Surface Evolver Examples


These are some examples of Surface Evolver surfaces. Some refer to separate pages, others are self-contained. The datafiles (*.fe) are in DOS text format (CR-NL end-of-line). Each datafile has comments in it, plus a typical evolution, usually in the form of a command "gogo". The first image in each self-contained example is of the surface as defined in the datafile, before evolution. The other images are evolved. The evolution generally is not carried to a high refinement, in order to give reasonable size facets for the images shown. Click on the small images to get larger images.

3.fe start 3.fe outer 3.fe inner

3.fe

Five bubbles, three in a ring around two. The initial inner film between the two axial bubbles shrinks to a point, and the resulting vertex needs to be popped. The evolved images show the outer films and the films between the bubbles respectively.

4.fe start 4.fe outer 4.fe inner

4.fe

Six bubbles, four in a ring around two. The central film shrinks here, but unlike 3.fe, it does not collapse to a point. The evolved images show the outer films and the films between the bubbles respectively.

4d.fe start 4d.fe refined

4d.fe

2D surface in 4D. Complex surface w = z^2 defined by constraints. No evolution, just surface display. Just refine, equiangulate, and admire.

5pb.fe start 5pb.fe evolved

5pb.fe

A cluster of 5 2-dimensional bubbles. Illustrates string model, fixed area facets, and vertex popping.

bubble2.fe start bubble2.fe evolved

bubble2.fe

A double bubble, starting as two cubes with a common face. Illustrates multiple bodies.

cat.fe start cat.fe evolved

cat.fe

A catenoid, which is the soap film formed on two parallel rings. Illustrates parameterized boundaries, energy saddle points, tiny edge deletion, and vertex popping. For more catenoids, see the catenoid soap film page.

cbga1.fe start cbga1.fe evolved

cbga1.fe

A liquid drop between a flat circular pad (green) and a sphere (red). The volume and contact energy under the sphere are represented by line integrals around the contact line on the sphere. For explicit contact facets on the sphere, see cbga2.fe

cube cone cube film

Conical soap films page

Soap films in the form of cones. There are eight of these fitting the equilibrium rules, but only one turns out to be stable. Illustrates vertex popping, which knows how to turn unstable vertices like these cones into combinations of stable tetrahedral vertices.

cubble.fe start cubble.fe evolved

cubble.fe

A bubble inside a cubical frame. Illustrates volume constraint, fixed vertices and edges.

cube.fe start cube.fe evolved

cube.fe

A unit cube evolving into a sphere. Illustrates volume constraint.

hncusp.fe start hncusp.fe evolved hncusp blow-up

hncusp.fe

The Hildebrandt-Nitsche cusp formed by a soap film whose boundary is a skewed spiral looping around the edge of a half-plane. The cusp is not actually a sharp cusp. The contact lines on the plane curve around to be tangent to the edge of the half-plane, and the points of tangency are separated by a short interval (about 0.0175 here) during which the tangent plane of the film rotates 180 degrees. A magnification of the cusp is shown in the last image.

loops.fe start loops.fe evolved

loops.fe

Soap film spanning one circle, with another circle poking through the first to act as a 1-dimensional barrier. The angle between the films on the barrier wire here is always over 120 degrees, and increases to 180 degrees where the film leaves the barrier. If the barrier penetrates too far, a stretch of triple line would form in the interior of the film, and there would be a single film on the barrier wire between junctions with the triple line.

mound.fe start mound.fe evolved mound.fe gravity

mound.fe

A droplet on a plane surface with gravity and surface contact energy. Illustrates volume constraint, level-set constraint, using Green's Theorem to represent contact energy, and the no_refine attribute. The center surface has no gravity and a 90 degree contact angle. The right surface has gravity 5 (in dimensionless units) and a 135 degree internal contact angle.

octahedron hex filmOctahedral films page

An octahedral frame bounds five stable films and several unstable films.

P surface Triply Periodic Minimal Surfaces page

These are minimal surfaces (in the sense of zero mean curvature) that repeat periodically in three directions.

quad.fe start quad.fe evolved

quad.fe

A soapfilm bounded by a skew quadrilateral. Illustrates fixed vertices and edges. This is as simple as it gets.

retract.fe start retract.fe evolved

retract.fe

A soap film that is a deformation retract onto its boundary. That is, the soap film can be deformed continuously to collapse to the boundary, with the deformation moving the film only where the original film was. Due to J. Frank Adams (appendix of E. R. Reifenberg, Solution of the Plateau problem for m-dimensional surfaces of varying topological type. Acta Math. 104, 1-92 (1960)). I have made a java applet illustrating how the retraction works.

ringblob.fe start ringblob.fe symmetric ringblob.fe first mode ringblob.fe second mode

ringblob.fe

A spinning liquid drop on a circular rod. Assuming an equatorial symmetry plane, only the top half is actually computed (first image). The evolved equilibrium shape for this particular spin (second image) is unstable, with two modes of instability, each of multiplicity two due to circular symmetry. The third image shows the most unstable mode, a bulging to one side, and the last image shows the other unstable mode, a bar shape.

sphere.fe start sphere.fe evolved

sphere.fe

A partially filled spherical tank, with a contact angle of 45 degrees between the liquid surface and the tank wall. The tricky part of this example is handling the gaps between the straight edges of the liquid surface facets and the curved wall of the tank.

spiral.fe start spiral.fe evolved

spiral.fe

A simple closed curve that bounds uncountably many different soap films. Each lane of the spiral may or may not have a film, and since there are infinitely many lanes, there are uncountably many subsets of lanes to fill. This film follows the repeating pattern of two full lanes, one empty lane. The Evolver model actually only contains one period of the pattern, and the image was formed by displaying four copies suitably sized.

tankex.fe start tankex.fe evolved

tankex.fe

A partially filled cylindrical tank with a horizontal axis, with a contact angle of 30 degrees between the liquid surface and the tank walls. Gravity is acting downward. Only the liquid surface is shown. The liquid forms an annulus in one end of the tank. The tricky part of this example is handling the gaps between the straight edges of the liquid surface facets and the curved wall of the tank.

twointor.fe start twointor.fe evolved

twointor.fe

A foam of 14-sided polyhedra, called Kelvin's Tetrakaidecahedra. The Evolver model actually consists of two polyhedra in a unit cube, with the opposite faces identified in what is called the 'torus model'. This foam has been beaten for efficient space-filling.

Williams cells

williams-2-balls.fe

A Williams cell foam, draped over balls inside the cells. More here.

tombstone 8 tombstone 9 tombstone 10

Tombstoning chips page

Micro chips flipped up by surface tension forces of liquid solder.


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