Multitype Multifield Visualization
Final Report Abstract
The project was concerned with developing visualization techniques for Multifield data in Scientific Visualization. The focus was on data where the different fields come in different physical units that cannot be directly compared. In particular, we have developed solutions for the following kinds of data: Inertial flow data: In inertial flow data, the trajectory of particle does not only depend on the underlying velocity field but also on its own mass, inertia and velocity. Inertial flows can be considered as higherdimensional flows. With this, we have studied singularities of the inertial flow map gradient. Further, we have introduced a topological visualization of uncertain 2D steady vector fields. Finally, we have presented a suction of the so-called source inversion problem without inertial backward integration. General second order tensors: We have developed new glyphs for general second order tensors with the following properties: invariance to (a) isometries and (b) scaling, (c) direct encoding of all real eigenvalues and eigenvectors, (d) one-to-one relation between the tensors and glyphs, (e) glyph continuity under changing the tensor. Multiple vector/eigenvector fields: We have developed a generalization of the well-known parallel vectors (PV) operator for two vector fields to the approximate parallel vectors (APV) operator for multiple vector field. This operator allows to compute e.g. vortices in ensemble flow simulations. Uncertain symmetric second order tensors: We have developed a glyph that uniquely encodes an uncertain symmetric second order tensor under the assumption of a normal distributions. This includes the 6 parameters of the mean tensor and the 21 additional parameters of the 4-th order covariance tensor. The approach is generic, i.e., it is applicable to any glyph construction for the mean tensor that is “complicated enough”, which is the case, e.g., for the standard representation by superquadrics.
Publications
- Inertial Steady 2D Vector Field Topology. Computer Graphics Forum (Proc. Eurographics), 2016
T. Günther and H. Theisel
(See online at https://doi.org/10.1111/cgf.12846) - Singularities of the Inertial Flow Map Gradient. Proceedings of the Conference on Vision, Modeling and Visualization, 2016
T. Günther and H. Theisel
(See online at https://doi.org/10.2312/vmv.20161344) - Source Inversion by Forward Integration in Inertial Flows. Computer Graphics Forum (Proc. EuroVis), 2016
T. Günther and H. Theisel
(See online at https://doi.org/10.1111/cgf.12913) - Glyphs for General Second-Order 2D and 3D Tensors. IEEE Transactions on Visualization and Computer Graphics (Proc. IEEE Scientific Visualization 2016), 2017
T. Gerrits, C. Rössl and H. Theisel
(See online at https://doi.org/10.1109/TVCG.2016.2598998) - Glyphs for Space-Time Jacobians of Time-Dependent Vector Fields. Journal of WSCG, 2017
T. Gerrits, C. Rössl and H. Theisel
- An Approximate Parallel Vectors Operator for Multiple Vector Fields. Computer Graphics Forum (Proc. EuroVis), 2018
T. Gerrits, C. Rössl and H. Theisel
(See online at https://doi.org/10.1111/cgf.13422) - Towards Glyphs for Uncertain Symmetric Second-Order Tensors. Computer Graphics Forum (Proc. EuroVis), 2019
T. Gerrits, C. Rössl and H. Theisel
(See online at https://doi.org/10.1111/cgf.13692)
