TY - CHAP A1 - Weinkauf, Tino A1 - Theisel, Holger A1 - Shi, Kuangyu A1 - Hege, Hans-Christian A1 - Seidel, Hans-Peter T1 - Topological simplification of 3D vector fields and extracting higher order critical points T2 - Proc. IEEE Visualization 2005 Y1 - 2005 SP - 631 EP - 638 CY - Minneapolis, USA ER - TY - CHAP A1 - Theisel, Holger A1 - Sahner, Jan A1 - Weinkauf, Tino A1 - Hege, Hans-Christian A1 - Seidel, Hans-Peter T1 - Extraction of parallel vector surfaces in 3D time-dependent fields and application to vortex core line tracking T2 - Proc. IEEE Visualization 2005 Y1 - 2005 SP - 559 EP - 566 CY - Minneapolis, USA ER - TY - JOUR A1 - Weinkauf, Tino A1 - Hege, Hans-Christian A1 - Theisel, Holger T1 - Advected Tangent Curves: A General Scheme for Characteristic Curves of Flow Fields JF - Computer Graphics Forum N2 - We present the first general scheme to describe all four types of characteristic curves of flow fields – stream, path, streak, and time lines – as tangent curves of a derived vector field. Thus, all these lines can be obtained by a simple integration of an autonomous ODE system. Our approach draws on the principal ideas of the recently introduced tangent curve description of streak lines. We provide the first description of time lines as tangent curves of a derived vector field, which could previously only be constructed in a geometric manner. Furthermore, our scheme gives rise to new types of curves. In particular, we introduce advected stream lines as a parameter-free variant of the time line metaphor. With our novel mathematical description of characteristic curves, a large number of feature extraction and analysis tools becomes available for all types of characteristic curves, which were previously only available for stream and path lines. We will highlight some of these possible applications including the computation of time line curvature fields and the extraction of cores of swirling advected stream lines. Y1 - 2012 U6 - https://doi.org/10.1111/j.1467-8659.2012.03063.x VL - 31 IS - 2pt4 SP - 825 EP - 834 ER - TY - JOUR A1 - Günther, Tobias A1 - Kuhn, Alexander A1 - Hege, Hans-Christian A1 - Theisel, Holger T1 - MCFTLE: Monte Carlo Rendering of Finite-Time Lyapunov Exponent Fields JF - Computer Graphics Forum Y1 - 2016 U6 - https://doi.org/10.1111/cgf.12914 N1 - By mistake the fourth author Hans-Christian Hege has been ommitted in the journal publication VL - 35 IS - 3 SP - 381 EP - 390 ER - TY - GEN A1 - Günther, Tobias A1 - Kuhn, Alexander A1 - Hege, Hans-Christian A1 - Gross, Markus A1 - Theisel, Holger T1 - Progressive Monte-Carlo Rendering of Atmospheric Flow Features Across Scales T2 - 69th Annual Meeting of the APS Division of Fluid Dynamics, Gallery of Fluid Motion, Nov 20-22, 2016, Portland, OR, USA. N2 - To improve existing weather prediction and reanalysis capabilities, high-resolution and multi-modal climate data becomes an increasingly important topic. The advent of increasingly dense numerical simulation of atmospheric phenomena, provides new means to better understand dynamic processes and to visualize structural flow patterns that remain hidden otherwise. In the presented illustrations we demonstrate an advanced technique to visualize multiple scales of dense flow fields and Lagrangian patterns therein, simulated by state-of-the-art simulation models for each scale. They provide a deeper insight into the structural differences and patterns that occur on each scale and highlight the complexity of flow phenomena in our atmosphere. Y1 - 2016 U6 - https://doi.org/10.1103/APS.DFD.2016.GFM.P0030 ER -