Representation and visualization of vector field topology.
Lambertus Hesselink, James L. Helman · 1997
Experiments and numerical simulations produce vast amounts of high resolution multivariate data. Techniques that use computer graphics for visualizing scalar fields are relatively well developed, but direct visualization methods are inadequate for gaining insight into complex vector and tensor fields. This thesis discusses methods for applying the theory of vector field topology from dynamical systems to analyze and visualize vector fields and the physical structure of fluid flows. The 2D work generates representations of velocity field topology by locating, characterizing' and connecting critical points in a 2D domain. In 2D, time-dependent flows, correspondences between instantaneous topology skeletons are identified and computer graphics used to display surface representations. In 3D flows, the critical points and curves of skin friction topology provide a basis for generating stream surfaces that provide insight into the 3D structure of flow separations. 3D critical points are identified and depicted using geometric icons to represent their eigenvalues and eigenvectors. Methods for the refinement, tessellation, clipping and display of surfaces defined by adjacent tangent curves are also discussed. In combination, these analysis and visualization techniques are effective and efficient at providing insight into the vector field topology in a data set. The methods are applicable to vector fields in general, but this work focuses on velocity fields from separated flows because vector field topology in these problems is very intimately tied to our physical understanding of these systems.