntax:
<pre>
   delete_text(<em>text_id</em>)
</pre>
where <em>text_id</em> is the value returned by the
call to <a href="#display_text"><tt>display_text</tt>
that created the string.



<hr>
<a name="dirichlet"></a><h2>DIRICHLET</h2>

<a href="#command language">Main prompt command</a>.
Does one iteration of minimizing the Dirichlet integral of the 
surface.
The current surface is the domain, and the Dirichlet integral is of 
the map from the current surface to the next.  This is according to
a scheme of Konrad Polthier and Ulrich Pinkall <a href="biblio.htm#ref[PP]">[PP]</a>.  
At minimum Dirichlet
integral, the area is minimized also.  Works only on area with fixed
boundary; no volume constraints or anything else.  Seems to converge
very slowly near minimum, so not a substitute for other iteration
methods.  But if you have just a simple soap film far, far from
the minimum, then this method can make a big first step.
<a href="#dirichlet_seek">DIRICHLET_SEEK</a>
  will do an energy-minimizing search in the
direction.  

<hr>
<a name="dirichlet_seek"></a><h2>DIRICHLET_SEEK</h2>
<a href="#command language">Main prompt command</a>.
Calculates a motion as in the
<a href="#dirichlet">DIRICHLET</a> command, but uses this as a direction
of motion instead of as the motion itself.  DIRICHLET_SEEK then uses
a line-search along this direction to find a minimum of energy.

<hr>
<a name="display_text"></a><h2>DISPLAY_TEXT</h2>
<a href="#command language">Main prompt command</a>.
Causes the display of simple text on the graphics display.
Currently implemented for OpenGL and PostScript graphics.
Syntax:
<pre>
  text_id := display_text(x,y,string)
</pre>
The x,y coordinates of the start of the string are in 
window units, i.e. the window coordinates run from 
(0,0) in the lower left to (1,1) in the upper right.
The return value should be saved in a variable in case you
want to delete the text later; even if you don't want to 
<a href="#delete_text">delete</a> it, you must have something
on the left of the assignment for syntax purposes.
No font size control or font type or color implemented.
Meant for captioning images, for example a timer in
frames of a movie.


<hr>
<a name="dissolve"></a><h2>DISSOLVE</h2>
<a href="#command language">Main prompt command</a>.
   Removes elements from the surface without closing the gap left.
   Syntax:
<pre>
  DISSOLVE  <em><a href="#generators">generator</a></em>
</pre>   
   The effect is the same as if the line for the element were
   erased from a datafile.  Hence no element will be dissolved that
   is used by a higher dimensional element. (There are three exceptions:
   dissolving an edge on a facet in the string model, and 
   dissolving a facet on one body or with both adjacent bodies the same
 in the soapfilm model.)
Thus "<tt>dissolve edges; dissolve vertices</tt>" is safe because
only unused edges and vertices will be dissolved.  No error messages
are generated by doing this.
   Good for poking holes in a surface. Example:
<pre>  dissolve facets where original == 2; 
  dissolve edges; dissolve vertices
</pre>
Thus "<tt>dissolve edges; dissolve vertices</tt>" is safe because
only unused edges and vertices will be dissolved.  No error messages
are generated by doing this.

<hr>
<a name="dump"></a><h2>DUMP</h2>
<a href="#command language">Main prompt command</a>.
   Dumps current surface to named file in datafile format. Syntax:
<pre>
  DUMP <em>filename</em>
</pre>
   The filename is a <a href="syntax.htm#stringexpr">string</a>.
   With no filename, dumps to the default dump file, which is 
   the current datafile name with ".dmp" extension.  Same as the 
'<a href="single.htm#d">d</a>' command,
   except 'd' requires a response from the user for the filename.
   Examples:
<pre>   dump "foo.dmp"
   dump sprintf "%s.%g.dmp",datafilename,counter
</pre>

<hr>
<a name="dump_memlist"></a><h2>DUMP_MEMLIST</h2>
<a href="#command language">Main prompt command</a>.
Lists the currently allocated memory blocks.  For my own use
in debugging memory problems.

<hr>
<a name="edge_merge"></a><h2>EDGE_MERGE</h2>
<a href="#command language">Main prompt command</a>.
Merges two edges into one in a side-by-side fashion. Meant for joining
together surfaces that bump into each other.  Should not be used
on edges already connected by a facet, but merging edges that
already have a common endpoint(s) is fine. Syntax:
<pre>
  edge_merge(integer,integer)
</pre>
Note the arguments are signed integer ids for the elements, not
element generators.
The tails of the edges are merged, and so are the heads.  Orientation
is important.
Example:
<pre>
   edge_merge(3,-12)
</pre>

<hr>
<a name="edgeswap"></a><h2>EDGESWAP</h2>
<a href="#command language">Main prompt command</a>.
For changing the endpoints of edges. Syntax:
<pre>
 EDGESWAP <em><a href="#generators">edgegenerator</a></em>
</pre>
   If any of the qualifying edges are diagonals of quadrilaterals,
   they are flipped in the same way as in 
   <a href="single.htm#u">equiangulation</a>, 
   regardless of whether equiangularity is improved.
   "edgeswap edge" will try to swap all edges, and is
   not recommended, unless you like weird things.
   Various conditions will prevent an edge from being swapped:
   <ul>
   <li> The edge is <a href="elements.htm#fixed edge">fixed</a>.
   <li> There are not exactly two facets adjacent to the edge.
   <li> The adjacent facets do not have equal 
<a href="elements.htm#facet density">density</a>. 
   <li> The adjacent facets are not on the same
<a href="constrnt.htm#level set constraints">level set constraints</a>
        as the edge.
   <li> The adjacent facets are not on the same 
<a href="constrnt.htm#parametric boundaries">parametric boundary</a> as 
   the edge.
   <li> Swapping would create an edge with both endpoints the same (a loop).
   <li> Swapping would create two edges with the same endpoints (an "ear").
   </ul>
All but the first two reasons print messages.  This is a compromise
between informing the user why edges were not switched and preventing
a cascade of messages.  When edge swapping is  invoked through the 
'<a href="single.htm#u">u</a>' command, none
of these messages are printed.
Examples:
<pre>
 edgeswap edge[22] 

 edgeswap edge where color == red
</pre>
<hr>
<a name="edgeweed"></a><h2>EDGEWEED</h2>
<a href="#command language">Main prompt command</a>.
 Deletes edges shorter than given value. Syntax:
 <pre>
 EDGEWEED <em>expr</em>
 </pre>
 Same as '<a href="single.htm#t">t</a>' command, except does not need interactive response.
 Same as "<tt>delete edge where length &lt; <em>expr</em></tt>".

<hr>
<a name="eigenprobe"></a><h2>EIGENPROBE</h2>
<a href="#command language">Main prompt command</a>.
For finding the number of eigenvalues of the energy
<a href="eigentut.htm">Hessian</a>
that are less than, equal to, and greater than a given value.
Syntax:
<pre>
EIGENPROBE <em>expr</em>
EIGENPROBE(<em>expr</em>,<em>expr</em>)
</pre>
The first form prints the number of
  eigenvalues of the energy Hessian that are less than, equal to, and
   greater than <em><a href="syntax.htm#expr">expr</a></em>. 
    It is OK to use an exact eigenvalue
    (like 0, often) for the value, but not really recommended. 
      Useful for probing stability.
    Second form will further do inverse power iteration to find an
    eigenvector.  The second argument is the limit on the number
    of iterations.  The eigenvalue will be stored in the
    <a href="syntax.htm#last_eigenvalue"><tt>last_eigenvalue</tt></a>
internal variable, and the eigenvector can
    be used by the <tt><a href="#move">move</a></tt> command.
      The direction of the 
    eigenvector is chosen to be downhill in energy, if the 
    energy gradient is nonzero.

<hr>
<a name="equiangulate"></a><h2>EQUIANGULATE</h2>
<a href="#command language">Main prompt command</a>.

  This command tests the given edges to see if flipping them would improve
equiangularity.  It is the <a href="single.htm">u</a>
 command applied to a specified set of edges.
It differs from the <a href="#edgeswap">edgeswap</a>
 command in that only edges that pass
the test are flipped.  Syntax:
<pre>
  EQUIANGULATE <em>edge_generator</em>
</pre>
Examples:
<pre>
  equiangulate edge[3];
  equilangulate edge where color == red;
</pre> 

<hr>
<a name="errprintf"></a><h2>ERRPRINTF</h2>
<a href="#command language">Main prompt command</a>.
Same as <a href="#printf">printf</a>, except it sends its output to
stderr instead of stdout.  Useful in reporting error messages in 
scripts that have their output redirected to a file.

<hr>
<a name="exec"></a><h2>EXEC</h2>
<a href="#command language">Main prompt command</a>.
Executes a command in string form.  Good for runtime generation of commands.
Syntax: 
<pre>
   EXEC <em>stringexpr</em>
</pre>
Example:
<pre>
   exec sprintf "define vertex attribute prop%d real",propnumber
</pre>

<hr>
<a name="exprint"></a><h2>EXPRINT</h2>
<a href="#command language">Main prompt command</a>.
Prints the original input string defining a user-defined command, including
comments.
Syntax: 
<pre>
   EXPRINT <em>commandname</em>
</pre>
Example:
<pre>
Enter command: aa := { print 5; /* this is a test */ }
Enter command: exprint aa
 { print 5; /* this is a test */ }
</pre>

<hr>
<a name="facet_merge"></a><h2>FACET_MERGE</h2>
<a href="#command language">Main prompt command</a>.
Merges two soapfilm-model facets into one in a side-by-side fashion. 
Meant for joining
together surfaces that bump into each other.   The pairs of vertices
to be merged are selected in a way to minimize the distance between
merged pairs subject to the orientations given, so there are three
choices the algorithm has to choose from.  It is legal to merge facets
that already have some endpoints or edges merged.
 Syntax:
<pre>
  facet_merge(integer,integer)
</pre>
Note the syntax is a function taking signed integer facet id
 arguments, not element generators.
IMPORTANT: The frontbody of the first facet should be equal to the
backbody of the second (this includes having no body); this is the 
body that will be squeezed out
when the facets are merged. If this is not true, then facet_merge
will try flipping the facets orientations until it finds a legal
match.
Example:
<pre>
   facet_merge(3,-12)
</pre>


<hr>
<a name="fix"></a><h2>FIX</h2>
<a href="#command language">Main prompt command</a>.
For setting the <a href="elements.htm">FIXED</a> attribute of elements. Syntax:
<pre>
   FIX <em><a href="#generators">generator</a></em>
</pre>
 Example:
<pre>
   fix vertices where on_constraint 2
</pre>
Can also convert a parameter from 
<a href="datafile.htm#optimizing_parameter">optimizing</a> to non-optimizing.
Example:
<pre>
  fix radius
</pre>
Can also convert a 
<a href="quants.htm">named quantity</a> from info_only to fixed.

