Tino Weinkauf

Learn More
Functions that optimize Laplacian-based energies have become popular in geometry processing, e.g. for shape deformation, smoothing, multiscale kernel construction and interpolation. Minimizers of Dirichlet energies, or solutions of Laplace equations, are harmonic functions that enjoy the maximum principle, ensuring no spurious local extrema in the interior(More)
One of the reasons that topological methods have a limited popularity for the visualization of complex 3D flow fields is the fact that such topological structures contain a number of separating stream surfaces. Since these stream surfaces tend to hide each other as well as other topological features, for complex 3D topologies the visualizations become(More)
One of the reasons that topological methods have a limited popularity for the visualization of complex 3D flow fields is the fact that their topological structures contain a number of separating stream surfaces. Since these stream surfaces tend to hide each other as well as other topological features, for complex 3D topologies the visualizations become(More)
In nature and in flow experiments particles form patterns of swirling motion in certain locations. Existing approaches identify these structures by considering the behavior of stream lines. However, in unsteady flows particle motion is described by path lines which generally gives different swirling patterns than stream lines. We introduce a novel(More)
Data sets coming from simulations or sampling of real-world phenomena often contain noise that hinders their processing and analysis. Automatic filtering and denoising can be challenging: when the nature of the noise is unknown, it is difficult to distinguish between noise and actual data features; in addition, the filtering process itself may introduce(More)
We describe an approach to visually analyzing the dynamic behavior of 3D time-dependent flow fields by considering the behavior of the path lines. At selected positions in the 4D space-time domain, we compute a number of local and global properties of path lines describing relevant features of them. The resulting multivariate data set is analyzed by(More)
This paper presents an approach to extracting and classifying higher order critical points of 3D vector fields. To do so, we place a closed convex surface s around the area of interest. Then we show that the complete 3D classification of a critical point into areas of different flow behavior is equivalent to extracting the topological skeleton of an(More)
We introduce an approach to tracking vortex core lines in timedependent 3D flow fields which are defined by the parallel vectors approach. They build surface structures in the 4D space-time domain. To extract them, we introduce two 4D vector fields which act as feature flow fields, i.e., their integration gives the vortex core structures. As part of this(More)
Characteristic curves of vector fields include stream, path, and streak lines. Stream and path lines can be obtained by a simple vector field integration of an autonomous ODE system, i.e., they can be described as tangent curves of a vector field. This facilitates their mathematical analysis including the extraction of core lines around which stream or path(More)