# Surface Evolver Documentation

Back to top of Surface Evolver documentation. Index.

# Evolver datafile format

The initial configuration of the surface is read from an ASCII datafile. See the cube or mound examples for samples. The datafile is organized into six parts:

- Definitions and options
- Vertices
- Edges
- Faces
- Bodies
- Initial commands

General datafile topics:

- General syntax (for datafiles and commands)
- Include files
- Macros

In the syntax descriptions below, keywords will be in upper case. constexpr means a constant expression, and expr means any expression. n or k means an integer, which may be signed if it is being used as an oriented element label. Square brackets denote optional items. '|' means 'or'.

NOTE: Usually a formula can occur anyplace a number is legal (except element numbers, constraint numbers, etc). Some formulas are stored as formulas and re-evaluated at each use; examples include constraint, boundary, and quantity formulas. Others, such as vertex coordinates, are evaluated when the datafile is read, and only the numeric value stored. Thus if a user defines a vertex coordinate as `3*width`, then changing the value of the variable `width` at runtime will not affect the vertex. If you are not clear on which interpretation applies in a certain spot, dump the datafile and look at the spot to see if a formula or number was dumped.

## Include files

The standard C language method of including other files is available. The file name must be in double quotes. If the file is not in the current directory, EVOLVERPATH will be searched. Includes may be nested to 10 deep. Example:

    	#include  "common.stuff"

## Macros

Macros are text substitutions done by replacing an identifier by a string of characters before parsing. Macros are only defined in the datafile, and do not work from the command prompt. Simple macros (no parameters) may be defined as in C:

             #DEFINE  identifier  string

identifier must be an identifier without other special meaning to the parser. string is the rest of the logical line, not including comments. It will be substituted for identifier whenever identifier occurs as a token subsequently. Substitutions are re-scanned. No checks for recursiveness are made. There is a maximum length (currently 500 characters) on a macro definition. Note: macro identifiers are separate tokens, so if "-M" translates into "-2", this will be read as two tokens, not a signed number. The keyword `keep_macros` in the datafile will keep macro definitions active during runtime, until the next datafile is loaded.

## Datafile top section

The datafile begins with optional definitions and specifications. These are definitions that need to be made before the geometric elements are defined, or for which command syntax is lacking or awkward. Other initializations can be made at the end of the datafile in the read section using the command language. Each line starts with a keyword. The order is immaterial, except for the usual rule that items must be defined before use. None of these are required if you are willing to accept various defaults. They are listed here in rough order of frequency of use; those in the first column you should know, those in the second column you might never use in a lifetime.

Variables Level set constraints Parametric boundaries Named quantities Named method instances Surface dimension Space dimension Extra attributes Quadratic model Gravity constant Torus model Torus_filled Torus periods Viewing matrix View transforms View transform generators Scale_limit Optimizing Parameters Gap constant Symmetric content Keep original ids | Squared mean curvature Constraint tolerance Version Metric Simplex model Symmetry group Length method Area method Volume method Hessian special normal vector Crystalline integrands Phase file Ideal gas model Interpolation of boundary parameters Mobility Merit factor Squared Gaussian curvature Zoom_vertex Zoom_radius Dynamic load library

## Definitions of variables

Variables may be defined in the datafile top section with this syntax:

          PARAMETER identifier = constexpr

This declares identifier to be a variable with the given initial value. The value may be changed at runtime with the A command, or by assignment. Variables may be used in any subsequent expression or constant expression. Changing variables defined here results in automatic recalculation of the surface when autorecalc is been toggled on. Hence only variables needed in other top section declarations should be defined here.

## Level set constraint declarations

The format for declaring a level set constraint in the top section of the datafile is

    CONSTRAINT n [GLOBAL] [CONVEX] [NONNEGATIVE] [NONPOSITIVE] [NONWALL]
    FORMULA FUNCTION  expr
    [ENERGY:
     E1: expr
     E2: expr
     E3: expr]
    [CONTENT:
     C1: expr
     C2: expr
     C3: expr]

