TY - GEN A1 - Pinkall, Ulrich A1 - Springborn, Boris A. A1 - Weißmann, Steffen T1 - A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow N2 - Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time simulation of smoke. Here we introduce a time-discrete evolution equation for arbitrary closed polygons in 3- space that is a discretisation of the localised induction approximation of filament motion. This discretisation shares with its continuum limit the property that it is a completely integrable system. We apply this polygon evolution to a significant improvement of the numerical algorithms used in Computer Graphics. Y1 - 2009 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/615 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-6158 ER -