Smoke Rings from Smoke

Steffen Weißmann (TU Berlin)    Ulrich Pinkall (TU Berlin)    Peter Schröder (Caltech)


We give an algorithm which extracts vortex filaments ("smoke rings") from a given 3D velocity field. For given filament strength, an optimal number of vortex filaments, together with their extent and placement, is given by the zero set of a complex valued function over the domain. This function is the global minimizer of a quadratic energy based on a Schrödinger operator. Computationally this amounts to finding the eigenvector belonging to the smallest eigenvalue of a Laplacian type sparse matrix.

Turning traditional vector field representations of flows, for example, on a regular grid, into a corresponding set of vortex filaments is useful for visualization, analysis of measured flows, hybrid simulation methods, and sparse representations. To demonstrate our method we give examples from each of these.

Supplemental Video