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<p><b>Abstract—</b>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.</p>
Visualization, flow fields, streamlines, tangent curves, vector fields, phase plane, phase volume, critical points, tetrahedral grids.

I. Jung and G. M. Nielson, "Tools for Computing Tangent Curves for Linearly Varying Vector Fields over Tetrahedral Domains," in IEEE Transactions on Visualization & Computer Graphics, vol. 5, no. , pp. 360-372, 1999.
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