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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.
Gregory M. Nielson, Il-Hong Jung, "Tools for Computing Tangent Curves for Linearly Varying Vector Fields over Tetrahedral Domains", IEEE Transactions on Visualization & Computer Graphics, vol. 5, no. , pp. 360-372, October-December 1999, doi:10.1109/2945.817352
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