Tools for computing tangent curves for linearly varying vector fields over tetrahedral domains

We present some very efficient and accurate methods for computing tangent curves for three-dimensional flows. Our methods work directly in physical coordinates, eliminating the usual need to switch back and forth with computational coordinates. Unlike conventional methods. such as Runge-Kutta, for computing tangent curves which give only approximations, our methods produce exact values based upon piece-wise linear variation over a tetrahedrization of the domain of interest. We use barycentric coordinates in order to efficiently track cell-to-cell movement of the tangent curves.