Surface Evolver Documentation - general syntax

# Surface Evolver Documentation

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# Surface Evolver syntax

Both the datafile and user commands follow a common general syntax described in this file, with a few differences as noted.

Lexical format Comments Line splicing Case Whitespace Identifiers Numbers Colors Expressions | Constant expressions String expressions Atomic values Internal variables Arithmetic operators Boolean operators Operator precedences Math functions Element attribute values

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## Lexical format

For those who know about such things, the datafile and commands are read with a lexical analyzer generated by the lex program. The specification is in datafile.lex. Commands are further parsed by a yacc-generated parser.

In parsing an expression, the longest legal expression is used. This permits coordinates to be specified by several consecutive expressions with no special separators.

## Comments

Comments may be enclosed in /* */ pairs (as in C) and may span lines. // indicates the rest of the line is a comment, as in C++.

## Lines and line splicing

The file is made up of lines. Line breaks are significant. The next physical line can be spliced onto the current line by having \ be the last character of the current line. Line splicing is not effective in // comments. Blank lines and comment lines may be placed freely anywhere. The various combinations of CR and NL that various computer systems use are all recognized

## Case

Case is not significant in the datafile. All letters are converted to lower case on input. In commands, case is only significant for single-letter commands.

## Whitespace

In the datafile, whitespace consists of spaces, tabs, commas, colons, and semicolons. So it's fine if you want to use commas to separate coordinate values, and colons to prettify constraint definitions. In commands, whitespace consists of spaces and tabs. CTRL-Z is also whitespace, for the benefit of files imported from DOS.

## Identifiers

Identifiers follow standard C rules (composed of alphanumeric characters and '_' with the leading character not a digit) and must not be keywords. Identifiers are used for macro names (in the datafile) and user-defined variables and commands. Identifiers must have at least two characters, since single characters can be confused with commands. To find out if a name is already in use as a keyword or user-defined name interactively, use help command. In scripts, one can use the is_defined function, which has the syntax

     is_defined(stringexpr)

The stringexpr must be a quoted string or other string expression. The return value is 0 if the name is undefined, 1 if defined. This function is evaluated at run-time, but variables in the whole command are parsed before the command is executed, so a command like `if is_defined("newvar") then newvar := 1 else newvar := 2` will give `newvar` the value 1 even if this is its first appearance. A better way in scripts to test is to use the define command to define the variable without initialization, and then test to see if it has the default value, i.e. 0 for a numeric variable and a sizeof 0 for a string variable.

## Numbers

Constant values may be in any of the usual forms. This includes integers, fixed point, and scientific notation such as

          2    -3    .5    23.    5e-10    +0.7D2

Hexadecimal integers starting with 0x, as in 0x12Af, are also accepted, as are binary numbers such as 11001b, indicated by a trailing 'b'. Color names are interpreted as integers.

## Colors

The colors of edges and facets are recorded as integers in the range -1 through 15. How these integers translate to colors on the screen is determined by how Evolver's graphics drivers are written. The following synonyms are supplied, and it is hoped that the graphics drivers will be written to display these correctly:

-1 CLEAR 0 BLACK 1 BLUE 2 GREEN 3 CYAN 4 RED | 5 MAGENTA 6 BROWN 7 LIGHTGRAY 8 DARKGRAY 9 LIGHTBLUE 10 LIGHTGREEN | 11 LIGHTCYAN 12 LIGHTRED 13 LIGHTMAGENTA 14 YELLOW 15 WHITE

The special color value CLEAR (-1) makes a facet transparent. These tokens are simply translated to integer values wherever they occur, so these are reserved words. Edge and facet colors may be set in the datafile or by the set command.

## Arithmetic expressions

Arithmetic expressions evaluate to real numbers. Boolean expressions are a subclass, with zero as false and nonzero as true; true results evaluate as 1. Ordinary algebraic notation is used.

- atomic values
- arithmetic operators
- boolean operators
- operator precedences
- math functions
- aggregate functions

## Constant expressions

Constant expressions are evaluated when parsed. They are denoted by constexpr in various syntax definitions. They occur mostly in the datafile. Although they may contain variables, changing the variable value after parsing has no effect. Variable expressions (denoted by expr in syntax definitions) are recorded as parse trees and are re-evaluated each time needed.

