Browsing by Author "Theisel, Holger"

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    Autonomous Particles for In-Situ-Friendly Flow Map Sampling
    (The Eurographics Association, 2023) Wolligant, Steve; Rössl, Christian; Chi, Cheng; Thévenin, Dominique; Theisel, Holger; Guthe, Michael; Grosch, Thorsten
    Computing and storing flow maps is a common approach to processing and analyzing large flow simulations in a Lagrangian way. Accurate Lagrangian-based visualizations require a good sampling of the flow map. We present an In-Situ-friendly flow map sampling strategy for flows using Autonomous Particles that do not need information of neighboring particles: they can be advected individually without knowing about each other. The main idea is to observe a linear neighborhood of a particle during advection. As soon as the neighborhood cannot be considered linear anymore, an adaptive splitting is performed. For observing the linear neighborhood, each particle is equipped with an ellipsoid that also gets advected by the flow. By splitting these ellipsoids into smaller ones in regions of non-linear behavior, critical and more interesting regions of the flow map are more densely sampled. Our sampling approach uses only forward integration and no adaptive integration from the past. This makes it applicable in and well-suited for in In-Situ environments. We compare our approach to existing sampling techniques and apply it to several artificial and real data sets.
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    EUROGRAPHICS 2021: Short Papers Frontmatter
    (Eurographics Association, 2021) Theisel, Holger; Wimmer, Michael; Theisel, Holger and Wimmer, Michael
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    The Parallel Eigenvectors Operator
    (The Eurographics Association, 2018) Oster, Timo; Rössl, Christian; Theisel, Holger; Beck, Fabian and Dachsbacher, Carsten and Sadlo, Filip
    The parallel vectors operator is a prominent tool in visualization that has been used for line feature extraction in a variety of applications such as ridge and valley lines, separation and attachment lines, and vortex core lines. It yields all points in a 3D domain where two vector fields are parallel. We extend this concept to the space of tensor fields, by introducing the parallel eigenvectors (PEV) operator. It yields all points in 3D space where two tensor fields have real parallel eigenvectors. Similar to the parallel vectors operator, these points form structurally stable line structures. We present an algorithm for extracting these lines from piecewise linear tensor fields by finding and connecting all intersections with the cell faces of a data set. The core of the approach is a simultaneous recursive search both in space and on all possible eigenvector directions. We demonstrate the PEV operator on different analytic tensor fields and apply it to several data sets from structural mechanics simulations.
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    The State of the Art in Vortex Extraction
    (© 2018 The Eurographics Association and John Wiley & Sons Ltd., 2018) Günther, Tobias; Theisel, Holger; Chen, Min and Benes, Bedrich
    Vortices are commonly understood as rotating motions in fluid flows. The analysis of vortices plays an important role in numerous scientific applications, such as in engineering, meteorology, oceanology, medicine and many more. The successful analysis consists of three steps: vortex definition, extraction and visualization. All three have a long history, and the early themes and topics from the 1970s survived to this day, namely, the identification of vortex cores, their extent and the choice of suitable reference frames. This paper provides an overview over the advances that have been made in the last 40 years. We provide sufficient background on differential vector field calculus, extraction techniques like critical point search and the parallel vectors operator, and we introduce the notion of reference frame invariance. We explain the most important region‐based and line‐based methods, integration‐based and geometry‐based approaches, recent objective techniques, the selection of reference frames by means of flow decompositions, as well as a recent local optimization‐based technique. We point out relationships between the various approaches, classify the literature and identify open problems and challenges for future work.Vortices are commonly understood as rotating motions in fluid flows. The analysis of vortices plays an important role in numerous scientific applications, such as in engineering, meteorology, oceanology, medicine and many more. The successful analysis consists of three steps: vortex definition, extraction and visualization. All three have a long history, and the early themes and topics from the 1970s survived to this day, namely, the identification of vortex cores, their extent and the choice of suitable reference frames.
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    Static Visualization of Unsteady Flows by Flow Steadification
    (The Eurographics Association, 2020) Wolligandt, Steve; Wilde, Thomas; Rössl, Christian; Theisel, Holger; Krüger, Jens and Niessner, Matthias and Stückler, Jörg
    Finding static visual representations of time-varying phenomena is a standard problem in visualization. We are interested in unsteady flow data, i.e., we want to find a static visualization - one single still image - that shows as much of the global behavior of particle trajectories (path lines) as possible. We propose a new approach, which we call steadification: given a time-dependent flow field v, we construct a new steady vector field w such that the stream lines of w correspond to the path lines of v. With this, the temporal behavior of v can be visualized by using standard methods for steady vector field visualization. We present a formal description as a constraint optimization that can be mapped to finding a set cover, a NP-hard problem that is solved approximately and fairly efficiently by a greedy algorithm. As an application, we introduce the first 2D image-based flow visualization technique that shows the behavior of path lines in a static visualization, even if the path lines have a significantly different behavior than stream lines.
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    Towards Glyphs for Uncertain Symmetric Second-Order Tensors
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Gerrits, Tim; Rössl, Christian; Theisel, Holger; Gleicher, Michael and Viola, Ivan and Leitte, Heike
    Measured data often incorporates some amount of uncertainty, which is generally modeled as a distribution of possible samples. In this paper, we consider second-order symmetric tensors with uncertainty. In the 3D case, this means the tensor data consists of 6 coefficients - uncertainty, however, is encoded by 21 coefficients assuming a multivariate Gaussian distribution as model. The high dimension makes the direct visualization of tensor data with uncertainty a difficult problem, which was until now unsolved. The contribution of this paper consists in the design of glyphs for uncertain second-order symmetric tensors in 2D and 3D. The construction consists of a standard glyph for the mean tensor that is augmented by a scalar field that represents uncertainty. We show that this scalar field and therefore the displayed glyph encode the uncertainty comprehensively, i.e., there exists a bijective map between the glyph and the parameters of the distribution. Our approach can extend several classes of existing glyphs for symmetric tensors to additionally encode uncertainty and therefore provides a possible foundation for further uncertain tensor glyph design. For demonstration, we choose the well-known superquadric glyphs, and we show that the uncertainty visualization satisfies all their design constraints.
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    Uncertain Stream Lines
    (The Eurographics Association, 2023) Zimmermann, Janos; Motejat, Michael; Rössl, Christian; Theisel, Holger; Guthe, Michael; Grosch, Thorsten
    We present a new approach for the visual representation of uncertain stream lines in vector field ensembles. While existing approaches rely on a particular seed point for the analysis of uncertain streamlines, our approach considers a whole stream line as seed structure. With this we ensure that uncertain stream lines are independent of the particular choice of seed point, and that uncertain stream lines have the same dimensionality as their certain counterparts in a single vector field. Assuming a Gaussian distribution of stream lines, we provide a visual representation of uncertain stream lines based on a mean map and a covariance map. The extension to uncertain path lines in ensembles of time-dependent vector fields is straightforward and is also introduced in the paper. We analyze properties, discuss discretization and performance issues, and apply the new technique to a number of flows ensembles.