You may use `EQUATION` or `FUNCTION` as synonyms for `FORMULA`. This defines constraint number n, where n is a positive integer. The optional keyword `GLOBAL` means the constraint automatically applies to all vertices (but not automatically to edges or faces). `GLOBAL` constraints count in the number limit. If `CONVEX` is given, then an additional gap energy is attributed to edges on the constraint to prevent them from trying to short-circuit a convex boundary. `NONWALL` indicates this constraint is to be ignored in vertex and edge popping. If `NONNEGATIVE` or `NONPOSITIVE` is given, then this is a one-sided constraint, and all vertices will be forced to conform appropriately to the constraint at each iteration. The `FORMULA` expression defines the zero level set which is the actual constraint. It may be written as an equation, since '=' is parsed as a low-precedence minus sign. The formula may include any expressions whose values are known to the Evolver, given the particular vertex. Most commonly one just uses the coordinates (x,y,z) of the vertex, but one can use variables, quantity values, or vertex extra attributes. Using a vertex extra attribute is a good way to customize one formula to individual vertices. For example, if there were a vertex extra attribute called zfix, one could force vertices to individual z values with one constraint with the formula z = zfix, after of course assigning proper values to zfix for each vertex (be sure to fix up zfix after refining or otherwise creating vertices). Do not use '>' or '<' to indicate inequalities; use `NONNEGATIVE` or `NONPOSITIVE`. Conditional expressions, as in C language, are useful for defining constraints composed of several surfaces joined smoothly, such as a cylinder with hemispherical caps. Assignments to variables may be made at the start of expressions, mainly for the purpose of evaluating common subexpressions only once in the integrands. The syntax for such a compound expression is

        variable :=  expr, expr

The value of the expression is the value of the second expression.

The optional `ENERGY` section signifies that vertices or edges on the constraint are deemed to have an energy. In the soapfilm model, the next lines give components of a vectorfield that will be integrated along each edge on the constraint. In the string model, just one component is needed, which is evaluated at each vertex on the constraint. The main purpose of this is to permit facets entirely on the constraint to be omitted. Any energy they would have had should be included here. One use is to get prescribed contact angles at a constraint. This energy should also include gravitational potential energy due to omitted facets. Integrals are now also evaluated on `fixed` edges, which is a change from earlier versions of Evolver.

The optional `CONTENT` section signifies that vertices (string model ) or edges (soapfilm model) on the constraint contribute to the area or volume of bodies. If the part of a body boundary that is on a constraint is not defined by facets, then the body volume must get a contribution from a content integral. It is important to understand how the content is added to the body in order to get the signs right. The integral is evaluated along the positive direction of the edge. If the edge is positively oriented on a facet, and the facet is positively oriented on a body, then the integral is added to the body. This may wind up giving the opposite sign to the integrand from what you think may be natural. Always check a new datafile when you load it to be sure the integrals come out right.

## Parameterized boundary declaration

A parameterized boundary may be declared in the top section of the datafile with the syntax

    BOUNDARY n PARAMETERS k [CONVEX]
    X1: expr
    X2: expr
    X3: expr

This defines boundary number n, where n is a positive integer and k is the number of parameters. If `CONVEX` is given, then an additional gap energy is attributed to edges on the boundary to prevent them from trying to short-circuit a convex boundary. The following lines have the functions for the coordinates in terms of the parameters `P1` and maybe `P2`, `P3`,.... See the catenoid example. Energy and content integrals for boundaries are implemented, with the same syntax as for level set constraints.

## Named quantities

The syntax for defining a named quantity in the data file is:

     QUANTITY name   ENERGY|FIXED=value|CONSERVED|INFO_ONLY [LAGRANGE_MULTIPLIER constexpr]
    [TOLERANCE constexpr]  [MODULUS constexpr] methodlist | FUNCTION methodexpr

Here name is an identifier assigned by the user in order to refer to the quantity. Any quantities must be declared to be one of three types:

- `ENERGY` quantities are added to the overall energy of the surface;
- `FIXED` quantities that are constrained to a fixed target value;
- `CONSERVED` quantities are like FIXED in that the motion is projected to conserve the quantity, but the actual value is not projected to a given value.
- `INFO_ONLY` quantities whose values are merely reported to the user.

For fixed quantities, the optional Lagrange multiplier value supplies the initial value of the Lagrange multiplier (the "pressure" attribute of the quantity). It is meant for dump files, so on reloading no iteration need be done to have a valid Lagrange multiplier.

For fixed quantities, the tolerance attribute is used to judge convergence. A surface is deemed converged when the sum of all ratios of quantity discrepancies to tolerances is less than 1. This sum also includes bodies of fixed volume. If the tolerance is not set or is negative, the value of the variable target_tolerance is used, which has a default value of 0.0001.