## Atomic values

The following evaluate to single numbers in expressions:

number
  An integer, real, or hexadecimal constant. Hex numbers begin with `0x`.
pi
  Mathematical constant, ratio of circle circumference to radius.
x1,x2,...; x,y,z,w
  Depending on context, space coordinates, vertex coordinates, edge vector components, or facet normal components.
p1,p2,...
  Parameters of vertices on boundaries.
G
  Current gravitational constant for calculating gravitational energy.
user-defined variables
  Arbitrary variables defined in the datafile or at runtime.
Indexed array variables.
internal variables
  Special pre-defined variables.
element attributes
  Things like vertex coordinates, edge length facet area, colors.
named quantity attributes
  Including modulus, target, value, pressure.
method instance attributes
  Including modulus, value.
toggle name
  Any toggle command name may be used as a Boolean variable in an expression (full word toggles, not single letters). But beware the ambiguity in interpreting a toggle as a command or a value. You may have to force the toggle to be interpreted as a value. "`ad := autodisplay`" sets ad as a command synonym for autodisplay, while "`ad := (autodisplay)`" records the current boolean value.

## String expressions

A string expression evaluates to a string of characters. At present, the only ways to produce strings are:

- double-quoted string literals, e.g. `"this is a string"`. The following standard C escape sequences are recognized:
  - \n newline
  - \r carriage return
  - \t tab
  - \b backspace
  - \q double-quote mark
  - \c the character c elsewise
  In DOS, MS-Windows, or Windows NT paths, use / as the directory separator, since \ is an escape character. DOS and Windows have always accepted / as a directory separator.
- string variables, either internal like `datafilename`, or user-defined.
- output from `sprintf`.

## Arithmetic operators

These are the arithmetic operators that may appear in expressions:

+,-,*,/
  Usual real arithmetic. NOTE: A '+' or '-' preceded by whitespace and followed by a number is taken to be a signed number. Thus "3 - 5" and "3-5" are single expressions, but "3 -5" is not. This is for convenience in separating multiple expressions listed on the same line for vertex coordinates, metric components, etc. in the datafile.
idiv
  Integer divide. Rounds toward zero, then does integer division. Ex: 7 idiv 2 is 3; -3.5 idiv 2.1 is -1; -3 idiv 2 is -1.
%, mod
  Real arithmetic modulus, x % y = x - floor(x/y)*y.
imod
  Integer arithmetic modulus, x imod y = floor(x) - floor(floor(x)/floor(y))*floor(y).
=
  NOT an assignment operator. Treated as low-precedence '-' so level-set constraint formulas like x^2 + y^2 - R^2 may be written naturally as x^2 + y^2 = R^2.
(,)
  Parentheses for grouping and functional notation.
^,**
  Raise to real power.
? :
  Conditional expression, as in the C language. x ? y : z evaluates to y if x is nonzero and to z if x is zero.

## Boolean operators

Boolean expressions are a subclass of arithmetic expressions, with zero as false and nonzero as true; true results evaluate as 1.

==,>,<,>=,<=,!= | Numerical or boolean comparison.
NOT, ! | Boolean NOT
AND, && | Boolean AND, with short-circuit evaluation.
OR, || | Boolean OR, with short-circuit evaluation.

## Operator precedences

Here is the order of operator precedence, listed from high to low with equal precedence on same line, with associativity.

Operator | Associativity
--- | ---
^,** | left associative
unary - | right associative
*,/,%,IMOD,IDIV | left associative
+,- | left associative
on_boundary on_constraint hit_constraint on_quantity on_method_instance | nonassociative
==,>,<,>=,<=,!= | right associative
NOT, ! | right associative
AND, && | left associative
OR, || | left associative
? : | left associative
= | left associative

## Math functions

These are the math functions available in expressions. They take one argument in parentheses, except where noted.

abs(x)
  Absolute value.
sqr(x)
  Square.
sqrt(x)
  Square root. Argument must be nonnegative.
sin(x),cos(x),tan(x)
  Trig functions, argument in radians.
acos(x),asin(x),atan(x)
  Inverse trig functions (acos, asin arguments clamped to [-1,1]).
atan2(y,x)
  Inverse tangent, range -pi to pi.
log(x) ,exp(x)
  Natural log, exponentiation base e.
sinh(x),cosh(x),tanh(x)
  Hyperbolic functions.
asinh(x),acosh(x),atanh(x)
  Inverse hyperbolic functions.
pow(x,y)
  Raise x to real power y; x may be negative if y is an integer.
ceil(x),floor(x)
  Round up or down to integer.
minimum(a,b),maximum(a,b)
  Extreme of two arguments.
ellipticE,ellipticK(x)
  Complete elliptic functions.
incompleteEllipticE(phi,m),incompleteEllipticF(phi,m)
  Incomplete elliptic functions of parameters (phi,m); agrees with Mathematica definition.
wrap_inverse(w)
  Inverse of symmetry group element w, in numerical representation. Useful only if a symmetry group has been declared in the datafile.
wrap_compose(w1,w2)
  Composition of symmetry group elements w1, w2, in numerical representation. Useful only if a symmetry group has been declared in the datafile.
usrn
  user-defined functions