See also <a href="#unfix">unfix</a>.

<hr>
<a name="flush_counts"></a><h2>FLUSH_COUNTS</h2>
<a href="#command language">Main prompt command</a>.
Causes the printing of various internal counters that have become nonzero.
The counters are: 
equi_count,
edge_delete_count,
facet_delete_count,
edge_refine_count,
facet_refine_count,
notch_count,
vertex_dissolve_count,
edge_dissolve_count,
facet_dissolve_count,
body_dissolve_count,
vertex_pop_count,
edge_pop_count,
facet_pop_count,
pop_tri_to_edge_count,
pop_edge_to_tri_count,
pop_quad_to_quad_count,
where_count,
edgeswap_count,
fix_count,
unfix_count,
t1_edgeswap_count, and
notch_count.
Normally, these counts are accumulated during the execution of a command
and printed at the end of the command.  Flush_counts can be used to 
display them at some point within a command.  Flush_counts is usually
followed by <a href="#reset_counts">reset_counts</a>, which resets all 
these counters to 0.

<hr>
<a name="free_discards"></a><h2>FREE_DISCARDS</h2>
<a href="#command language">Main prompt command</a>.
Frees deleted elements in internal storage.  Ordinarily,
deleting elements does not free their memory for re-use
until the command completes, so that element iteration
loops do not get disrupted.  If for some reason this
behavior leads to excess memory usage or some other
problem, the user may use the <tt>free_discards</tt>
command to free element storage of deleted elements.
Just be sure not to do this inside any element iteration
loop that might be affected.




<hr>
<a name="geompipe"></a><h2>GEOMPIPE</h2>
<a href="#command language">Main prompt command</a>.
Redirects Evolver's geomview output to a command
 in place of sending it to geomview.  Syntax:
<pre>
   geompipe <em>stringexpr</em>
</pre>
The redirection can be closed with the command
"<a href="single.htm#P">P 9</a>".  <tt>geompipe</tt> is useful for debugging geomview data; but
be sure to toggle <tt><a href="toggle.htm#gv_binary">gv_binary</a> OFF </tt>to
get ascii data to look at.
<hr>
<a name="geomview command"></a><h2>GEOMVIEW</h2>
<a href="#command language">Main prompt command</a>.
The plain form "<tt>geomview</tt>" toggles the 
<a href="graphics.htm#geomview">geomview</a> display on and off.
The form 
<pre>   geomview <a href="syntax.htm#stringexpr"><em>stringexpr</em></a>
</pre> will send a command
to an already started geomview. 
 This string must be in the geomview command language, for which
consult the geomview documentation.
<hr>
<a name="help"></a><h2>HELP</h2>
<a href="#command language">Main prompt command</a>.
Main prompt command.  Prints what Evolver knows about an identifier
or keyword.  User-defined variables, named quantities, named methods,
named constraints, and element attributes are identified as such.
Information for syntax keywords comes from a file evhelp.txtt in
the doc subdirectory of your Evolver installation, so that subdirectory
should be on your EVOLVERPATH environment variable.
Syntax:
<pre>
   help <em>keyword</em>
</pre>
The <em>keyword</em> need not be in quotes, unless there are
embedded blanks.   After printing the help
section exactly matching the keyword, a list of related terms
is printed.  These are just the keywords containing your keyword
as a substring.
<p>
The built-in browser is in no way a complete substitute for
using a full-fledged browser such as Netscape or Mosaic.
<hr>
<a name="hessian"></a>
<a name="hessian command"></a><h2>HESSIAN</h2>

<a href="#command language">Main prompt command</a>.
        Does one step using Newton's method
	with the 
<a href="eigentut.htm">Hessian matrix</a> of the energy.  If the Hessian is
	not positive definite, a warning will be printed, but the move
	will be made anyway.  If the <a href="toggle.htm#check_increase">
	check_increase</a> toggle is on, then no move will be made if it
	would increase energy.  <a href="#hessian_seek">Hessian_seek</a>
 will use a variable
	step size to seek minimum energy in the direction of motion.
 The motion vector is stored, and may
	be accessed with the <a href="#move">move</a> command.  Not all
	energies and constraints have Hessian calculations yet.  See
	the <a href="eigentut.htm">Hessian tutorial</a> for more.

<hr>
<a name="hessian_menu"></a><h2>HESSIAN_MENU</h2>

<a href="#command language">Main prompt command</a>.
	Brings up a menu of experimental stuff involving the energy
<a href="eigentut.htm">Hessian
	matrix</a>. Not all of it works well, and may disappear in future
        versions.  A one-line prompt with options appears. Use option
	'<tt>?</tt>' to get a fuller description of the choices.
For those options that calculate an eigenvalue, the eigenvalue
(or first, if several) is saved in the internal variable
<a href="syntax.htm#last_eigenvalue">last_eigenvalue</a>.
	A quick summary of the current options:
<dl>
<dt><tt> 1. Fill in hessian matrix.

</tt></dt><dd>Allocation and calculation of Hessian matrix.</dd>

<dt><tt> 2. Fill in right side. (Do 1 first)

</tt></dt><dd>Calculates gradient and constraint values.</dd>

<dt><tt> 3. Solve. (Do 2 first) 

</tt></dt><dd>Solves system for a motion direction.</dd>

<dt><tt> 4. Move. (Do 3, A, B, C, E, K, or L  first) 

</tt></dt><dd>Having a motion direction, this will move some stepsize in that direction.
Will prompt for stepsize.  The direction of motion is saved and is
available in the <a href="#move">move</a> command.</dd>

<dt><tt> 7. Restore original coordinates. 

</tt></dt><dd>Will undo any moves.  So you can move without fear.</dd>

<dt><tt> 9. Toggle debugging. (Don't do this!) 

</tt></dt><dd>Prints Hessian matrix and right side as they are calculated in other
options.  Produces copious output, and is meant for development only.
Do NOT try this option.</dd>

<dt><tt> B. Chebyshev (For Hessian solution ). 

</tt></dt><dd>Chebyshev iteration to solve system.  This option takes care of its
own initialization, so you don't have to do steps 1 and 2 first.
Not too useful.</dd>

<dt><tt> C. Chebyshev (For most negative eigenvalue eigenvector). 

</tt></dt><dd>Chebyshev iteration to find most negative eigenvalue and eigenvector.
Will ask for number of iterations, and will prompt for further
iterations.  End by just saying 0 iterations.
 Prints Rayleigh quotient every 50 iterations.  After finding an
eigenpair, gives you the chance to find next lowest. Last eigenvector
found becomes motion for step 4.  Self initializing.
Not too useful.</dd>

<dt><tt> E. Lowest eigenvalue. (By factoring. Do 1 first) 

</tt></dt><dd>Uses factoring to probe the inertia of the shifted
Hessian H-cI until it has
the lowest eigenvalue located within .01.  Then uses inverse iteration
to find eigenpair.</dd>
<dt><tt> F. Lowest eigenvalue. (By conjugate gradient. Do 1 first) 

</tt></dt><dd>Uses conjugate gradient to minimize the Rayleigh quotient.</dd>

<dt><tt> L. Lanczos. (Finds eigenvalues near probe value. ) 

</tt></dt><dd>Uses Lanczos method to solve for 15 eigenvalues near the probe value
left over from menu choices 'P' or 'V'.  These are approximate
eigenvalues, but the first one is usually very accurate. Do not
trust apparent multiplicities.  From the main command prompt,
you can use the <a href="#lanczos"><tt>lanczos</tt></a> command.</dd>

<dt><tt> R. Lanczos with selective reorthogonalization. 

</tt></dt><dd>Same as 'L', but a little more elaborate to cut down on spurious
multiplicities by saving some vectors to reorthogonalize the
Lanczos vectors.  Not quite the same as the official
"selective reorthogonalization" found in textbooks.</dd>

<dt><tt> Z. Ritz subspace iteration for eigenvalues. (Do 1 first)</tt>
</dt><dd>
Calculate a number of eigenpairs near a probe value.
Will prompt for probe value and number of eigenpairs.
Same as <a href="#ritz"><tt>ritz</tt></a> main command.  
Can be interrupted gracefully by keyboard interrupt.
Afterwards, one can use the X option to pick a particular
eigenvector to look at.</dd>

<dt><tt> X. Pick Ritz vector for motion. (Do Z first)

</tt></dt><dd>Selects an eigenvector calculated by the Z option for use
in motion (option 4).
First eigenvalue listed is number 1, etc. 
Particularly useful for discriminating among high multiplicity 
eigenvalues, which the V option does not let you do.
 You can enter
the eigenvector by its number in the list from the  Z option.
As a special bonus useful when there are multiple eigenvectors for an
eigenvalue, you can enter the vector as a linear combination of
eigenvectors, e.g. ``0.4 v1 + 1.3 v2 - 2.13 v3''.</dd>

<dt><tt> P. Eigenvalue probe. (By factoring. Do 1 first) 

</tt></dt><dd>Reports the inertia of the shifted Hessian H-cI
 for user-supplied values of the shift c.
The Hessian H includes the effects of constraints.  Will prompt
repeatedly for c.  Null response exits.  From the main
command prompt, you can use the <a href="#eigenprobe"><tt>eigenprobe</tt>
</a> command.</dd>

<dt><tt> V. Eigenvalue probe with eigenvector. (By factoring. Do 1 first) 

</tt></dt><dd>Reports the inertia of the shifted Hessian H-cI
 for user-supplied values of the shift c, and calculates the
eigenvector for the eigenvalue nearest c by inverse power iteration.
You will be prompted for c and for the maximum number of iterations
to do.  From the main
command prompt, you can use the <a href="#eigenprobe"><tt>eigenprobe</tt>
</a> command.</dd>

<dt><tt> S. Seek along direction. (Do 3, A, B, E, C, K, or L first) 

</tt></dt><dd>Can do this instead of option 4 if you want Evolver to seek to
lowest energy in an already found direction of motion.  Uses the
same line search algorithm as the optimizing 
`<a href="single.htm#g"><tt>g</tt></a>' command.</dd>

<dt><tt> Y. Toggle YSMP/alternate minimal degree factoring.

