Tools for computing tangent curves for linearly varying vector fields overtetrahedral domains

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