## Miscellaneous functions

### sizeof

Returns the number of entries in an array or array extra attribute. Can also be applied to a string or string variable to get the number of characters in the string. Syntax:

      SIZEOF(name)
      SIZEOF(string)

where name is the name of the extra attribute, not in quotes.

### is_defined

To find out if a name is already in use as a keyword or user-defined name, use the is_defined function, which has the syntax

     is_defined(stringexpr)

The stringexpr must be a quoted string or other string expression. The return value is 0 if the name is undefined, 1 if defined. This function is evaluated at run-time, but variables in the whole command are parsed before the command is executed, so a command like `if is_defined("newvar") then newvar := 1 else newvar := 2` will give `newvar` the value 1 even if this is its first appearance. A better way in scripts to test is to use the define command to define the variable without initialization, and then test to see if it has the default value, i.e. 0 for a numeric variable and a sizeof 0 for a string variable.

## User-defined built-in functions

User-defined functions can be defined in C in userfunc.c. They are meant for situations where expression interpretation is too slow, or functions such as elliptic integrals are wanted. Currently, they are automatically functions of the coordinates. Do not give any arguments in the expression; for example "(usr1 + usr3)/usr10".

## Aggregate functions

The maximum, minimum, sum, or average of an expression over a set of elements may be done with aggregate functions. The syntax is

       aggregate(generator,expr)

where aggregate is `max, min, sum,` or `avg`, and generator is an element generator. Example: this prints the total area of all green facets:

       print sum(facet where color == green, area)

"Count" is an aggregate function that gives the number of elements generated, regardless of the expression.

## Element attribute values in expressions

The value of any element attribute may be used in an expression. The attribute name alone may be used if there is a default element active. Example:

       foreach facet do print area

Otherwise the attribute is referred to as a field of the element:

       foreach facet ff do print ff.area

Indexed extra attributes need an index in square brackets:

       foreach facet ff do print ff.something[3]

Index values are rounded down to integer values. Indexing starts with 1.

Most attributes are numerical or boolean, but some are element generators.

The following attributes are available (for details, see elements):

X1,X2,...,X,Y,Z,W
  Coordinates of vertices, components of edge vector or facet normal
P1,P2
  Parameters for boundaries
ID
  Element identifying number
OID
  Oriented element identifying number
ORIGINAL
  Number of parent datafile element
COLOR
  Integer representing color of facet (color of front if back different) or edge
FRONTCOLOR
  Color of front of facet
BACKCOLOR
  Color of back of facet
VALENCE
  Number of edges on a vertex, facets on edge, edges on a facet, or facets, or on a body
AREA
  Area of facet
LENGTH
  Length of edge
VOLUME
  Actual volume of body
TARGET
  Target fixed volume of body
VOLCONST
  Constant added to calculated volume of body
DENSITY
  Density of edge, facet, or body
DIHEDRAL
  Dihedral angle of facets on an edge
ORIENTATION
  Sign for oriented integrals of edges or facets
ON_CONSTRAINT n
  True if element on given constraint
HIT_CONSTRAINT n
  True if element is exacty on a constraint. Useful for one-sided constraints.
ON_BOUNDARY n
  True if element on given boundary
ON_QUANTITY quantityname
  True if the given named quantity applies to the element.
ON_METHOD_INSTANCE instancename
  True if the given method instance applies to the element.
WRAP
  numerical edge wrap in torus model or other quotient space
quantity_name
  contribution of an element to a named quantity
instance_name
  contribution of an element to a named method instance
extra_attribute[expr]
  name of user-defined extra attribute, with subscript if needed.
VERTEX
  Generator of edge or facet vertices.
MIDV
  Id of edge midpoint in quadratic model.
EDGE
  Generator of edges attached to vertex, or edges around a facet.
FACET
  Generator of facets around a vertex or an edge.
BODY
  Generator of bodies that a facet is on.