Each quantity has a modulus, which is just a scalar multiplier of the whole quantity. A modulus of 0 will turn off an energy quantity. The default modulus is 1. The methodlist version of the quantity definition may contain one or more method instances. To incorporate a previously explicitly defined instance, include `METHOD` instancename. `GLOBAL_METHOD` may be used instead of `METHOD` to indicate the method applies to all elements of the appropriate type; it is equivalent to using `GLOBAL` in the method definition. To instantiate a method in the quantity definition, you essentially incorporate the instance definition, but without an instance name. Example of a quantity with one predefined method instance and one implicitly defined instance:

       method_instance qwerty method facet_scalar_integral
         scalar_integrand: x^2
       quantity foobar energy method qwerty method edge_scalar_integral
         scalar_integrand: y^3

Usually the second, implicit definition will be more convenient. Several method instances may be included in one methodlist (up to a current limit of 50), and their values are added together and multiplied by the quantity modulus to get the quantity value. The `FUNCTION` methodexpr variant defines the quantity as a function of previously defined method instances. Example:

       method_instance qwerty method facet_scalar_integral
         scalar_integrand: x^2
       quantity foobar energy function qwerty^3

Non-global quantities may be applied to elements individually by adding the quantity name to the datafile line defining an element. They may also be applied or unapplied at runtime with the set and unset commands. Orientable methods can be applied with negative orientation in the datafile by following the name with a dash. The orientation in a set command follows the orientation the element is generated with.

Methods applying to different types of elements may be combined in one quantity. If such a quantity is applied to an element, then all method instances of that quantity of the appropriate type are applied to the element. Original attachments of quantities are remembered, soIf an edge method is applied to a facet, then edges created from refining that facet will inherit the edge method.

## Named method instances declaration

Method instances are usually defined as part of the definition of a named quantity, but there are circumstances where a quantity is composed of several method instances and the method instances need to be referred to individually; perhaps the user wants to know the values of the individual instances. The general syntax for defining an instance of a named method in a datafile is:

      METHOD_INSTANCE name METHOD methodname [MODULUS constexpr]
       [ELEMENT_MODULUS attrname]  [GLOBAL] [parameters]

Here, name is a user-assigned name for referring to this particular instance. methodname is one of the pre-defined methods in Evolver. The modulus value multiplies the method value to give the instance value. The default modulus is 1. Individual elements may be given multipliers by specifying an extra attribute attrname for the type of element; the attribute must have been defined earlier. `GLOBAL` makes the method apply to all elements of the appropriate type. Non-global instances may be applied to elements individually by adding the instance name to the datafile line defining an element. They may also be applied or unapplied at runtime with the set and unset commands. Orientable methods can be applied with negative orientation in the datafile by following the name with a dash. The orientation in a set command follows the orientation the element is generated with.

Each method may have various parameters to specialize it to an instance. Currently the only parameters specified are:

`SCALAR_INTEGRAND: expr`
  where expr is a scalar function of coordinates (and of tangent or normal vector components in edge_general_integral or facet_general_integral). Element attributes of the appropriate type element may also be used.

`VECTOR_INTEGRAND:
Q1: expr
Q2: expr
Q3: expr
`
  where the expressions are functions of the coordinates. Element attributes of the appropriate type element may also be used.

`FORM_INTEGRAND:
Q1: expr
Q2: expr
Q3: expr
...
`
  where the expressions are functions of the coordinates. Element attributes of the appropriate type element may also be used. When used in the facet_2form_integral method. The form components are listed in lexicographic order, i.e. in 4D the six components 12,13,14,23,24,34 would be listed as `Q1` through `Q6`.

`PARAMETER_1 constexpr`
  For specifying miscellaneous numeric parameters to certain methods.

`K_FORM_ORDER constexpr`
  For methods that use differential k-forms, this specifies the value of k. Should occur before `FORM_INTEGRAND` when needed.

## Surface dimension

The default dimension of the surface is 2. If not, it must be declared in the top section of the datafile. For a 1-dimensional surface (the string model), simply include the line

     STRING

The default dimension 2 soapfilm model is equivalent to using

     SOAPFILM

In general, the line

     SURFACE_DIMENSION n

defines the surface to have dimension n. Dimension over 2 is valid only in the simplex model. The surface dimension may be accessed at runtime through the read-only variable surface_dimension.

## Space dimension

The default dimension of space is 3. Otherwise it must be declared in the top section of the datafile, with syntax

    SPACE_DIMENSION n

The dimension must be at most the value of MAXCOORD in model.h, which is 4 in the distributed version. The space dimension may be accessed at runtime through the read-only variable space_dimension.

