Hashimoto surfaces
The following images are a space and time discretized Hashimoto or smoke ring flow. You can find the theory behind it
here (interactive online version) or
here.
- the discrete smoke ring flow of a triangle with subdivided edges
- the discrete smoke ring flow of an oval shaped curve
minimal surfaces
The next three images are s-minimal surfaces: a discretization of minimal surfaces using the notion of discrete s-isothermality. The theory behind it can be found in
this article.
- a discrete s-minimal catenoid
- a discrete s-minimal Enneper surface
- a discrete s-minimal surface half way in the associated family of the helicoid and catenoid
cmc surfaces
The next two images show discrete cmc surfaces generated by a discrete version of the DPW mathod. The method is described in
T. Hoffmann. Discrete cmc surfaces and discrete holomorphic maps. In A. Bobenko and R. Seiler, editors, Discrete integrable geometry and physics, pages 97-112. Oxford University Press, 1999.
- a 6-legged Smyth surface (or Mr Bubble)
- a 3-legged Smyth surface (or Mr Bubble)
- an s-cmc Delaunay surface -- a cmc surface of revolution.
K-surfaces
- a discrete Kuehn surface. This surface is a Bäcklund transform of the wellknown Pseudosphere. The discretization is described in
Wunderlich, W.; Zur Differenzengeometrie der Flächen konstanter
negativer Krümmung, Sitzungsber. Ak. Wiss., 1951, 160,pages 39-77
and
A. Bobenko and U. Pinkall,
Discrete Surfaces with Constant Negative Caussian Curvature
and the Hirota Equation,
J. Diff. Geom.,
1996,
43,
pages 527--611.
other
- a spin transform of the s-isothermic cylinder
[an error occurred while processing this directive]