## Variables

The Evolver command language has its own version of the user-defined variables common to most programming languages. Variables are typed according to the types of the values assigned to them: numeric or string. Users may define numeric variables either by variable declarations in the datafile, or both types by assigning a value to an identifier in a command. A variable may be subjected to optimization by declaring it an optimizing_parameter in the datafile.

## Arrays

It is possible to define multidimensional arrays of integers or reals with the syntax

       DEFINE variablename  REAL|INTEGER [expr]...

This syntax works both in the datafile header and at the command prompt. If the array already exists, it will be resized, with old elements kept as far as possible. Do not resize with a different number of dimensions. Note that array indexing starts at 1. A size of 0 is legal, and useful if you are not using an array at the moment and want to free storage space. There is runtime checking of array bounds. Example:

      define fvalues integer[10][4]
      define basecoord real[10][space_dimension]

Array elements may be used and assigned as is usual for programming languages:

      fvalues[3][4] := 234;
      if basecoord[3][1] > 2 then print "hello world!\n";

The print command may be used to print whole arrays or array slices in bracketed form. Example:

       print fvalues
       print fvalues[4]

## Internal variables

These are pre-defined names for some of Evolver's internal variables. They may be used in the same way as user-defined variables, except the values of read-only variables may not be changed by the user.

ambient_pressure_value background body_count breakflag body_dissolve_count brightness check_count clock constraint_tolerance cpu_counter datafilename date_and_time delete_count dissolve_count edge_count edge_delete_count edge_dissolve_count edge_refine_count edge_pop_count edgeswap_count eigenneg eigenpos eigenzero | equi_count estimated_change facet_count facetedge_count facet_delete_count facet_dissolve_count fix_count gravity_constant hessian_epsilon hessian_slant_cutoff instance_name.modulus instance_name.value inverse_periods integral_order integral_order_1d integral_order_2d iteration_counter jiggle_temperature lagrange_order last_eigenvalue last_error last_hessian_scale | linear_metric_mix memory_arena memory_used notch_count pickvnum pickenum pickfnum pop_count pop_edge_to_tri_count pop_quad_to_quad_count pop_tri_to_edge_count quadratic_metric_mix quantity_name.modulus quantity_name.pressure quantity_name.target quantity_name.value random random_seed refine_count rotation_order scale | scale_scale scrollbuffersize simplex_representation space_dimension surface_dimension symmetry_group t1_edgeswap_count target_tolerance temperature thickness torus torus_periods total_area total_energy total_length total_time transform_count unfix_count vertex_count vertex_dissolve_count vertex_pop_count where_count window_aspect_ratio