## Extra attribute declarations

It is possible for the user to define extra attributes for elements, which may be single values or up to eight-dimensional arrays. If these attributes are to be included in the datafile, then the top section of the datafile must contain appropriate definitions. The definition syntax is the same as used by the define runtime command:

     DEFINE elementtype ATTRIBUTE name type [dim]...

where elementtype is `vertex`, `edge`, `facet`, or `body`, name is an identifier of your choice, type is `REAL` or `INTEGER` (internally, there is also a `ULONG` unsigned long type also), and dim is an optional expression for the vector dimension. There is no practical distinction between real and integer types at the moment, since everything is stored internally as reals. But there may be more datatypes added in the future. Extra attributes are inherited by elements of the same type generated by subdivision. The type may be followed by `FUNCTION` followed by a procedure in brackets to be evaluated whenever the value of the attribute is read; in the formula, `self` may be used to refer to the element in question to use its attributes, in particular to at some point assign a value to the attribute. The print command may be used to print attribute arrays or array slices in bracketed form. Examples:

      define edge attribute charlie real
      define vertex attribute oldx real[3]
      define facet attribute knots real[5][5][5]
      define edge attribute bbb real function { self.bbb := self.x+self.y }

## Quadratic declaration

To declare that the datafile lists a surface in the quadratic model, the top section of the datafile should contain the line

    QUADRATIC

The only effect on datafile syntax is that the edge section may list edge midpoint vertices.

## Gravity constant declaration

The initial value of the gravitational constant may be set in the datafile with the syntax

      GRAVITY_CONSTANT value

The default value is 1.

## Torus model declaration

To declare periodic boundary conditions (i.e. make the domain a flat torus), include in the top section of the datafile the line

    TORUS

All space dimensions will be periodic, with the period vectors given in the periods declaration. If the domain is completely filled by bodies with prescribed volumes, then the line

    TORUS_FILLED

should be used instead to prevent degenerate volume constraints.

## Torus periods

If periodic boundary conditions are used (the torus model) , the period vectors of the fundamental unit cell parallelpiped may be defined in the top section of the datafile. Default is the unit cube. The syntax is the keyword `PERIODS` followed by expressions for the components of each period vector:

    PERIODS
    expr expr expr
    expr expr expr
    expr expr expr

The size of this matrix depends on the space dimension. Variables may be used in the expressions, so the fundamental domain may be changed interactively by assigning new values to the variables. Be sure to give a recalc command whenever you change such a variable, in order to get the period matrix re-evaluated.

## Viewing matrix

The top section of the datafile may contain an initial viewing matrix:

    VIEW_MATRIX
      constexpr constexpr constexpr constexpr
      constexpr constexpr constexpr constexpr
      constexpr constexpr constexpr constexpr
      constexpr constexpr constexpr constexpr

The matrix is in homogeneous coordinates with translations in the last column. The size of the matrix is one more than the space dimension. This matrix will be part of all dump files, so the view can be saved between sessions. This matrix is used and set by native screen graphics ('s' command) and only applies to internal graphics (Postscript, Xwindows, etc.) but not external graphics (geomview). The elements may be read or set at runtime by `view_matrix[i][j]`, where the indices start at 1. In particular, one can write command scripts to save and reload particular view matrices; see `saveview.cmd` in the distribution package.

## View transforms

For the display of several transformations of the surface simultaneously, a number of viewing transformation matrices may be given in the top section of the datafile:

    VIEW_TRANSFORMS n
    COLOR color
    SWAP_COLORS
      constexpr constexpr constexpr constexpr
      constexpr constexpr constexpr constexpr
      constexpr constexpr constexpr constexpr
      constexpr constexpr constexpr constexpr
        ...

The transforms apply to all graphics, internal and external, and are prior to the viewing matrix for internal graphics. The identity transform is always done, so it does not need to be specified. The number of matrices follows the keyword `VIEW_TRANSFORMS`. Each matrix is in homogeneous coordinates, with translation in the last column. The size of each matrix is one more than the space dimension. Individual matrices need no special separation; Evolver just goes on an expression reading frenzy until it has all the numbers it wants. Each matrix may be preceded by an optional color that applies to facets transformed by that matrix. The color applies to one transform only; it does not continue until the next color specification. If SWAP_COLORS is present instead, facet frontcolor and backcolor will be swapped when this matrix is applied. Transforms may be activated or deactivated interactively with the transforms toggle. The internal variable `transform_count` records the number of transforms, and the transform matrices are accessible at runtime as a three-dimensional matrix view_transforms[][][]. View transform generators are a more sophisticated way to control view transforms.