</tt></dt><dd>Default Hessian factoring is by Yale Sparse Matrix Package.
The alternate is a minimal degree factoring routine of my
own devising that is a little more aware of the surface structure,
and maybe more efficient.  If YSMP gives problems, like running
out of storage, try the alternate. This option is available
at the main prompt as the <tt><a href="toggle.htm#ysmp">ysmp</a></tt> 
 toggle.</dd>

<dt><tt> U. Toggle Bunch-Kaufman version of min deg. 

</tt></dt><dd>YSMP is designed for positive definite matrices, since it doesn't
do any pivoting or anything.  The alternate minimal degree
factoring method, though, has the option of handling negative
diagonal elements in a special way.  This option is available
at the main prompt as the 
<a href="toggle.htm#bunch_kaufman"><tt>bunch_kaufman</tt></a> toggle.</dd>

<dt><tt> M. Toggle projecting to global constraints in move.

</tt></dt><dd>Toggles projecting to global constraints, such as volume constraints.
Default is ON.  Don't mess with this.  Actually, I don't remember
why I put it in.</dd>

<dt><tt> G. Toggle minimizing square gradient in seek.

</tt></dt><dd>For converging to unstable critical points.  When this is on,
option '<tt>S</tt>' will minimize the square of the energy gradient
rather than minimizing the energy.  Also the regular 
<a href="#saddle"><tt>saddle</tt></a>
and <a href="#hessian_seek"><tt>hessian_seek</tt></a>
 commands will minimize square gradient
instead of energy.</dd>

<dt><tt> =. Subshell.

</tt></dt><dd> Starts a command prompt while still in hessian_menu.
You can do pretty much any command, but you should not do anything
that changes the surface, thus invalidating the Hessian data.
This is meant, for example, for creating a graphics file of
an eigenvalue perturbation and then returning to the hessian_menu
prompt.  You exit the subshell with the "q" command.</dd>

<dt><tt> 0. Exit hessian.

</tt></dt><dd>Exits the menu.  `<tt>q</tt>' also works.</dd>
</dl>

For example, to inspect what eigenvectors look like, one would do
steps 1 and z, then repeatedly use x to pick an eigenvector, 4 to move, and
7 to restore.
<hr>
<a name="hessian_seek"></a><h2>HESSIAN_SEEK</h2>

<a href="#command language">Main prompt command</a>.
        Seeks to minimize energy along the direction found by Newton's
	method using the Hessian.  Otherwise same as the 
	<a href="#hessian command">hessian</a> command.
Syntax:
<pre> 
  HESSIAN_SEEK <em>maxscale</em>
</pre>
        where <em>maxscale</em> is an optional upper
        bound for the distance to seek.  The default maxscale is 1,
        which corresponds to a plain hessian step.  The seek will
        look both ways along the direction, and will test down to
        1e-6 of the maxscale before giving up and returning a scale of 0.
        This command is meant to be used when the surface is far enough
        away from equilibrium that the plain hessian command is unreliable,
        as hessian_seek guarantees an energy decrease, if it moves at all.

<hr>
<a name="loghistogram"></a>
<a name="histogram"></a><h2>HISTOGRAM, LOGHISTOGRAM</h2>
<a href="#command language">Main prompt command</a>.
For printing histograms in text form to standard output.
Syntax:
<pre>
HISTOGRAM(<em><a href="#generators">generator</a></em>, <em><a href="syntax.htm#expr">expr</a></em>)
LOGHISTOGRAM(<em>generator</em>, <em>expr</em>)
</pre>

Prints a histogram of the values of <em>expr</em> for the generated
elements.  
 It uses 20 bins evenly divided between minimum and maximum values.
 It finds its own maximum and 
minimum values, so the user does not have to specify binsize.
The log version will lump all zero and negative values into one bin.
Examples:
<pre>
 histogram(edge,dihedral*180/pi) 
 loghistogram(facet where color == red, area)
 histogram(vertex where on_constraint 1, sqrt(x^2+y^2+z^2))
</pre>

<hr>
<a name="history"></a><h2>HISTORY</h2>
 
<a href="#command language">Main prompt command</a>.
	Print the saved <a href="#history list">history list</a> of commands.

<hr>
<a name="lagrange"></a>
<a name="lagrange command"></a><h2>LAGRANGE</h2>
 
<a href="#command language">Main prompt command</a>.
   Changes to <a href="model.htm#Lagrange model">Lagrange model</a> from 
   <a href="model.htm#quadratic model">quadratic</a> or 
   <a href="model.htm#linear model">linear models</a>.  Syntax:
<pre>LAGRANGE <em>n</em>
</pre>
   where <em>n</em> is the <a href="syntax.htm#lagrange_order">
   lagrange_order</a>, which is between 1 and some built-in maximum
   (currently 8).   This command can also convert between Lagrange
   models of different orders.  
  Note that <tt>lagrange 1</tt>
gives the Lagrange model of order 1, which has a different internal
representation than the linear model.  Likewise, <tt>lagrange 2</tt> does
not give the quadratic model.

<hr> 
<a name="lanczos"></a><h2>LANCZOS</h2>
<a href="#command language">Main prompt command</a>.
For finding eigenvalues of the energy 
<a href="eigentut.htm">Hessian</a> near a given value.
Syntax:
<pre>
   LANCZOS <em><a href="syntax.htm#expr">expr</a></em>

   LANCZOS (<em>expr</em>,<em>expr</em>)
</pre>
 Does a little Lanczos algorithm and reports
 the nearest approximate eigenvalues to the given probe value.  
 In the first form, <em>expr</em> is the probe value, and 15
 eigenvalues are found.  In the second form, the first
  argument is the probe value, the second is the number of
  eigenvalues desired.  The output begins with the number
  of eigenvalues less than, equal to, and greater than the
  probe value.  Then come the eigenvalues in distance order
  from the probe.  Not real polished yet.  Beware that
  multiplicities reported can be inaccurate.  The eigenvalue
  nearest the probe value is usually very accurate, but others
  can be misleading due to incomplete convergence.  Since the
  algorithm starts with a random vector, running it twice can
  give an idea of its accuracy.
 
<hr>
<a name="linear"></a><h2>LINEAR</h2>
 
<a href="#command language">Main prompt command</a>.
   Changes to <a href="model.htm#linear model">linear model</a> from 
   <a href="model.htm#quadratic model">quadratic</a> or 
   <a href="model.htm#Lagrange model">Lagrange models</a>.

<hr>
<a name="list"></a><h2>LIST</h2>
<a href="#command language">Main prompt command</a>.
   List elements on the screen in the same format as in the datafile,
   or lists individual
   constraint, boundary, quantity, or method instance definitions.
   Syntax:
   <pre>
   LIST  <em><a href="#generators">generator</a></em>
   LIST <em>constraintname</em>
   LIST CONSTRAINT <em>constraintnumber</em>
   LIST <em>boundaryname</em>
   LIST BOUNDARY <em>boundarynumber</em>
   LIST <em>quantityname</em>
   LIST <em>instancename</em>
</pre>   
On unix systems, piping to <tt>more</tt> can be used for long displays. Examples:
<pre>
   list edges where id &lt;= 12  
   list vertices | "more"
   list vertices where x &lt; 1 and y &gt; 2 and z &gt;= 3  | "tee vfile"
   list facet[3]
   list facet[3].edges where on_constraint 1
   list facet[3].edge[2].vertex[1]
   list constraint 1
</pre>
See also
<a href="#list attributes">LIST ATTRIBUTES</a>,
<a href="#list bottominfo">LIST BOTTOMINFO</a>,
<a href="#list procedures">LIST PROCEDURES</a>, and
<a href="#list topinfo">LIST TOPINFO</a>.

<hr>
<a name="list attributes"></a><h2>LIST ATTRIBUTES</h2>

Prints a list of the "extra attributes" of each type of element.
Besides user-defined extra attributes, this list also contains
the predefined attributes that make use of the extra attribute
mechanism (being of variable size),
such as coordinates, parameters, forces, and velocities.
It does not list permanent, fixed-size attributes such as color
or fixedness, or possible attributes that are not used at all.

<hr>
<a name="bottominfo"></a>
<a name="list bottominfo"></a><h2>LIST BOTTOMINFO</h2>

<a href="#command language">Main prompt command</a>.
  Prints what would  be dumped in the 
 "<a href="datafile.htm#read section"><tt>read</tt></a>" section at the
  end of a dumpfile:  command definitions and various toggle states.

<hr>
<a name="procedures"></a>
<a name="procedure"></a>
<a name="list procedures"></a><h2>LIST PROCEDURES</h2>

<a href="#command language">Main prompt command</a>.
Prints names of all current user-defined commands.

