Equi-flux streamline seeding for three-dimensional vector fields

Appropriate streamline placement is important in the visualisation of 3D vector fields and many streamline seeding algorithms exist that produce evenly spaced or feature-based streamlines. However, in many areas of applied science, such as 3D coil design for magnetic resonance imaging hardware or in meteorology, interest lies with obtaining streamlines that represent equal flux across the entire 3D vector field. In this article, an equi-flux streamline seeding method is presented in the context of a 3D volumetric current density. Streamline density is controlled by a density map that evolves with the placement of each streamline. A novel Gaussian filter is described as part of the process, which has amplitude equal to the updated density map maximum and variance related to the inverse cube root of this amplitude such that each streamline represents approximately fixed flux or integrated current. The method is verified by applying it to simple 1D, 2D and 3D examples for which exact results can be obtained for comparison. In addition, the method allows streamline count to be varied in a straightforward manner, and can be applied to complicated 3D vector fields for which no exact result can be obtained.