## View transform generators

Listing all the view transforms is tedious and inflexible. An alternative is to list just a few matrices that can generate transforms. See the transform_expr command for instructions on entering the expression that generates the actual transforms. Special Note: in the torus model, the period translations are automatically added to the end of the list. So in the torus model, these are always available, even if you don't have view_transform_generators in the datafile. Syntax in the top of the datafile:

    VIEW_TRANSFORM_GENERATORS n
    SWAP_COLORS
      constexpr constexpr constexpr constexpr
      constexpr constexpr constexpr constexpr
      constexpr constexpr constexpr constexpr
      constexpr constexpr constexpr constexpr
        ...

The number of matrices follows the keyword `VIEW_TRANSFORM_GENERATORS`. Each matrix is in homogeneous coordinates, with translation in the last column. The size of each matrix is one more than the space dimension. Individual matrices need no special separation; Evolver just goes on an expression reading frenzy until it has all the numbers it wants. If SWAP_COLORS is present, facet frontcolor and backcolor will be swapped when this matrix is applied. The internal variable `transform_count` records the number of transforms, and the transform matrices are accessible at runtime as a three-dimensional matrix view_transforms[][][].

## Scale limit

To set an upper bound of valueon the gradient descent scale factor, include the line

       SCALE_LIMIT value

in the top section of the datafile. The upper bound can be changed at runtime with the m command, or by setting the `scale_limit` variable. If surface tension is the main energy, the scale_limit should be set to the inverse of the surface tension.

## Optimizing parameter

A variable may be made subject to optimization during iteration or hessian commands with the datafile declaration

          OPTIMIZING_PARAMETER identifier = constexpr PDELTA = constexpr PSCALE = constexpr

Such a variable joins the vertex coordinates as an independent variable during optimization. However, it differs from a coordinate in that gradients with respect to it are calculated numerically, rather than analytically. Thus it may be used anywhere a variable is permitted. Hessians with optimizing parameters are implemented. The optional pdelta value is the parameter difference to use in finite differences; the default value is 0.0001. The optional pscale value is a multiplier for the parameter's motion, to do "impedance matching" of the parameter to the surface energy. These attributes may be set on any parameter, for potential use as an optimizing parameter. At runtime, a parameter may be toggled to be optimizing or not with the FIX and UNFIX commands. That is, `fix radius` would make the radius variable non-optimizing (fixed value). Also, the pdelta and pscale attributes may be accessed at runtime, as in

    height.pscale := 2*height.pscale

"Optimising_parameter" is a synonym.

## Gap constant declaration

The initial value of the gap constant for gap energy may be set in the datafile with the syntax

      GAP_CONSTANT value

The default value is 1. Synonym: spring_constant.

## Symmetric content

The datafile keyword `SYMMETRIC_CONTENT` triggers the use of an alternate surface integral for calculating body volumes, namely the vectorfield (x,y,z)/3. It is useful if unmodelled sides of a body are radial from the origin, or if constraint content integrals (which is evaluated by an approximation) lead to asymmetric results on what should be a symmetric surface.

## Keep original ids

The presence of the keyword

    keep_originals

in the top of the datafile has the same effect as the -i command line option, which is to keep the id numbers internally the same as in the datafile, instead of renumbering them in the order they are read in.

## Version

If a datafile contains features present only after a certain version of the Evolver, the datafile can contain a line of the form
`evolver_version "2.10"`
This will generate a version error message if the current version is earlier, or just a syntax error if run on an Evolver version earlier than 2.10.

## Constraint tolerance

This is datafile declaration of the tolerance within which a vertex is deemed to satisfy a level-set constraint. Default is 1e-12. Syntax:

      CONSTRAINT_TOLERANCE const_expr

Sets the value of the internal variable constraint_tolerance.

## Symmetry group declaration

To declare that the domain is the quotient space of a symmetry group, the top section of the datafile must contain a line of the form

    SYMMETRY_GROUP "name"

"name" is a double-quoted name that is matched against the list of defined symmetry groups.

## Length method

This item, `length_method_name`, specifies the name of the pre-defined method to use as the method to compute edge length in place of the default edge_length method. It is optional. Developed so circular arcs can be used in two-dimensional foams. Current reasonable methods are circular_arc_length and spherical_arc_length. Usage implies converting to everything_quantities mode. Syntax:

    length_method_name quoted_method_name

For example,

    string
    space_dimension 2
    length_method_name "circular_arc_length"

## Area method

This item, `area_method_name`, specifies the name of the pre-defined method to use as the method to compute facet areas in place of the default edge_area method in the string model or facet_area method in the soapfilm model. It is optional. Developed so circular arcs can be used in two-dimensional foams. Current reasonable methods are circular_arc_area and spherical_arc_area. Synonymous with volume_method_name in the string model. Usage implies converting to everything_quantities mode. Syntax:

    area_method_name quoted_method_name

For example,

    string
    space_dimension 2
    area_method_name "circular_arc_area"