<hr>
<a name="topinfo"></a>
<a name="list topinfo"></a><h2>LIST TOPINFO</h2>

<a href="#command language">Main prompt command</a>.
  Prints the <a href="datafile.htm#datafile header">first section</a>
 of the datafile on the screen. This is 
  everything before the vertices section.
<hr>
<a name="load"></a><h2>LOAD</h2>
<a href="#command language">Main prompt command</a>.
For loading a new surface. Syntax:
<pre>
LOAD <em>filename</em>
</pre> 
 Terminates the current surface and loads a new datafile.  The filename is
 the datafile name, and can be either a quoted string or a string variable.
 This completely re-initializes everything, including the command 
 interpreter.  In particular, the currently executing command ends.
 Useful only as the last command in a script.  For loading a new surface
 and continuing with the current command, see <a href="#permload">permload</a>.
  Wildcard matching is in effect
on some systems (Windows, linux, maybe others), but be very careful when
using wildcards since there can be unexpected matches.

<hr>
<a name="logfile"></a><h2>LOGFILE</h2>
<a href="#command language">Main prompt command</a>.
Syntax:
<pre>
LOGFILE <i>stringexpr</i>
LOGFILE OFF
</pre>
Starts recording all input and output to the file specified by
<i> stringexpr</i>, which must be a quoted string or a string variable or
expression.  Appends to an existing file.  To end logging, use
<tt>logfile off</tt>.  To record just input keystrokes, use
<a href="#keylogfile">keylogfile</a>.

<hr>
<a name="keylogfile"></a><h2>KEYLOGFILE</h2>
<a href="#command language">Main prompt command</a>.
Syntax:
<pre>
KEYLOGFILE <i>stringexpr</i>
KEYLOGFILE OFF
</pre>
Starts recording all input keystrokes to the file specified by
<i> stringexpr</i>, which must be a quoted string or a string variable or
expression.  Appends to an existing file.  To end logging, use
<tt>keylogfile off</tt>.  To record both input and output, use
<a href="#logfile">logfile</a>.

<hr>
<a name="kmetis"></a>
<a name="metis"></a><h2>METIS, KMETIS</h2>
<a href="#command language">Main prompt command</a>.
Partitions the set of facets (edges in string model) into n parts using the 
<a href="http://www.cs.umn.edu/~karypis/metis/metis/index.html">METIS</a>
library of Karypis and Kumar, if this library has been compiled into
the Evolver.  
Meant for experiments in partitioning the surface for
multiprocessors. The partition number of facet is left in the
facet extra attribute
fpart (edge epart for string model), which will be created if it 
does not already exist. 
METIS uses the PMETIS algorithm,
KMETIS uses the KMETIS algorithm. Syntax:
<pre>
  <tt>METIS</tt> <i>n</i>
  <tt>KMETIS</tt> <i>n</i>
</pre>
Example:
<pre>  metis 20;
  set facet color (fpart imod 15) + 1;
</pre>
For partitioning bodies, see <a href="#body_metis">body_metis</a>.
<hr>
<a name="longj"></a><h2>LONGJ</h2>
<a href="#command language">Main prompt command</a>.
For perturbing the surface. This does a "long jiggle", which
provides long wavelength 
                    perturbations that can test a surface for stability.
                    The parameters are a wavevector, a phase, and a 
		    vector amplitude.  The user will be prompted for
		    values.  Numbers for vectors should be entered
		    separated by blanks, not commas.  An empty reply
		    will accept the defaults.  A reply of <tt>r</tt> will
		    generate random values.  Any other will exit the
		    command without doing a jiggle.  In the random cases,
                    a random amplitude $\vec A$ and a random wavelength
                    $\vec L$ are chosen from a sphere whose radius is
                    the size of the object. The wavelength is inverted
                    to a wavevector $\vec w$.  A random phase $\psi$
                    is picked.  Then each vertex $\vec v$ is moved by
                    $\vec A\sin(\vec v \cdot \vec w + \psi)$.  This command
                    is archaic. More control
		    over perturbations may be had with the 
		    "<tt><a href="#set">set</a> vertex x ...</tt>" type of command.


<hr>
<a name="matrix_inverse"></a><h2>MATRIX_INVERSE</h2>
<a href="#command language">Main prompt command</a>. For computing
the inverse of a square matrix.  Currently applies only to global
matrices, not element attribute matrices.
 Syntax:
<pre>
  MATRIX_INVERSE(<em>matrix1</em>, <em>matrix2</em>)
</pre>
Here <em>matrix1</em> is the name of the original matrix, and <em>matrix2</em>
is the name of the inverse matrix.  They may be the same matrix to get an
in-place inverse.
Examples:
<pre>  define mata real[5][5]
  define matb real[5][5]
  ...  // fill in values of mata
  matrix_inverse(mata,matb)
  matrix_inverse(mata,mata)  
</pre>


<hr>
<a name="matrix_multiply"></a><h2>MATRIX_MULTIPLY</h2>
<a href="#command language">Main prompt command</a>. For computing
the product of matrices.  Currently applies only to global
matrices, not element attribute matrices.
 Syntax:
<pre>
  MATRIX_MULTIPLY(<em>matrix1</em>, <em>matrix2</em>, <em>matrix3</em>)
</pre>
Here <em>matrix1</em> and <em>matrix2</em> are the names of the multiplicands,
 and <em>matrix3</em>
is the name of the product matrix.  The product matrix may be the same as
one (or both) of the multiplicands.  The matrices can be one-dimensional
or two-dimensional, so you can do vector-matrix or
matrix-vector multiplication (but you can't do vector times vector).
Examples:
<pre>  define mata real[5][5]
  define matb real[5][5]
  define matc real[5][5]
  ...  // fill in values of mata and matb
  matrix_multiply(mata,matb,matc)
  matrix_multiply(mata,mata,mata)  
</pre>

<hr>
<a name="move"></a><h2>MOVE</h2>
<a href="#command language">Main prompt command</a>.
For moving along the current direction of motion. Syntax:
<pre>
  MOVE <em><a href="syntax.htm#expr">expr</a></em>
</pre> 
 Moves the surface along the previous direction of motion by the
 stepsize given by <em>expr</em>.  The previous direction can be
 either from a gradient step 
 (<a href="single.htm#g">g</a> command) or a hessian step 
 (<a href="#hessian command">hessian</a>, <a href="#saddle">saddle</a>,  
 <a href="#hessian_seek">hessian_seek</a>,
  <a href="#hessian_menu">hessian_menu</a> option 4, etc.). 
 The stepsize does not affect the current
 scale factor.  A negative step is not a perfect undo, since
 it cannot undo projections to constraints.  "Move" sometimes
 does not work well with optimizing parameters and hessian together.

<hr>
<a name="new_vertex"></a><h2>NEW_VERTEX</h2>
<a href="#command language">Main prompt command</a>. For creating
a new vertex.  The syntax is that of a function instead of a verb,
since it returns the id number of the new vertex.  The arguments
are the coordinates of the vertex.  The new vertex is not connected
to anything else; use the <a href="#new_edge">new_edge</a> command
to connect it. Syntax:
<pre>
  newid := NEW_VERTEX(<em><a href="syntax.htm#expr">expr</a></em>, <em><a href="syntax.htm#expr">expr</a></em>,...)
</pre>
Examples:
<pre>  newid1 := new_vertex(0,0,1)
  newid2 := new_vertex(pi/2,0,max(vertex,x))
</pre>

<hr>
<a name="new_edge"></a><h2>NEW_EDGE</h2>
<a href="#command language">Main prompt command</a>. For creating
a new edge.  The syntax is that of a function instead of a verb,
since it returns the id number of the new edge.  The arguments
are the id's of the tail and head vertices. Syntax:
<pre>
  newid := NEW_EDGE(<em><a href="syntax.htm#expr">expr</a></em>, <em><a href="syntax.htm#expr">expr</a></em>)
</pre>
The new edge has the same default properties as if it had been created
in the datafile with no attributes, so you will need to explicitly add
any attributes you want.
Example to create a set of coordinate axes in 3D:
<pre>  newv1 := new_vertex(0,0,0); fix vertex[newv1]; 
  newv2 := new_vertex(1,0,0); fix vertex[newv2];
  newv3 := new_vertex(0,1,0); fix vertex[newv3];
  newv4 := new_vertex(0,0,1); fix vertex[newv4];
  newe1 := new_edge(newv1,newv2); fix edge[newe1]; 
  newe2 := new_edge(newv1,newv3); fix edge[newe2];
  newe3 := new_edge(newv1,newv4); fix edge[newe3];
  set edge[newe1] no_refine; set edge[newe1] bare;
  set edge[newe2] no_refine; set edge[newe2] bare;
  set edge[newe3] no_refine; set edge[newe3] bare;
</pre>

<hr>
<a name="new_facet"></a><h2>NEW_FACET</h2>
<a href="#command language">Main prompt command</a>. For creating
a new facet.  The syntax is that of a function instead of a verb,
since it returns the id number of the new facet.  The arguments
are the oriented id's of the edges around the boundary of the
facet, in the same manner that a face is defined in the datafile.
The number of edges is arbitrary, and they need not form a closed
loop in the <a href="model.htm#string model">string model</a>.
In the <a href="model.htm#soapfilm model">soapfilm model</a>, 
if more than three edges are given, the new
face will be triangulated by insertion of a central vertex. In that
case, the returned value will be the <a href="elements.htm#original">
original</a> attribute of the new facets. In
the <a href="model.htm#simplex model">simplex model</a>, 
the arguments are the id's of the facet vertices.
Syntax:
<pre>
  newid := NEW_FACET(<em><a href="syntax.htm#expr">expr</a></em>, <em><a href="syntax.htm#expr">expr</a></em>,...)
</pre>
The new facet has the same default properties as if it had been created
in the datafile with no attributes, so you will need to explicitly add
any attributes you want.
Example:
<pre>  newf := new_facet(1,2,-3,-4); fix facet where original == newf;
</pre>
<hr>
<a name="new_body"></a><h2>NEW_BODY</h2>
<a href="#command language">Main prompt command</a>. For creating
a new body.  The syntax is that of a function instead of a verb,
since it returns the id number of the new body.  There are no arguments.
 Syntax:
<pre>
  newid := NEW_BODY
</pre>
The body is created with no facets. Use the <a href="elements.htm#frontbody">
set facet frontbody</a> and <a href="elements.htm#backbody">
set facet backbody</a> commands to install the body's facets.
The new body has the same default properties as if it had been created
in the datafile with no attributes, so you will need to explicitly add
any attributes you want, such as density or target volume.
Example:
<pre>  newb := new_body
  set facet frontbody newb where color == red
</pre>
<hr>
<a name="notch"></a><h2>NOTCH</h2>
<a href="#command language">Main prompt command</a>.
For refining a surface in regions of high curvature. Syntax:
<pre>
 NOTCH <em><a href="syntax.htm#expr">expr</a></em>
</pre>
  Notches all edges with dihedral angle greater than
  given value.  Same as '<tt><a href="single.htm#n">n</a></tt>' command, or 
<pre>   foreach edge ee where ee.dihedral &gt; <em>expr</em> do refine ee.facet
</pre>  Notching is done
  by adding a vertex in the middle of adjacent facets.  Should be
  followed by <a href="single.htm#u">equiangulation</a>.

