Mass conservation is a key issue for accurate streamline and stream surface visualization of flow fields. This paper complements an existing method (Feng et al. 1997) for CFD velocity fields defined at discrete locations in space that uses dual stream functions to generate streamlines and stream surfaces. Conditions for using the method have been examined and its limitations defined. A complete set of dual stream functions for all possible cases of the linear fields on which the method relies are presented. The results in this paper are important for developing new methods for mass conservative streamline visualization from CFD and using the existing method.