Until recently it was extremely difficult to obtain 3d representations of the surfaces which geometers have been studying since the 19th Century. Now this is possible using computer visualisation: this page uses a java applet from JavaView to view the output of experiments run using CMCLab and MinLab . The software performs highly non-trivial calculations to produce surfaces, some of which are of classical origin and others of which are at the cutting edge of research. In particular, the trinoids were found numerically by Nick Schmitt at GANG, and are part of his CMCLab surface library.

**Constant Mean Curvature Surfaces**

CMC surfaces arise when we try to minimize the surface area of a membrane which contains some fluid (e.g. air) - they are commonly called soap bubbles. Most of the examples below are unstable critical points of the area functional. This variational property is equivalent to insisting that the mean curvature be constant over the surface (hence the name). Modern research is trying to describe all CMC surfaces with a given underlying topology - the surfaces below demonstrate some of the possibilities.

** How to use the gallery **

Clicking on the surface name launches a separate browser window
containing a JavaView applet of the surface. You can interact with the
surface by placing your pointer in the applet window and clicking:
left click to move the surface, right click to list the options available.
Some of the surface files may be
slow to move, due to file size.
The responsiveness can be improved by viewing the surface as a mesh only.
To achieve this, right click in the applet window and choose Control Panel.
Then switch off "Element" under "Material".

Round sphere [110KB] | Delaunay unduloid [120KB] | Delaunay nodoid [120KB] |

Smyth surface (3-legged) [380KB] | Smyth-Delaunay (2-legged) [250KB] | Generalized Smyth surface [210KB] |

Wente torus [260KB] | Twisty torus [380KB] | Single bubbleton [430KB] |

Triunduloid (equilateral) [440KB] |
Triunduloid (scalene) [450KB] |
Trinoid (nodoid end) [440KB] |

Nick Schmitt now has a java applet called Noid to compute polyunduloids. Visit his site at SFB 288, TU Berlin