Principal Stream Surfaces

The use of stream surfaces and streamlines is well established in vector visualization. However, the proper placement of starting points is critical for these constructs to clearly illustrate the flow topology. In this paper, we present the principal stream surface algorithm, which automatically generates stream surfaces that properly depict the topology of an irrotational flow. For each velocity point in the fluid field, construct normal to the principal stream surface through the point. The set of all such normal vectors is used to construct the principal stream function, which is a scalar field describing the direction of velocity in the fluid field. Volume rendering can then be used to visualize the principal stream function, which is directly related to flow topology. Thus, topology in a fluid field can be easily modeled and rendered.