ambient_pressure_value
  Internal read-write variable. Value of the external pressure in the ideal gas model.
background
  Internal read-write variable. Background color used in certain screen graphics (xgraph and Windows, at the moment).
body_count
  Internal read-only variable. Number of bodies.
breakflag
  Internal read-write variable. When set to a non-zero value, causes the command interpreter to abort and return to the command prompt. Software equivalent of hitting the keyboard interrupt (typically CTRL-C). The break doesn't happen immediately, but at a certain point in the interpreter loop when it periodically checks for user interrupt. Meant for bailing out of nested commands, since return only breaks out of the current procedure.
body_dissolve_count
  Internal read-only variable. Number of bodies dissolved by dissolve command. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
brightness
  Internal read-only variable. Median gray level used in PostScript output and screen graphics.
check_count
  Internal read-only variable. Number of errors found by the most recent C command.
clock
  Internal read-only variable. Total elapsed Evolver execution time in seconds. Reads system process elapsed time, which often has a fairly coarse resolution of 0.01 seconds. For nanosecond timing, see cpu_counter.
constraint_tolerance
  Internal read-write variable. When vertices are projected to level-set constraints, projection by Newton's method is repeated until the level-set function is smaller than constraint_tolerance. Default value 1e-12.
cpu_counter
  Internal read-only variable. Processor cycle counter, available only on systems I know how to access this (x86 for now). Gives the number of CPU cycles since the system booted. Note that this is wall clock time, not process time. Also note that it resets to zero when a notebook computer hibernates, so it is not guaranteed to be monotone increasing during the life of a process! time in seconds. Reads system process elapsed time, which often has a fairly coarse resolution of 0.01 seconds. For process elapsed time, see clock.
datafilename
  Internal read-only variable. String containing name of current datafile.
delete_count
  Internal read-only variable. Sum of edge_delete_count and facet_delete_count. Kept for backwards compatibility.
dissolve_count
  Internal read-only variable. Sum of vertex_dissolve_count edge_dissolve_count, facet_dissolve_count, and body_dissolve_count. Kept for backwards compatibility.
date_and_time
  Internal read-only variable. String containing current date and time.
edge_count
  Internal read-only variable. Number of edges.
edge_delete_count
  Internal read-only variable. Number of edges deleted by delete command. This does not count the secondary edge deletions caused by deleting an edge. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
edge_dissolve_count
  Internal read-only variable. Number of edges dissolved by dissolve command. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
edge_refine_count
  Internal read-only variable. Number of edges refined by refine edges command. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
edge_pop_count
  Internal read-only variable. Number of edges popd by pop edges, o, or O, commands. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
edgeswap_count
  Internal read-only variable. Number of edges swapped by edgeswap command. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
eigenneg
  Internal read-only variable. Number of negative eigenvalues in last Hessian factoring.
eigenpos
  Internal read-only variable. Number of positive eigenvalues in last Hessian factoring.
eigenzero
  Internal read-only variable. Number of zero eigenvalues in last Hessian factoring.
equi_count
  Internal read-only variable. Number of edges flipped by equiangulation. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
estimated_change
  Internal read-only variable. Estimated change of energy during last iteration with estimate option in effect.
facet_count
  Internal read-only variable. Number of facets.
facetedge_count
  Internal read-only variable. Number of facetedges.
facet_delete_count
  Internal read-only variable. Number of facets deleted by delete command. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
facet_dissolve_count
  Internal read-only variable. Number of facets dissolved by dissolve command. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
facet_refine_count
  Internal read-only variable. Number of facets refined by refine facets command. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
fix_count
  Internal read-only variable. Number of elements fixed by fix command. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
gravity_constant
  Internal read-write variable. Value of the gravitational constant, which can also be set by the G command.
hessian_epsilon
  Internal read-write variable. Magnitude regarded as zero by hessian command when factoring the Hessian matrix. If a zero appears on the diagonal at the pivot during factoring, a check is made to see if the rest of the row is zero. If it is, then a 1 is placed on the diagonal; else an error is reported.
hessian_slant_cutoff
  Internal read-write variable. Hessian commands treat vertices whose normal vector is nearly perpendicular to constraints as fixed. hessian_slant_cutoff is the cosine of angle. Works on vertices with one degree of freedom in hessian_normal mode. Default value 0.
instance_name.modulus
  Internal read-write variable. Modulus of a named method instance.
instance_name.value
  Internal read-only variable. Value of a named method instance.
inverse_periods[expr][expr]
  Internal read-only variable. Inverse matrix of the torus_periods matrix. Uses 1-based indexes. Useful for normalizing vertex coordinates to period basis.
integral_order
  Internal read-write variable. Order of polynomial done by 1D and 2D Gaussian integration. Much better to set 1D and 2D separately. Synonym: integration_order
integral_order_1d
  Internal read-write variable. Order of polynomial done by 1D Gaussian integration. Synonym: integration_order_1D
integral_order_2d
  Internal read-write variable. Order of polynomial done by 2D Gaussian integration. Synonym: integration_order_2D
iteration_counter
  Internal read-only variable. Loop count of last loop in a command.
jiggle_temperature
  Internal read-only variable. Current temperature for jiggling.
lagrange_order
