Browsing by Author "Hofmann, Lutz"

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    The Dependent Vectors Operator
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Hofmann, Lutz; Sadlo, Filip; Gleicher, Michael and Viola, Ivan and Leitte, Heike
    In this paper, we generalize the parallel vectors operator due to Peikert and Roth to arbitrary dimension, i.e., to four-dimensional fields and beyond. Whereas the original operator tested for parallelism of two (derived) 2D or 3D vector fields, we reformulate the concept in terms of linear dependency of sets of vector fields, and propose a generic technique to extract and filter the solution manifolds.We exemplify our approach for vortex cores, bifurcations, and ridges as well as valleys in higher dimensions.
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    Local Extraction of 3D Time-Dependent Vector Field Topology
    (The Eurographics Association and John Wiley & Sons Ltd., 2021) Hofmann, Lutz; Sadlo, Filip; Borgo, Rita and Marai, G. Elisabeta and Landesberger, Tatiana von
    We present an approach to local extraction of 3D time-dependent vector field topology. In this concept, Lagrangian coherent structures, which represent the separating manifolds in time-dependent transport, correspond to generalized streak manifolds seeded along hyperbolic path surfaces (HPSs). Instead of expensive and numerically challenging direct computation of the HPSs by intersection of ridges in the forward and backward finite-time Lyapunov exponent (FTLE) fields, our approach employs local extraction of respective candidates in the four-dimensional space-time domain. These candidates are subsequently refined toward the hyperbolic path surfaces, which provides unsteady equivalents of saddle-type critical points, periodic orbits, and bifurcation lines from steady, traditional vector field topology. In contrast to FTLE-based methods, we obtain an explicit geometric representation of the topological skeleton of the flow, which for steady flows coincides with the hyperbolic invariant manifolds of vector field topology. We evaluate our approach on analytical flows, as well as data from computational fluid dynamics, using the FTLE as a ground truth superset, i.e., we also show that FTLE ridges exhibit several types of false positives.