## Volume method

This item, `volume_method_name`, specifies the name of the pre-defined method to use as the method to compute body volumes in place of the default edge_area method in the string model or facet_volume method in the soapfilm model. It is optional. Developed so circular arcs can be used in two-dimensional foams. Synonymous with area_method_name in the string model. Usage implies converting to everything_quantities mode. Syntax:

    volume_method_name quoted_method_name

For example,

    string
    space_dimension 2
    volume_method_name "circular_arc_area"

## Hessian special normal vector

When hessian_special_normal is on, hessian commands use a special vectorfield for the direction of the perturbation, rather than the usual surface normal. The vectorfield is specified in the format

    HESSIAN_SPECIAL_NORMAL_VECTOR
    c1: expr
    c2: expr
    c3: expr

One can use vertex attributes in the expressions. Beware that hessian_special_normal also applies to the normal calculated by the vertexnormal attribute and the normal used by regular vertex averaging.

## Simplex model declaration

To declare that the datafile lists a surface in the simplex model, the top section ot the datafile should contain the line

    SIMPLEX_REPRESENTATION

The main effect on the datafile is that faces are defined by oriented vertex lists rather than edge lists.

## Dynamic load library

To load a dynamic library of compiled functions, the syntax is

     LOAD_LIBRARY "filename"

where the double-quoted filename is the library. The current directory and the EVOLVERPATH will be searched for the library.

## Crystalline integrands

To declare that surface area energy should be calculated with a crystalline integrand, the top section of the datafile should contain a line of the form

     WULFF "filename"

The double-quoted filename (with path) refers to a file giving the Wulff vectors of the integrand. The format of the file is one Wulff vector per line with its components in ASCII decimal format separated by spaces. The first blank line ends the specification. Some special integrands can be used by giving a special name in place of the file name. Currently, these are "hemisphere" for a Wulff shape that is an upper unit hemisphere, and "lens" for two unit spherical caps of thickness 1/2 glued together on a horizontal plane. These two don't need separate files.

## Phase file declaration

To declare that the surface tension of an edge or facet depends on the phases of its adjacent facets or bodies, the top section of the datafile should contain a line of the form

     PHASEFILE "filename"

The information is read from an ASCII file, whose name is given in a double-quoted string. The first line of the file has the number of different phases. Each line after consists of two phase numbers and the surface tension between them. Lines not starting with a pair of numbers are taken to be comments. If a pair of phases is not mentioned, the surface tension between them is taken to be 1.0. Facets in the string model or bodies in the soapfilm model can be labelled with phases with the `PHASE` n phrase in the datafile.

## Ideal gas model

A line in the top section of the datafile of the form

    PRESSURE constexpr

specifies that bodies are compressible and the ambient pressure is the value of constexpr. The default is that bodies with given volume are not compressible.

## Interpolation of parameters

To use interpolation instead of extrapolation in calculating the parameters of edge midpoints during refining, use the keyword

       INTERP_BDRY_PARAM

This should be done only if there are no periodic parameters.

## Everything_quantities

Keyword in top section of the datafile. Causes all areas, volumes, etc. to be converted to named quantities and methods. Equivalent to the command line option -q, or the convert_to_quantities command.

## Mobility declaration

A mobility matrix may be defined in the top section of the datafile by the syntax

    MOBILITY_TENSOR
    expr expr expr
    expr expr expr
    expr expr expr

or

    MOBILITY expr

The first form gives the full mobility matrix, and the second form gives the matrix as a scalar multiple of the identity matrix. The formulas are evaluated at each vertex at each iteration, and so formulas may depend on vertex position and any vertex attributes.

## Metric declaration

A Riemannian metric on the ambient space may be declared in the top section of the datafile with the syntax

    METRIC
    expr expr expr
    expr expr expr
    expr expr expr

or

    CONFORMAL_METRIC expr

or

    KLEIN_METRIC

The keyword `METRIC` is followed by the N^2 components of the metric tensor, where N is the dimension of space. The components do not have to obey any particular line layout; they may be all on one line, or each on its own line, or any combination. It is up to the user to maintain symmetry. A conformal metric is a scalar multiple of the identity matrix, and only the multiple need be given. A conformal metric will run about twice as fast. The Klein metric is a built-in metric for hyperbolic n-space modelled on the unit disk or ball.

## Merit factor

If the keyword `MERIT_FACTOR` is present, then the i command will print the ratio total_area^3/total_volume^2, which measures the efficiency of area enclosing volume. A holdover from the early days of trying to beat Kelvin's partition of space.