<hr>
<a name="ometis"></a><h2>OMETIS</h2>
<a href="#command language">Main prompt command</a>.
Computes an ordering for Hessian factoring using the 
<a href="http://www.cs.umn.edu/~karypis/metis/metis/index.html">METIS</a>
library of Karypis and Kumar, if this library has been compiled into
the Evolver (not part of the public distribution yet). 
Prints ordering tree.  To actually use METIS ordering
during factoring, use the toggle <a href="toggle.htm#metis_factor">metis_factor</a>.
Note: ometis no longer works for Metis version 3 or later, since Metis
does not return the tree any more.  But metis_factor still works.
Syntax:
<pre>
  <tt>OMETIS</tt> <i>n</i>  // n is smallest partition size
  <tt>OMETIS</tt>           // defaults to n = 100
</pre>

<hr>
<a name="ooglfile"></a><h2>OOGLFILE</h2>
<a href="#command language">Main prompt command</a>.
Writes a file containing OOGL-formatted graphics data for the surface as a
POLY or CPOLY quad file.  This is a non-interactive version of the 
<a href="single.htm#P">P 2</a> command.  Syntax:
<pre> <tt>ooglfile</tt> <i>stringexpr</i>
</pre>
The string gets ".quad" appended to form the filename.
This command does not ask any of the other questions the <tt>P 2</tt> command
asks; it uses the default values, or whatever the last responses were to
the previous use of the interactive <tt>P 2</tt> command. Good for use in
scripts.  Example:
<pre>   ooglfilename := sprintf "frame%d",framecounter;
   ooglfile ooglfilename;
   framecounter += 1;
</pre>


<hr>
<a name="optimizing"></a>
<a name="optimise"></a>
<a name="optimize"></a><h2>OPTIMIZE</h2>
<a href="#command language">Main prompt command</a>.
Set gradient descent iteration to
 <a href="iterate.htm#optimizing scale">optimizing mode</a>,
with an upper bound on the <a href="iterate.htm#scale factor">scale factor</a>.
"Optimise" is a synonym.
  Syntax:
<pre>  OPTIMIZE <i>expr</i>
</pre>

<hr>
<a name="pause"></a><h2>PAUSE</h2>
<a href="#command language">Main prompt command</a>.
Pauses execution until the user hits RETURN.  Useful in scripts to
give the user a chance to look at some output before proceeding.

<hr>
<a name="permload"></a><h2>PERMLOAD</h2>
<a href="#command language">Main prompt command</a>.
Loads a new datafile and continues with the current command after the
<tt>read</tt> section of the datafile finishes.  The filename is
the datafile name, and can be either a quoted string or a string variable.
Since the automatic re-initialization makes Evolver forget all non-permanent
variables, care should be taken that the current command only uses
permanently assigned variables (assigned with <tt>::=</tt> ).  Useful for
writing scripts that run a sequence of evolutions based on varying
parameter values.  Using <tt>permload</tt> is a little tricky, since
you don't want to be redefining your permanent commands and variables
every time you reload the datafile, and your permanent command cannot
refer directly to variables parameterizing the surface.  One way to do it
is to read in commands from separate files.  For example, the catenoid
of <tt>cat.fe</tt> has height controlled by the variable <tt>zmax</tt>.
 You could have
a file <tt>permcat.cmd</tt> containing the overall series script command
<pre>
  run_series ::= {
    for ( height ::= 0.5 ; height &lt; 0.9 ; height ::= height + .05 )
    { permload "cat"; read "permcat.gogo"; }
  }
</pre>
and a file <tt>permcat.gogo</tt> containing the evolution commands
<pre>
  u; zmax := height; recalc; r; g 10; r; g 10; hessian;
  printf "height: %f  area: %18.15f\n",height,total_area &gt;&gt; "permcat.out";
</pre>
Then at the Evolver command prompt,
<pre>
  Enter command: read "permcat.cmd"
  Enter command: run_series
</pre>
For loading a new surface and not continuing with the current command,
see <a href="#load">load</a>.
  Wildcard matching is in effect
on some systems (Windows, linux, maybe others), but be very careful when
using wildcards since there can be unexpected matches.




<hr>
<a name="pop"></a><h2>POP</h2>
<a href="#command language">Main prompt command</a>.
Pops an individual edge or vertex or set of edges or vertices, 
giving finer control than
the universal popping of the 
<a href="single.htm#O">O</a> and <a href="single.htm#o">o</a>
 commands.  The specified vertices or edges are
tested for not being minimal in the soap film sense. For vertices, this
means having more than four triple edges adjacent; higher valence
edges are automatically popped.  For edges, this means
having more than three adjacent facets when not on constraints or
otherwise restricted.  It tries to act properly on constrained edges
also, but beware that my idea of proper behavior may be different from
yours.  Normally, popping puts in new edges and facets to keep originally
separated regions separate, but that behavior can be changed with the
<a href="toggle.htm#pop_disjoin">pop_disjoin</a> toggle.  The style
of popping a cone over a triangular prism can be controlled with
the <a href="toggle.htm#pop_to_edge">pop_to_edge</a>
and <a href="toggle.htm#pop_to_face">pop_to_face</a> commands.
The <a href="toggle.htm#pop_enjoin">pop_enjoin</a> toggle forces
joining cones to be popped by widening the vertex into a neck.  
 Examples:
<pre>
   pop edge[2]
   pop edge where valence==5
</pre>

<hr>
<a name="pop_edge_to_tri"></a><h2>POP_EDGE_TO_TRI</h2>
<a href="#command language">Main prompt command</a>.
 This command does a particular topological transformation common in
three-dimensional foam evolution.  An edge with tetrahedral point endpoints 
is transformed to a single facet.  A preliminary geometry check is made to
be sure the edge satisfies the necessary conditions, one of which is that 
the triple edges radiating from the endpoints have no common farther endpoints.
If run in <a href="toggle.htm#verbose">verbose</a> mode, messages are printed
when a specified edge fails to be transformed. This command
 is the inverse of the
<a href="#pop_tri_to_edge">pop_tri_to_edge</a> command.
  Works in linear and quadratic mode. 
Examples:
<pre>
   pop_edge_to_tri edge[2]
   pop_edge_to_tri edge where valence==3 and length &lt; 0.001
</pre>


<hr>
<a name="pop_quad_to_quad"></a><h2>POP_QUAD_TO_QUAD</h2>
<a href="#command language">Main prompt command</a>.
 This command does a particular topological transformation common in
three-dimensional foam evolution. A quadrilateral bounded by four
triple edges is transformed to a quadrilateral oriented in the opposite
direction.  The shortest pair of opposite quadrilateral edges are shrunk
to zero length, converting the quadrilateral to an edge, then the edge
is expanded in the opposite direction to form the new quadrilateral. 
The new quadrilateral inherits attributes such as color from the first
quadrilateral, although all the facet numbers are different.
A preliminary geometry check is made to
be sure the edge satisfies the necessary conditions, one of which is that 
the triple edges radiating from the quadrilateral corners
 have no common farther endpoints.
If run in <a href="toggle.htm#verbose">verbose</a> mode, messages are printed
when a specified quadriteral fails to be transformed. 
The specified facet can be any one of the facets of the quadrilateral
with a triple line on its border.  It doesn't hurt to apply the command to
all the facets of the quadrilateral, or to facets of multilple quadrilaterals.
Quadrilaterals may be arbitrarily subdivided into facets; in particular,
they may have some purely interior facets.
  Works in linear and quadratic mode.
 Examples:
<pre>
   pop_quad_to_quad facet[2]
   pop_quad_to_quad facet where color==red
</pre>



<hr>
<a name="pop_tri_to_edge"></a><h2>POP_TRI_TO_EDGE</h2>
<a href="#command language">Main prompt command</a>.
 This command does a particular topological transformation common in
three-dimensional foam evolution.  A facet with three tetrahedral point
vertices
is transformed to a single facet.  A preliminary geometry check is made to
be sure the edge satisfies the necessary conditions, one of which is that 
the triple edges radiating from the vertices have no common farther endpoints.
If run in <a href="toggle.htm#verbose">verbose</a> mode, messages are printed
when a specified edge fails to be transformed. This command
 is the inverse of the
<a href="#pop_edge_to_tri">pop_edge_to_tri</a> command.
  Works in linear and quadratic mode. 
 Examples:
<pre>
   pop_tri_to_edge facet[2]
   pop_tri_to_edge facet where color == red
</pre>



<hr>
<a name="postscript command"></a><h2>POSTSCRIPT</h2>
<a href="#command language">Main prompt command</a>.
Creates a PostScript file of the current surface in a file. Syntax:
<pre>  POSTSCRIPT <i>stringexpr</i> </pre>
The string gives the name of the file; a <tt>.ps</tt> extension will
be appended if it is missing.  It is the same as the 
<a href="graphics.htm#postscript">P</a> option 3 command, except that
there are no interactive responses needed.  Output options are
controlled by the 
<a href="toggle.htm#ps_colorflag">ps_colorflag</a>,
<a href="toggle.htm#ps_gridflag">ps_gridflag</a>,
<a href="toggle.htm#ps_crossingflag">ps_crossingflag</a>, and
<a href="toggle.htm#ps_labelflag">ps_labelflag</a> toggles.
<a href="toggle.htm#full_bounding_box">full_bounding_box</a> toggles.