  Internal read-only variable. Order of Lagrange model. Set with the lagrange n command.
last_eigenvalue
  Internal read-only variable. Eigenvalue from last saddle, ritz, or eigenprobe command.
last_error
  Internal read-write variable. Has error number of last error message.
last_hessian_scale
  Internal read-only variable. Stepsize from last
saddle or hessian_seek command.
linear_metric_mix
  Internal read-write variable. Fraction of linear interpolation in Hessian metric.
memory_arena
  Internal read-only variable. Total memory allocated to the program's heap. Available only on SGI and Win32 versions.
memory_used
  Internal read-only variable. Total memory used in the program's heap. Available only on SGI and Win32 versions.
notch_count
  Internal read-only variable. Number of edges notched in last notch command.
pickvnum
  Internal read-write variable. Number of last vertex picked in geomview.
pickenum
  Internal read-write variable. Number of last edge picked in geomview.
pickfnum
  Internal read-write variable. Number of last facet picked in geomview.
pop_count
  Internal read-only variable. Sum of vertex_pop_count and edge_pop_count. Kept for backwards compatibility.
pop_edge_to_tri_count
  Internal read-only variable. Number of edges flipped to triangles by the pop_edge_to_tri command. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
pop_quad_to_quad_count
  Internal read-only variable. Number of quadrilaterals flipped by the pop_quad_to_quad command. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
pop_tri_to_edge_count
  Internal read-only variable. Number of triangles flipped to edges by the pop_tri_to_edge command. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
quadratic_metric_mix
  Internal read-write variable. Fraction of linear interpolation in Hessian metric in the quadratic model. Not very useful.
quantity_name.modulus
  Internal read-write variable. Modulus of a named quantity.
quantity_name.pressure
  Internal read-only variable. Lagrange multiplier for a constrained named quantity.
quantity_name.target
  Internal read-write variable. Constrained value of a named quantity.
quantity_name.value
  Internal read-only variable. Value of a named quantity.
random
  Internal read-only variable. Random number between 0 and 1.
random_seed
  Internal read-write variable. Seed for random number generator, used for example in jiggling or in finding random initial vectors in various Hessian eigenvector algorithms. Defaults to 1 at start of datafile.
refine_count
  Internal read-only variable. Number of elements refined in last refine command.
rotation_order
  Internal read-write variable. Order of rotation group for symmetry groups rotate and flip_rotate.
scale
  Internal read-write variable. Current scale factor for multiplying the force to get the motion in the '`g`' command.
scale_scale
  Internal read-write variable. Multiplier for the scale factor used in the '`g`' command. Default value 1.
scrollbuffersize
  Internal read-write variable. The command window scroll buffer size on Windows machines. Meant for non-NT Windows that don't have menu properties option for this.
simplex_representation
  Internal read-only variable. Whether the simplex model is in effect.
space_dimension
  Internal read-only variable. Dimension of ambient space.
surface_dimension
  Internal read-only variable. Dimension of surface.
symmetry_group
  Internal read-only variable. Whether any symmetry group is active (Boolean).
t1_edgeswap_count
  Internal read-only variable. Number of edges swapped by t1_edgeswap command. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
target_tolerance
  Internal read-write variable. When volume constraints or named quantity constraints are enforced, Newton's method is repeated until the total deviation from target values is less than `target_tolerance`. Default value 1e-4.
temperature
  Internal read-only variable. Amplitude for jigglinge.
thickness
  Internal read-only variable. Thickness for thickened surfaces in graphics output in P command. Used when facet frontcolor and backcolor are different. Default value 0.001 times the maximum linear dimension of the surface. If you get backside color showing through, increase the thickness.
torus
  Internal read-only variable. Whether the torus model is in effect. (Boolean).
torus_periods[expr][expr]
  Internal read-only variable. Current values of the period vectors in the torus model. Torus_periods[i][j] is component j of vector i. Uses 1 based indexes. For changing the torus_periods, define the periods in the datafile with variables, and alter the variables.
total_area
  Internal read-only variable. Total area of the surface in soapfilm or simplex models.
total_energy
  Internal read-only variable. Total energy of the surface.
total_length
  Internal read-only variable. Total length of the surface in the string model.
total_time
  Internal read-only variable. Elapsed evolution time in the form of total scale factors.
transform_count
  Internal read-only variable. Number of image transforms active, as generated by the `transform_expr` command.
fix_count
  Internal read-only variable. Number of elements unfixed by unfix command. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
vertex_count
  Internal read-only variable. Number of vertices.
vertex_dissolve_count
  Internal read-only variable. Number of vertices dissolved by dissolve command. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
vertex_pop_count
  Internal read-only variable. Number of vertices popped by pop or o command. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
where_count
  Internal read-only variable. Number of items satisfying last `where` condition. Prints and resets to 0 at the end of a command execution, or when flush_counts is done. Also reset by reset_counts.
window_aspect_ratio
  Internal read-write variable. The ratio of the the vertical to horizontal dimensions of the display window. If set, this locks the aspect ratio to the given value. The window may be resized with the mouse, but the aspect ratio will stay the same. The unset value of window_aspect_ratio is 0; setting window_aspect_ratio to 0 will unlock the aspect ratio. Applies also to the PostScript bounding box, if full_bounding_box is on. Currently implemented only in Evolver with GLUT graphics. Caveat: the window doesn't always fully follow the mouse; just keep trying.

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