Sfb 288 Differential Geometry and Quantum Physics

Discrete Curves
Doubly Discrete Smoke Ring Flow

There is also a generalization of the above construction, that allows to apply a similar evolution for a complex parameter in space: On each edge of the curve apply a parallelogram, that is folded along the diagonal. This leads to a doubly discrete smoke ring flow, if the parallelogram is a rhombus.

A doubly discrete smokering surface	This smoke ring moves periodicly. The resultig surface is a torus

Author: Tim Hoffmann, Ulrich Pinkall