<hr>
<a name="warning_messages"></a>
<a name="arrayslice"></a>
<a name="print"></a><h2>PRINT</h2>
<a href="#command language">Main prompt command</a>.
For printing expression values, strings, commands, arrays, or accumulated
warning messages. Syntax:
<pre>
PRINT <em><a href="syntax.htm#expr">expr</a></em>
PRINT <em><a href="syntax.htm#stringexpr">stringexpr</a></em>
PRINT <em><a href="commands.htm#command definition">commandname</a></em>
PRINT <em>arrayslice</em>
PRINT WARNING_MESSAGES
</pre>
  The arrayslice option takes an array name or a partially indexed array name.
  If more than one element results, the slice is printed in nested curly 
  braces.  The arrayslice can also be that of an array attribute of an
  element.  The warning_messages option is handy for reviewing warning
  messages that occur early in the loading of a datafile but scroll off the
  screen too rapidly to see.
  <tt>PRINT</tt> <em>expr</em> can also be used
  inside an expression, where it prints the expression and evaluates to 
  the value of its expression.  Examples:
<pre>
  print datafilename;
  print max(edge,length);
  print max(vertex, print (x^2+y^2+z^2) );
  gg := {list vertex where id &lt; 10; g 5};
  print gg;
  define parts real[3][2][3];
  print parts;
  print parts[3][2];
</pre>

<hr>
<a name="printf"></a><h2>PRINTF</h2>
<a href="#command language">Main prompt command</a>.
For printing formatted output.  Syntax:
<pre>PRINTF <em>string,expr,expr,...</em>
</pre>
  Prints to standard output using the standard C sprintf function.  
  All string, integer, and floating point formats are valid.
  Integer formats force floating point arguments to be converted to integer.
  The format string can be a string variable or a quoted string.
  There is a limit of 1000 characters on the format string, otherwise
  there is no limit on the number of arguments.
 Example:
<pre>
  printf "This is %s with total energy %f\n",datafilename,total_energy
</pre>

<hr>
<a name="quadratic"></a><h2>QUADRATIC </h2>

<a href="#command language">Main prompt command</a>.
   Changes to <a href="model.htm#quadratic model">quadratic model</a>
    from <a href="model.htm#linear model">linear</a>
     or <a href="model.htm#Lagrange model">Lagrange models</a>.

<hr>
<a name="bye"></a>
<a name="exit"></a>
<a name="quit"></a><h2>QUIT, BYE, EXIT</h2>

<a href="#command language">Main prompt command</a>.
 Exits Evolver or starts new datafile. Same as 
 `<tt><a href="single.htm#q">q</a></tt>' command.  

<hr>
<a name="rawestv"></a><h2>RAWESTV</h2>

<a href="#command language">Main prompt command</a>.
Does <a href="single.htm#V">vertex averaging</a>
for all vertices without regard for conserving volume or
whether averaged vertices have like constraints.   But doesn't
move vertices on boundaries.
To do a selected group of vertices, use
<a href="#rawest_vertex_average">rawest_vertex_average</a>.

<hr>
<a name="rawest_vertex_average"></a><h2>RAWEST_VERTEX_AVERAGE</h2>

<a href="#command language">Main prompt command</a>.
Does <a href="single.htm#V">vertex averaging</a>
on selected vertices
 without conserving volume on each side of surface,
 or attention to being on like constraints.
Doesn't move vertices on boundaries.
Using the <a href="toggle.htm#verbose">verbose</a> toggle
will print messages.
Syntax:
<pre>
RAWEST_VERTEX_AVERAGE <em><a href="#generators">generator</a></em>
</pre>
Example:
<pre>
rawest_vertex_average vertex[3]
</pre>

<hr>
<a name="rawv"></a><h2>RAWV</h2>

<a href="#command language">Main prompt command</a>.
Does <a href="single.htm#V">vertex averaging</a>
for all vertices without conserving volume on each side of surface.
Will only average vertices with those of like type of constraints.
Doesn't move vertices on boundaries.
To do a selected group of vertices, use
<a href="#raw_vertex_average">raw_vertex_average</a>.

<hr>
<a name="raw_vertex_average"></a><h2>RAW_VERTEX_AVERAGE</h2>

<a href="#command language">Main prompt command</a>.
Does <a href="single.htm#V">vertex averaging</a>
on selected vertices
 without conserving volume on each side of surface.
Will only average vertices with those of like type of constraints.
Doesn't move vertices on boundaries.
Using the <a href="toggle.htm#verbose">verbose</a> toggle
will print messages.
Syntax:
<pre>
RAW_VERTEX_AVERAGE <em><a href="#generators">generator</a></em>
</pre>
Example:
<pre>
raw_vertex_average vertex where valence == 6
</pre>

<hr>
<a name="read"></a><h2>READ</h2>

<a href="#command language">Main prompt command</a>.
For reading commands from a file. Syntax:
<pre>
READ <em>filename</em>
</pre>
   The filename can be either a quoted string or a string variable.
   The effect is as if the file were typed in at the keyboard.
   Hence main commands, responses to commands, and graphics mode
   commands can be included.  Read commands may be nested.
   On the occurence of an error, input reverts to the original
   standard input.  Example:
<pre>   read "zebra.cmd"
</pre>

<hr>
<a name="rebody"></a><h2>REBODY</h2>

<a href="#command language">Main prompt command</a>.
Recalculates connected bodies.  Useful after a body has been disconnected
by a neck pinching off.  Facets of an old body are divided into 
edge-connected sets, and each set defines a new body (one of which gets
the old body <a href="elements.htm#id">id</a>).  
The new bodies inherit the attributes of the
old body.  If the original body volume was fixed, 
then the new bodies' target volumes become the
new actual volumes.  If the original body had a 
<a href="elements.htm#body volconst">volconst</a>, the new bodies will
inherit the same value.  This will likely lead to incorrect values,
so you will have to adjust the volconsts by hand.
  In commands, you may specify the new bodies 
descended from an original body by using the 
'<a href="elements.htm#original">original</a>' atttribute.

<hr>
<a name="recalc"></a><h2>RECALC</h2>

<a href="#command language">Main prompt command</a>.
   Recalculates and redisplays everything.  Useful after changing some variable
   or something and recalculation is not automatically done.  Evolver tries
   to automatically recalculate when some significant change is made,
   but doesn't always know.  Also see <a href="toggle.htm#autorecalc">
   autorecalc</a>.

<hr>
<a name="refine"></a><h2>REFINE</h2>

<a href="#command language">Main prompt command</a>.
For subdividing  sets of edges or facets. Syntax:
<pre>
REFINE <em><a href="#generators">generator</a></em>
</pre>
Subdivides the generated edges or facets.
   Subdivides edges by putting a vertex in the middle
   of each edge, and splitting neighboring facets in two in the 
   <a href="model.htm#soapfilm model">soapfilm model</a>. It is the
   same action as the long edge subdivide command (command 
   <a href="single.htm#l">l</a>).
   Facets will be subdivided by putting a vertex in the center and
   creating edges out to the old vertices.  It is strongly suggested
   that you follow this with 
   <a href="single.htm#u">equiangulation</a> to nicen up the triangulation.
   Edge refinement is better than facet refinement as facet refinement
   can leave long edges even after equiangulation.  This command does not respect the <a href="elements.htm#no_refine">
no_refine</a> attribute.
   Example:
<pre>
       refine edges where not fixed and length &gt; .1 
</pre>

<hr>
<a name="reset_counts"></a><h2>RESET_COUNTS</h2>
<a href="#command language">Main prompt command</a>.
Resets to 0 various internal counters.
The counters are: 
<ul>
<li>equi_count,
<li>edge_delete_count,
<li>facet_delete_count,
<li>edge_refine_count,
<li>facet_refine_count,
<li>notch_count,
<li>vertex_dissolve_count,
<li>edge_dissolve_count,
<li>facet_dissolve_count,
<li>body_dissolve_count,
<li>vertex_pop_count,
<li>edge_pop_count,
<li>facet_pop_count,
<li>pop_tri_to_edge_count,
<li>pop_edge_to_tri_count,
<li>pop_quad_to_quad_count,
<li>where_count,
<li>edgeswap_count,
<li>fix_count,
<li>unfix_count,
<li>t1_edgeswap_count, and
<li>notch_count.
</ul>
Normally, a count is set to 0 at the start of a command that
potentially affects it, 
 accumulated during the execution of the command,
and printed at the end of the command.  To be precise, each counter has
a "reported" bit associated with it, and if the "reported" bit is set when
the appropriate command (such as 'u') is encountered, the counter will
be reset to 0 and the "reported" bit cleared. The "reported" bit is set by
either <a href="#flush_counts">flush_counts</a> or the end of a command.  
The idea is to have the counts from previous commands available to 
subsequent commands as long as possible, but still have the counter
reflect recent activity.


