# Visualization (Labs)

Here some interactive labs of minimal, CMC, HSL and Willmore surfaces

# Labs

by
Leschke, Dr K.
—
last modified
25 September 2007 11:28

** Labs **

To start a lab just click on the screenshot. If the application does
not start, have a look at the Help
page at TU Berlin.

*This lab shows a 1-parameter family of Double Enneper surfaces (converging to the catenoid as the parameter goes to infinity).*

Warning; this is still a rather incomplete applet.

Here is what you see: n is the maximal period after which the Darboux transforms close; k and l are free (integer) parameters, with k*k + l*l < 2*n*n.

Unfortunately, you still have to adjust the periods by hand, that is if n=6 you have to have x max = y max =6. Note that there are examples with smaller periods.

The green point in the left plane is a free (complex) parameter, you can move it around.

These examples are computed by the methods in [LR].

These examples are computed by the methods in [LR].

Warning; this is still a rather incomplete applet.

Here is what you see: n is the maximal period after which the Darboux transforms close; k and l are free (integer) parameters, with k*k + l*l < 2*n*n.

Unfortunately, you still have to adjust the periods by hand, that is if n=6 you have to have x max = y max =6. Note that there are examples with smaller periods.

The green point in the left plane is a free (complex) parameter, you can move it around.

This lab shows the μ-Darboux transforms (see CLP) of Delaunay surfaces. Uses heavily a Delaunay implementation and the elliptic functions library of Nick Schmitt, Universität Tübingen. Thanks also to Nick Schmitt and Alexander Gouberman for the refining programs.

This lab shows the μ-Darboux transforms (see CLP) of Delaunay surfaces. Uses heavily a Delaunay implementation and the elliptic functions library of Nick Schmitt, Universität Tübingen. Thanks also to Nick Schmitt and Alexander Gouberman for the refining programs.

*This lab shows Wente tori and is completely due to Nick Schmitts CMC library which gives the java classes for Wente tori. I just provided the oorange network...*

This lab is based on the Wente-java library of Nick Schmitt. By choosing the parameters L, N so that L/N is in the open interval from 1 to 2 one obtains Wente tori with more lobes. |

*This lab shows the μ-Darboux transforms (see CLP) of a Wente torus. Thanks to Nick Schmitt for the underlying CMC library.*

*This lab shows the μ-Darboux transforms (see CLP) of a 1-Bubbleton. Thanks to Nick Schmitt and Alexander Gouberman for the refining programs.*

*This lab shows the μ-Darboux transforms (see RL) for μ=-1 of the Clifford torus. The μ-Darboux transforms were computed by using the family of flat connections, which is given by the harmonic left normal of the Clifford torus.*

*Use the spectral parameter to transform the helicoid into the catenoid.*

*This lab shows the associated family of the helicoid.*

This lab shows a family of Castro Urbano tori, see [LR].
This family shows a deformation of a (3-fold covering of a)
rectangular torus, all surfaces are Hamiltonian Stationary tori. The
family is due to Castro/ Urbano. |