## Squared mean curvature

To add an energy of squared mean curvature, include a line in the top of the datafile

      SQUARED_CURVATURE modulus

The modulus is a multiplier for the energy. This is the original squared mean curvature energy; later versions are in the squared curvature named methods.

## Squared Gaussian curvature

To add an energy of squared Gaussian curvature, include a line in the top of the datafile

      SQUARED_GAUSSIAN_CURVATURE modulus

The modulus is a multiplier for the energy. Synonyms: `square_gaussian_curvature`, `sqgauss`

## Zoom_vertex

Datafile keyword setting the current zoom vertex. Used in dump files after a zoom command has been given.

## Zoom_radius

Datafile keyword setting the current zoom radius. Used in dump files after a zoom command has been given.

## Element lists

The lists of geometric elements follow a general format. Each element is defined on one line. The first entry on a line is the element number. Numbering need not be consecutive, and may omit numbers, but be aware that internally elements will be renumbered in order. The original number in the datafile is accessible as the original attribute of an element. After the element number comes the basic defining data, followed by optional attributes in arbitrary order. Besides the particular attributes for each element type listed below, one may specify values for any extra attributes defined earlier. The syntax is attribute name followed by the appropriate number of values. Also an arbitrary number of named quantities or method instances may be listed. These add method values for this element to the named quantity. The named quantity or instance must have been declared in the top section of the datafile.

## Vertex list

The datafile vertex list is started by the keyword `VERTICES` at the start of a line. It is followed by lines with one vertex specification per line. If the vertex is not on a parametric boundary, the syntax is

    k   x y ... [FIXED] [CONSTRAINT c1 c2 ...]  [BARE]
                [quantityname ...] [methodname ...]

The syntax for a vertex on a parametric boundary is

    k p1 [p2 ...]  BOUNDARY b [FIXED] [BARE] [quantityname ...]
       [methodname ...]

Here k is the vertex number, a positive integer. Vertices do not need to be listed in order, and there may be gaps in the numbering. However, if they are not in consecutive order, then the numbering in dump files will be different. x y ... are constant expressions for coordinates. In the parametric boundary format, the boundary parameter values are given instead of the coordinates. If `FIXED` is given, then the vertex never moves, except possibly for an initial projection to constraints. If `CONSTRAINT` is given, then one or more constraint numbers must follow. You can list as many constraints as you want, as long as those that apply exactly at any time are consistent and independent. The given coordinates need not lie exactly on the constraints; they will be projected onto them. A vertex on a parametric boundary cannot also be on a constraint.

The `BARE` attribute is just an instruction to the checking routines that this vertex is not supposed to have an adjacent facet in the soapfilm model, so spurious warnings will not be generated. This is useful when you want to show bare wires or outline fundamental domains.

An arbitrary number of named quantities or method instances may be listed. These add method values for this element to the named quantity. The named quantity or instance must have been declared in the top section of the datafile.

The list vertices command prints the datafile format listing of vertices.

## Edge list

The datafile edge list follows the vertex list, and is started by the keyword `EDGES` at the start of a line. It is followed by lines with one edge specification per line in this format (linespliced here):

    k v1 v2 [midv] [s1 s2 s3] [WRAP w] [FIXED] [BOUNDARY b] \
       [CONSTRAINTS c1 [c2 ...]] [TENSION constexpr] [COLOR n] \
         [BARE]  [quantityname ...] [methodname ...]

Here k is the edge number, with numbering following the same rules as for vertices. v1 and v2 are the numbers of the tail and head vertices of the edge. In the quadratic model, the edge midpoint may be listed as a third vertex midv (otherwise a midpoint vertex will be created). In the torus model, there must follow signs s1 s2 s3 indicating how the edge wraps around each unit cell direction: + for once positive, * for none, and - for once negative. In non-torus symmetry groups, each edge should have a `WRAP` symmetry group element encoded as an integer. `FIXED` means that all vertices and edges resulting from subdividing this edge will have the `FIXED` attribute; it does not mean that the endpoints will be automatically fixed. Likewise the `BOUNDARY` and `CONSTRAINT` attributes will be inherited by all edges and vertices derived from this edge. If a constraint has energy or content integrands, these will be done for this edge. IMPORTANT: If a constraint number is given as negative, the edge energy and content integrals will be done in the opposite orientation. In the string model, the default tension is 1, and in the soapfilm model, the default tension is 0. However, edges may be given nonzero tension in the soapfilm model, and they will contribute to the energy.

If the simplex model is in effect, edges are one less dimension than facets and given by an ordered list of vertices. Only edges on constraints with integrals need be listed.