<hr>
<a name="reverse_orientation"></a><h2>REVERSE_ORIENTATION</h2>

<a href="#command language">Main prompt command</a>.
For reversing the orientation of  sets of edges or facets. Syntax:
<pre>
REVERSE_ORIENTATION <em><a href="#generators">generator</a></em>
</pre>
Reverses the internal orientation of selected edges or facets,
as if they had been entered in the datafile with the opposite
orientation.  Useful, for example, when edges come in contact
with a constraint and you want to get them all oriented in the
same direction.  Relative orientations of constraint and quantity
integrals change to compensate, so energy, volumes, etc. should
be the same after the command, but it would be wise to check in
your application.  Examples:
<pre>
   reverse_orientation edge[7]
   reverse_orientation facets where backbody != 0
</pre>



<hr>
<a name="ritz"></a><h2>RITZ</h2>

<a href="#command language">Main prompt command</a>.
For finding eigenvalues of the energy Hessian near a given value.
Syntax:
<pre>
RITZ(<em>expr</em>,<em>expr</em>)
</pre>
Applies powers of inverse shifted Hessian to a random subspace
to calculate eigenvalues near the shift value.  First argument
is the shift.  Second argument is the dimension of the subspace.
Prints out eigenvalues as they converge to machine accuracy.
This may happen slowly, so you can interrupt it by hitting
whatever your interrupt key is, such as CTRL-C, and the current
values of the remaining eigenvalues will be printed out.  Good
for examining multiplicities of eigenvalues.  It is legal to 
shift to an exact eigenvalue, but not wise, as they will not
be printed.  See the <a href="eigentut.htm">Hessian tutorial</a>
for more.
The first eigenvalue is subsequently available in the
<a href="syntax.htm#last_eigenvalue">last_eigenvalue</a> internal
variable.
 The full list of eigenvalues produced is subsequently 
available in the <tt>eigenvalues[]</tt> array.
  Example: To get the lowest 5 eigenvalues of a Hessian
you know is positive definite:
<pre>
   ritz(0,5)
</pre>

<hr>
<a name="renumber_all"></a><h2>RENUMBER_ALL</h2>

Reassigns element id numbers of all types of elements
in accordance with order in storage, i.e.
as printed with the LIST commands.  Besides renumbering after massive
topology changes, this can be used with the <a href="#reorder_storage">
reorder_storage</a>
command to number elements as you desire.  Do NOT use this command
inside an element generator loop!

<hr>
<a name="reorder_storage"></a><h2>REORDER_STORAGE</h2>

Reorders the storage of element data structures, sorted by the
extra attributes <tt>vertex_order_key</tt>, <tt>edge_order_key</tt>,
<tt>facet_order_key</tt>,
<tt>body_order_key</tt>, and <tt>facetedge_order_key</tt>. 
 Originally written
for testing dependence of execution speed on storage ordering, but
could be useful for other purposes, particularly when 
<a href="#renumber_all">renumber_all</a>
is used afterwards.  Example:
<pre>
   define vertex attribute vertex_order_key real
   define edge attribute edge_order_key real
   define facet attribute facet_order_key real
   define body attribute body_order_key real
   define facetedge attribute facetedge_order_key real

   reorder := {
     set vertex vertex_order_key x+y+z;
     set edge ee edge_order_key min(ee.vertex,vertex_order_key);
     set facetedge fe facetedge_order_key fe.edge[1].edge_order_key;
     set facet ff facet_order_key min(ff.vertex,vertex_order_key);
     set body bb body_order_key min(bb.facet,facet_order_key);
     reorder_storage;
     }
</pre>



<hr>
<a name="saddle"></a><h2>SADDLE</h2>

<a href="#command language">Main prompt command</a>.
Seek to minimum energy along the eigenvector of the lowest negative
eigenvalue of the <a href="eigentut.htm">Hessian</a>. 
If there is no negative eigenvalue,
then the surface is unchanged. The alternate form 
<pre>SADDLE <em>expr</em>
</pre>
will limit the step size to <em>expr</em>.  The motion vector is
available afterwards through the <a href="#move">move</a> command.

<hr>
<a name="set"></a><h2>SET</h2>
<a href="#command language">Main prompt command</a>.
For  setting <a href="elements.htm#attributes">element attributes</a>
 to values. Syntax:
<pre>
 SET <em>elementtype</em> [<em>name</em>] <em>attrib expr1 where expr2</em> 
 
 SET <em>elementtype.attrib expr1 where expr2</em> 
 
 SET <em>name</em> <em>attrib expr</em>
 
 SET <em>name.attrib expr</em>

 SET <em>quantityname attrib expr</em>

 SET <em>instancename attrib expr</em>
</pre>
The first two forms set the value of the attribute <i>attrib</i> to the
value <i>expr1</i> for all elements of the given type that satisfy
<i>expr2</i>. 
<i>elementtype</i> can be vertex, edge, facet, or body, or any
<a href="#generators">element generator</a> without a <tt>where</tt>
clause.  The optional <i>name</i> refers to the element under
consideration, and can be used in <i>expr1</i> and <i>expr2</i> to
refer to attributes of that element.  Even without <i>name</i>, 
attributes of the element can be referred to if the references are
not nested in 
<a href="#generators">element generators</a> in <i>expr1</i> or <i>expr2</i>.
The next two forms can be used inside an element <a href="#generators">
generator</a> which defines <em>name</em>.
When <em>name</em> is not used, a '.' can be used, for those who like
that sort of thing.
 SET can change
   the following attributes: constraint, coordinates, density, orientation,
    non-global named quantity or named method, user-defined extra attributes,
    body target volume, body volconst, fixed, frontbody, backbody,
    pressure, color, frontcolor, backcolor, boundary, and opacity
    (for the appropriate type elements).  Fixed, named quantity, and named
    method attributes are just toggled on; they do not need the first
    <i>expr</i>.  Setting the pressure on a body automatically unfixes
    its volume. For constraint, the <i>expr</i> is the constraint number.
    If using set to put a vertex on a parametric boundary, set the 
    vertex's boundary parameters p1, p2, etc. first.
Examples:
<pre>
  set facets density 0.3 where original == 2
  set vertices x 3*x where id &lt; 5  // multiplies x coordinate by 3
  set body target 5 where id == 1   // sets body 1 target volume to 5
  set vertices constraint 1 where id == 4
  set facet color clear where original &lt; 5
  foreach facet ff do set ff color red
  define vertex attribute weight real; set vertex weight 3
  set vertex quantity my_quantity
  set vertex[1].facet color red
</pre>
Note the first form of syntax has the attribute and new value in the middle of 
an element generator.  Syntactically inconsistent with other commands
that use element generators, but more natural
English.   Actually, the syntactically consistent <br>
    <tt>set facet where id &lt; 5 color red</tt> <br> does
work. <p>

 The last two forms set the value of a named quantity or named method instance attribute.
 For a named quantity, the settable attributes are target, modulus, volconst, and
 tolerance. For a named method instance, only modulus.  There is no implicit
 reference to the quantity in the expression, so say
<pre>
   set myquant target myquant.value 
</pre>
 rather than  <tt>set myquant target value</tt>.

Also see <a href="#unset">unset</a>.
<hr>
<a name="shell"></a><h2>SHELL</h2>

<a href="#command language">Main prompt command</a>.
   Invokes a system subshell for the user on systems where this is 
   possible.  No arguments.  See the <a href="#system">system</a>
command for execution of an explicit shell command.

<hr>
<a name="show"></a><h2>SHOW</h2>
<a href="#command language">Main prompt command</a>.
Which edges and facets are actually shown in graphics displays
can be controlled by defining boolean expressions that edges or
facets must satisfy in order to be passed to the graphics display.
There are two expressions internally: one for edges and one for facets.
They may be set with the syntax
<pre>
   show edges where <em>expr</em>
   
   show facets where <em>expr</em>
</pre>
The default is to show all facets, and to show all special edges:
<a href="elements.htm#fixed edge">fixed</a> edges, 
<a href="elements.htm#edge constraints">constraint</a> edges, 
<a href="elements.htm#edge boundary">boundary</a> edges, and edges without
exactly two adjacent facets.  The defaults can be restored with
"<tt>show facets</tt>" and "<tt>show edges</tt>".  Some graphics
modules (like geomview) can show edges of facets on their own initiative.
This is separate from the edge show criterion here;  to show the colors
of edges, the edges must satisfy the criterion.  <tt>Show</tt> causes
graphics to be redrawn. If a graphics display
is not active, <tt>show</tt> will start <a href="graphics.htm#screen graphics">
screen graphics</a>.  <a href="#show_expr"><tt>Show_expr</tt></a> is the same as
<tt>show</tt> in setting the show expressions, except it does not start
graphics.  <tt>Show</tt> alone will just start screen graphics.
Examples:
<pre> show facets where color == red
 show edges where 1
 show edges where color != black
</pre>
The string model will show facets (default is not to show them) as
the facet show expression specifies, but the triangulation algorithm
is fairly simple.
<p>
As an edge or facet attribute, "show" is a Boolean read-only
attribute giving the current status of the edge or facet, for
example, to report the number of edges being shown, do
<pre>
   print sum(edge,show)
</pre>

<hr>
<a name="show_expr"></a><h2>SHOW_EXPR</h2>
<a href="#command language">Main prompt command</a>.
This does the same as <a href="#show"><tt>show</tt></a>, except it does
not start or redraw graphics; it just sets a show expression.  Good for
use in the <a href="datafile.htm#read section">read</a> section of the
datafile for controlling which elements will be displayed without
automatically starting a display.
<hr>

<a name="show_trans"></a><h2>SHOW_TRANS</h2>
<a href="#command language">Main prompt command</a>.
  Applies string of graphics commands to the image transformation
   matrix without doing any graphic display.   The string must be in 
   double quotes or be a string variable, and
     is the same format as is accepted by the regular graphics command
 prompt. Example:
<pre>
  show_trans "rrdd5z" 
</pre>

<hr>
<a name="showq"></a><h2>SHOWQ</h2>
<a href="#command language">Main prompt command</a>.
Displays <a href="graphics.htm#screen graphics">screen graphics</a>,
 but returns immediately to the main prompt and
 does not go into graphics command mode.



<hr>
<a name="simplex_to_fe"></a><h2>SIMPLEX_TO_FE</h2>
<a href="#command language">Main prompt command</a>.
Converts a 
<a href="model.htm#simplex model">simplex model</a>
 surface to a <a href="model.htm#string model">string</a>
 or <a href="model.htm#soapfilm model">soapfilm
model</a> surface. Only works for dimension 1 or 2 surfaces,
but works in any ambient dimension.






