One of the most important ways of visualizing fluid flow is the construction of streamlines, which are lines that are everywhere tangential to the local fluid velocity. Stream surfaces are defined as surfaces through which no fluid penetrates. Streamlines can therefore be computed from the intersection of two nonparallel stream surfaces. This paper presents new algorithms for the computation of dual stream functions from computational fluid dynamics data that is defined on an unstructured tetrahedral mesh. These algorithms are compared with standard numerical routines for computing streamlines, and are shown to be quicker and more accurate than techniques involving numerical integration along the streamline.