The `BARE` attribute is just an instruction to the checking routines that this ede is not supposed to have an adjacent facet in the soapfilm model, so spurious warnings will not be generated. This is useful when you want to show bare wires or outline fundamental domains.

An arbitrary number of named quantities or method instances may be listed. These add method values for this element to the must have been declared in the top section of the datafile. If the quantity or instance has orientation-dependent methods, the name may be followed by a dash to reverse the applied orientation.

The list edges command prints the datafile format listing of edges.

## Face list

The datafile face list follows the edge list, and is started by the keyword `FACES` at the start of a line. It is followed by lines with one facets specification per line in this format:

      k   e1 e2 ...  [FIXED] [TENSION constexpr] [BOUNDARY b] \
      [CONSTRAINTS c1 [c2 ...]]     [NODISPLAY]   \
       [COLOR n]} [FRONTCOLOR n] [BACKCOLOR n] \
       [PHASE n] [quantityname ...] [methodname ...]

Here k is the face number, with numbering following the same rules as for vertices. There follows a list of oriented edge numbers in counterclockwise order around the face. A negative edge number means the opposite orientation of the edge from that defined in the edge list. The head of the last edge must be the tail of the first edge (except if you're being tricky in the string model). There is no limit on the number of edges. The face will be automatically subdivided into triangles if it has more than three edges in the soapfilm model. The `TENSION` (synonym: `DENSITY`) value is the energy per unit area (the surface tension) of the facet; the default is 1. Density 0 facets exert no force, and can be useful to define volumes or in displays. Fractional density is useful for prescribed contact angles. `NODISPLAY` prevents the facet from being displayed. The `COLOR` attribute applies to both sides of a facet; `FRONTCOLOR` applies to the positive side (edges going counterclockwise) and `BACKCOLOR` to the negative side. The `PHASE` number is used in the string model to determine the surface tension of edges between facets of different phases, if phases are used.

If the simplex model is in effect, the edge list should be replaced by an oriented list of vertex numbers.

An arbitrary number of named quantities or method instances may be listed. These add method values for this element to the must have been declared in the top section of the datafile. If the quantity or instance has orientation-dependent methods, the name may be followed by a dash to reverse the applied orientation.

The faces section is optional in the string model.

The list facets command prints the datafile format listing of facets.

## Body list

The datafile body list follows the face list, and is started by the keyword `BODIES` at the start of a line. It is followed by lines with one body specification per line in this format:

    k  f1 f2 f3 .... [VOLUME constexpr] [VOLCONST constexpr] [ACTUAL_VOLUME constexpr] \
    [PRESSURE p] [DENSITY constexpr] [PHASE ]

Here k is the body number, and f1 f2 f3 ... is an unordered list of signed facet numbers. Positive sign indicates that the facet normal (as given by the right-hand rule from the edge order in the facet list) is outward from the body and negative means the normal is inward. Giving a `VOLUME` value constexpr means the body has a volume constraint, unless the ideal gas model is in effect, in which case constexpr is the volume at the ambient pressure. `VOLCONST` is a value added to the volume; it is useful when the volume calculation from facet and edge integrals differs from the true volume by a constant amount, as may happen in the torus model. `ACTUAL_VOLUME` is a number that can be specified in the rare circumstances where the torus volume volconst calculation gives the wrong answer; volconst will be adjusted to give this volume of the body. Giving a `PRESSURE` value means that the body is deemed to have a constant internal pressure; this is useful for prescribed mean curvature problems. It is incompatible with prescribed volume. Giving a `DENSITY` value means that gravitational potential energy will be included.

To endow a facet with `VOLUME`, `PRESSURE`, or `DENSITY` attributes in the string model, define a body with just the one facet.

The `PHASE` number is used in the soapfilm model to determine the surface tension of facets between bodies of different phases, if phases are used.

The `BODIES` section is optional.

The list bodies command prints the datafile format listing of bodies.

## READ section

The final section of the datafile may contain commands. These commands are read and executed immediately, just as if they had been entered at the command prompt. Encountering the keyword `READ` in the datafile causes the Evolver to switch from datafile mode to command mode and read the rest of the datafile as command input. This feature is useful for automatic initialization of the surface with refining, iteration, defining your own commands, etc. The `READ` section is optional. Example:

      bodies
      1   1 2 3 4 5 6 volume 1

      read

      // automatically do this when datafile is loaded
      refine edge where on_constraint 1

      // typical evolution
      gogo := { g 5; r; g 10; r; g 20 }

The list bottominfo command prints the `READ` section that would be printed in a dump file.

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