<hr>
<a name="sobolev_seek"></a>
<a name="sobolev"></a><h2>SOBOLEV</h2>

<a href="#command language">Main prompt command</a>.
Uses a positive definite approximation to the area Hessian
to do one Newton iteration, following a scheme due to
Renka and Neuberger <a href="biblio.htm#ref[RN]">[RN]</a>. 
Works only on area with fixed
boundary; no volume constraints or anything else.  Seems to converge
very slowly near minimum, so not a substitute for other iteration
methods.  But if you have just a simple soap film far, far from
the minimum, then this method can make a big first step.
SOBOLEV_SEEK will do an energy-minimizing search in the
direction. 

<hr>
<a name="sprintf"></a><h2>SPRINTF</h2>
<a href="#command language">Main prompt command</a>.
  Prints to a string  using the standard C sprintf function. May
  be used whereever a <a href="syntax.htm#stringexpr"><em>stringexpr</em></a>
 is called for in syntax.
  Otherwise same as <a href="#printf">printf</a>.
Syntax:
<pre>SPRINTF <em>stringexpr,expr,expr,...</em>
</pre>
Example:
<pre>
   dumpname := SPRINTF "file%04g.dmp",counter
</pre>



<hr>
<a name="subcommand"></a><h2>SUBCOMMAND</h2>
<a href="#command language">Main prompt command</a>.
Invokes a subsidiary command interpreter.  Useful
if you want to pause in the middle of a script to
give the user the chance to enter commands.
A subcommand interpreter gives the prompt
<tt>Subcommand:</tt> instead of <tt>Enter command:</tt>.
Subcommands may be nested several deep, in which case
the prompt will display the subcommand level.  To 
exit a subcommand prompt, use <tt>q</tt>, <tt>quit</tt>,
or <tt>exit</tt>.  The <a href="#abort"><tt>abort</tt></a>
command will return to the prompt on the same
subcommand level.



<hr>
<a name="system"></a><h2>SYSTEM</h2>
<a href="#command language">Main prompt command</a>.
For executing a program. Syntax:
<pre>
  SYSTEM <em>stringexpr</em>
</pre>
   Invokes a subshell to execute the given command, on systems
   where this is possible. Command must be
   a quoted string or a string variable.  
   Will wait for command to finish before resuming.

<hr>
<a name="transform_depth"></a><h2>TRANSFORM_DEPTH</h2>
<a href="#command language">Main prompt command</a>.
Quick way of generating all possible view transforms from
<a href="datafile.htm#view generators">view transform generators</a>,
to a given depth <i>n</i>.  Syntax:
<pre>
  TRANSFORM_DEPTH n
</pre>
where n is the maximum number of generators to multiply together.
This will toggle immediate showing of 
<a href="toggle.htm#transforms">transforms</a>, if they are
not already being shown.

<hr>
<a name="transform_expr"></a><h2>TRANSFORM_EXPR</h2>
<a href="#command language">Main prompt command</a>.
If <a href="datafile.htm#view generators">view transform generators</a>
were included in the datafile, then a set of view transforms may be
generated by an expression with syntax much like a regular expression.
An expression generates a set of transform matrices, and are compounded
by the following rules.  Here a lower-case letter stands for one of the
generators, and an upper-case letter for an expression.
<table>
<tr><td>a</td><td>  Generates set {I,a}.</td></tr>
<tr><td>!a</td><td>  Generates set {a}.</td></tr>
<tr><td>AB</td><td>  Generates all ordered products of pairs from A and B.</td></tr>
<tr><td>nA</td><td>  Generates all n-fold ordered products.</td></tr>
<tr><td>A|B</td><td>  Generates union of sets A and B.</td></tr>
<tr><td>(A)</td><td>  Grouping; generates same set as A.</td></tr>
</table>
The precedence order is that nA is higher than AB which is higher than A|B.
The "!" character suppresses the identity matrix in the set of matrices
generated so far.
Note that the expression string must be enclosed in double quotes or be
a string variable.  Examples:
<pre>
  transform_expr "3(a|b|c)"    //all products of 3 or fewer generators
  transform_expr "abcd"  // generates 16 transforms
  transform_expr "!a!a!a!a!"  // generates one transform
</pre>
All duplicate transforms are removed, so the growth of the sets does not
get out of hand.  Note the identity transform is always included.  The 
letter denoting a single generator may be upper or lower case.  The order
of generators is the same as in the datafile.  In the 
<a href="model.htm#torus model">torus model</a>,
transforms along the three period vectors are always added to the end
of the list of generators given in the datafile. If 26 generators are not
enough for somebody, let me know.
The current value of the expression may be accessed as a string
variable, and the number of transformations generated can be
accessed as <a href="syntax.htm#transform_count">transform_count</a>. 
For example, 
<pre>  print transform_expr
  print transform_count
</pre>

<hr>
<a name="t1_edgeswap"></a><h2>T1_EDGESWAP</h2>
<a href="#command language">Main prompt command</a>.
Does a T1 topological transition in the string model. 
When applied to an edge joining two triple points, it reconnects edges
so that opposite faces originally adjacent are no longer adjacent, but
two originally non-adjacent faces become adjacent.  
<pre>
      \_/   =&gt;   \ /
      / \         |
                 / \
</pre>
It will silently
skip edges it is applied to that don't fulfill the two triple endpoint
criteria, or whose flipping is barred due to fixedness or constraint
incompatibilities.  The number of edges flipped can be accessed through
the <a href="syntax.htm#t1_edgeswap_count">t1_edgeswap_count</a> internal
variable. Running with the <a href="toggle.htm#verbose">verbose</a>
toggle on will print details of what it is doing.
Syntax:
<pre> T1_EDGESWAP <em>edge_generator</em>
</pre>
Examples:
<pre>
   t1_edgeswap edge[23]
   t1_edgeswap edge where length &lt; 0.1
</pre>

<hr>
<a name="unfix"></a><h2>UNFIX</h2>
<a href="#command language">Main prompt command</a>.
   Removes the FIXED attribute from a set of elements. Syntax:
<pre> UNFIX <em>generator</em>
</pre>
 Example:
<pre>  unfix vertices where on_constraint 2
</pre>
Can also convert a parameter from non-optimizing to
<a href="datafile.htm#optimizing_parameter">optimizing</a>.
Example:
<pre>
  unfix radius
</pre>
Can also convert a 
<a href="quants.htm">named quantity</a> from fixed to info_only.

<hr>
<a name="unset"></a><h2>UNSET</h2>
<a href="#command language">Main prompt command</a>.
Removes an attribute from a set of elements. Syntax:
<pre>
UNSET <em>elements</em> [<em>name</em>] <em>attrib where clause</em>
</pre>
 Unsettable attributes 
   are fixed (<a href="elements.htm#fixed vertex">vertices</a>,
   <a href="elements.htm#fixed edge">edges</a>, or
   <a href="elements.htm#fixed facet">facets</a>)
   , body <a href="elements.htm#target volume">target volume</a>,
   body <a href="elements.htm#body pressure">pressure</a>, body 
   gravitational <a href="elements.htm#body density">density</a>,
   non-global <a href="quants.htm">named quantities</a>,
   non-global <a href="quants.htm">named methods</a>,
   level-set <a href="constrnt.htm">constraints</a>, 
   <a href="constrnt.htm#parametric boundaries">parametric boundary</a>.
   <a href="elements.htm#frontbody">frontbody</a>, or
   <a href="elements.htm#backbody">backbody</a>.
     A use for the
   last is to use a boundary or constraint to define an initial
   curve or surface, refine to get a decent triangulation, then
   use "unset vertices boundary 1" and "unset edges boundary 1"
   to free the curve or surface to evolve.  The form "unset
   facet bodies ..." is also available to disassociate given
   facets from their bodies. Examples:
<pre>   unset body[1] target
   unset vertices constraint 1; unset edges constraint 1
</pre>

<hr>
<a name="vertex_average"></a><h2>VERTEX_AVERAGE</h2>
<a href="#command language">Main prompt command</a>.
Does vertex averaging for one vertex at a time. Syntax:
<pre>  VERTEX_AVERAGE <em>vertex_generator</em>
</pre>
The action is the same as the <a href="single.htm#V">V</a> command,
except that each new vertex position is calculated sequentially,
instead of simultaneously, and an arbitrary subset of vertices 
may be specified. Fixed vertices do not move. Examples:
<pre>  vertex_average vertex[2]
  vertex_average vertex where id &lt; 10
  vertex_average vertex vv where max(vv.facet,color==red) == 1
</pre>

<hr>
<a name="vertex_merge"></a><h2>VERTEX_MERGE</h2>
<a href="#command language">Main prompt command</a>.
Merges two soapfilm-model vertices into one. 
Meant for joining together surfaces that bump into each other. 
Should not be used for vertices already joined by an edge.
 Syntax:
<pre>
  vertex_merge(integer,integer)
</pre>
Note the syntax is a function taking integer vertex id arguments, not element
generators.
Example:
<pre>
   vertex_merge(3,12)
</pre>

<hr>
<a name="whereami"></a><h2>WHEREAMI</h2>
<a href="#command language">Main prompt command</a>.
If Evolver is at a debugging breakpoint,
then <tt>whereami</tt> will print a stack trace
of the sequence of commands invoked to get to
the current breakpoint.

<hr>
<a name="wrap_vertex"></a><h2>WRAP_VERTEX</h2>
<a href="#command language">Main prompt command</a>.
Syntax:
<pre> wrap_vertex(<em>vexpr</em>,<em>wexpr</em>)
</pre>
In a symmetry group model, transforms the coordinates of
vertex number <em>vexpr</em> by symmetry group element <em>wexpr</em>
and adjusts wraps of adjacent edges accordingly.


<hr>
<a name="zoom"></a><h2>ZOOM</h2>
<a href="#command language">Main prompt command</a>.
For isolating a region of a surface. Syntax:
<pre>
 ZOOM <em>integer expr</em>
</pre>
   Zooms in on vertex whose id is the given <em>integer</em>, with radius the
   given <em>expr</em>.  Same as the '<a href="single.htm#Z">Z</a>' command, 
   but not interactive.  

<hr>
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