The usual mode of operation of the Surface Evolver is to minimize energy subject to constraints. There are two broad categories of constraints:

- Pointwise constraints:
- Global constraints:

- Vertices may be required to lie on a constraint (equality constraint) or on one side (inequality constraint). A constraint may be declared GLOBAL, in which case it applies to all vertices. See mound.fe for an example.
- A constraint may have an energy vectorfield associated with it that is integrated over edges lying in the constraint to give an energy. This is useful for specifying wall contact angles and for calculating gravitational energy. Integrals are not evaluated over edges that are FIXED. See mound.fe for an example. In the string model, the energy integrand is a single component evaluated on vertices on the constraint.
- A constraint may have a content vectorfield associated with it that is integrated over edges lying in the constraint to give a volume contribution to a body whose boundary facets contain the edges. This is useful for getting correct volumes for bodies without completely surrounding them with otherwise useless facets. 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. Integrals are not evaluated over edges that are FIXED. See tankex.fe for an example. In the string model, the content integrand is a single component evaluated on vertices on the constraint.
- A constraint may be declared CONVEX, in which case edges in the constraint have an energy associated with them that is proportional to the area between the straight edge and the curved wall. This energy (referred to as "gap energy") is meant to compensate for the tendency for flat facets meeting a curved wall to minimize their area by lengthening some edges on the wall and shortening others, with the net effect of increasing the net gap between the edges and the wall. See tankex.fe for an example.

Level set constraints are declared in the top section of the datafile. They may be applied to vertices, edges, or facets. Constraints are usually applied to vertices and edges, as in mound.fe. Remember that you need to apply a constraint to an edge to get that constraint to apply to vertices created on that edge by refining. Sometimes one applies constraints to facets, usually to get the facet to conform to a predetermined shape. Be sure that the constraints applied to a vertex are linearly independent at the vertex.

Constraints are usually applied in the datafile vertices, edges, and faces sections, but they may also be set or removed with the set or unset commands. Example:

set vertex[4] constraint 4 unset edge constraint 1 where id < 10It does not hurt to unset an element that isn't on the constraint. When a vertex is set to a constraint, the vertex coordinates are immediately projected to the constraint. Setting an edge on a constraint does not set its vertices. Likewise for facets.

Example: Suppose one wanted to keep a bubble inside a spherical tank of radius 5. Then one would define the constraint in the datafile

constraint 1 nonpositive formula: x^2 + y^2 + z^2 = 25For purposes of evaluating nonnegativity or nonpositivity, all terms are shifted to the left side of the formula. One would then apply this constraint to all vertices, edges, and facets of the bubble surface.

Boundaries are defined in the top section of the
datafile. Vertices on boundaries
are listed in the datafile with their parameter values instead of their
coordinates, with "`boundary `*n*" appended to each such
vertex definition.
Edges and faces on boundaries are defined as usual, but with
"`boundary `*n*" appended to each definition.
So the datafile has lines like these:

boundary 1 parameters 1 x1: cos(p1) x2: sin(p1) x3: 0.75 ... Vertices 1 0.0 boundary 1 2 pi/3 boundary 1 ... Edges 1 1 2 boundary 1 ...

Putting an edge on a boundary means that vertices created on that edge
will be on the boundary. An edge on a boundary must have at least one
endpoint on the boundary, for use in extrapolating the boundary parameters
of any created vertices. Extrapolating instead of interpolating
midpoint parameters solves the problem of wrap-arounds on a boundary such as
a circle or cylinder. However if you do want interpolation, you can use
the keyword
`INTERP_BDRY_PARAM`
in the top of the datafile, or use the
toggle command interp_bdry_param.
Interpolation requires that both endpoints of an edge be on the same
boundary, which cannot happen where edges on different boundaries meet.
To handle that case, it is possible to add extra boundary information to
a vertex by declaring two particular vertex extra attributes,
`extra_boundary` and `extra_boundary_param`:

interp_bdry_param define vertex attribute extra_boundary integer define vertex attribute extra_boundary_param real[1]Then declare attribute values on key vertices, for example

vertices 1 0.00 boundary 1 fixed extra_boundary 2 extra_boundary_param 2*piIf the extra_boundary attribute is not set on a vertex when wanted, Evolver will silently fall back on interpolation.

Putting a face on a boundary means that all edges and vertices created from refining the face will be on the boundary. In this case, the boundary should have two parameters (or whatever the dimension of the surface is). This is good for getting a surface to conform to a known parametric shape.

Edges on boundaries have energy and content integrals like level-set constraints edges, but they are internally implemented as. named quantities.

Whether an element is on a particular boundary can be queried with
the on_boundary Boolean attribute.
Elements can be removed from boundaries with the
unset command, but they cannot be
set on boundaries. A typical use
of `unset` is to define an initial surface using a 2-parameter
boundary, refine a couple of times, then unset. Examples:

list vertex where on_boundary 2 unset vertex boundary 1 where on_boundary 1 unset edge boundary 1 unset facet boundary 1It does not hurt to unset an element not on the boundary.

Vertex parameters can be accessed in expressions as the attribute p1 (and p2,... for further parameters). Vertex parameters can be changed with the set command. Example:

print vertex[5].p1 set vertex p1 p1+.1 where id < 4 vertex[2].p1 := 3It is not an error to access the parameters of a vertex not on a boundary as long as some vertex is on a boundary (so that space is allocated in the vertex structure for parameters).

A general guideline is to use constraints for two-dimensional walls and boundaries for one-dimensional wires. If you are using a boundary wire, you can probably declare the vertices and edges on the boundary to be FIXED. Then the boundary becomes just a guide for refining the boundary edges.

NOTE: A vertex on a boundary cannot also have constraints.

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