Implicit Stream Surfaces

Streamlines and stream surfaces are well known techniques for the visualization of fluid flow. For steady velocity fields, a streamline is the trace of a particle, and a stream surface is the trace of a curve. Here a new method is presented for the construction of stream surfaces. The central concept is the representation of a stream surface as an implicit surface f (x) = C. After the initial calculation of f a family of stream surfaces can be generated efficiently by varying C. The shapes of the originating curves are defined by the value of f at the boundary. Two techniques are presented for the calculation of f: one based on solving the convection equation, the other on backward tracing of the trajectories of grid points. The flow around objects is discussed separately. With this method irregular topologies of the originating curves and of the stream surfaces can be handled easily. Further, it can also be used for other visualization techniques, such as time surfaces and stream volumes. Finally, an effective method for the automatic placement of originating curves is presented. >