Methods for automating the analysis and display of vector field topology in general, and flow topology in particular, are described. By using techniques to extract and visualize topological information, it is possible to combine the simplicity of schematic depictions with the quantitative accuracy of curves and surfaces computed directly from the data. Two-dimensional vector field topology is discussed, covering critical points and time-dependent flows, to provide a basis for the examination of topology in three-dimensional separated flows. Surface topology and separation structures in three-dimensional flows are then addressed. The construction of representations of tangent surfaces that are accurate, as well as efficient to compute and display, is examined, covering tessellation, clipping, and refinement. Locating, characterizing, and displaying three-dimensional critical points are considered.
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