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Keywords
A framework is proposed for extracting features in 2D transient flows, based on the acceleration field to ensure Galilean invariance. The minima of the acceleration magnitude, i.e. a superset of the acceleration zeros, are extracted and discriminated into vortices and saddle points --- based on the spectral properties of the velocity Jacobian. The extraction of topological features is performed with purely combinatorial algorithms from discrete computational topology. The feature points are prioritized with persistence, as a physically meaningful importance measure. These features are tracked in time with a robust algorithm for tracking features. Thus a space-time hierarchy of the minima is built and vortex merging events are detected. The acceleration feature extraction strategy is applied to three two-dimensional shear flows:
(1) an incompressible periodic cylinder wake,
(2) an incompressible planar mixing layer and
(3) a weakly compressible planar jet.
The vortex-like acceleration feature points are shown to be well aligned with acceleration zeros, maxima of the vorticity magnitude, minima of pressure field and minima of λ2.
A framework is proposed for extracting features in 2D transient flows, based on the acceleration field to ensure Galilean invariance. The minima of the acceleration magnitude, i.e. a superset of the acceleration zeros, are extracted and discriminated into vortices and saddle points --- based on the spectral properties of the velocity Jacobian. The extraction of topological features is performed with purely combinatorial algorithms from discrete computational topology. The feature points are prioritized with persistence, as a physically meaningful importance measure. These features are tracked in time with a robust algorithm for tracking features. Thus a space-time hierarchy of the minima is built and vortex merging events are detected. The acceleration feature extraction strategy is applied to three two-dimensional shear flows: (1) an incompressible periodic cylinder wake, (2) an incompressible planar mixing layer and (3) a weakly compressible planar jet. The vortex-like acceleration feature points are shown to be well aligned with acceleration zeros, maxima of the vorticity magnitude, minima of pressure field and minima of λ2.
2D Tensor Field Segmentation
(2009)
Many scientific applications deal with data from a multitude of different sources, e.g., measurements, imaging and simulations. Each source provides an additional perspective on the phenomenon of interest, but also comes with specific limitations, e.g. regarding accuracy, spatial and temporal availability. Effectively combining and analyzing such multimodal and partially incomplete data of limited accuracy in an integrated way is challenging. In this work, we outline an approach for an integrated analysis and visualization of the atmospheric impact of volcano eruptions. The data sets comprise observation and imaging data from satellites as well as results from numerical particle simulations. To analyze the clouds from the volcano eruption in the spatiotemporal domain we apply topological methods. Extremal structures reveal structures in the data that support clustering and comparison. We further discuss the robustness of those methods with respect to different properties of the data and different parameter setups. Finally we outline open challenges for the effective integrated visualization using topological methods.
This work is concerned with adaptive screen-space sampling for volume ray-casting. The goal is to reduce the
number of rays being cast into the scene and, thus, the overall number of sampling points. We guarantee reliable
images through explicit error control using an error estimator that is founded in the field of finite element methods
(FEM). FEM theory further provides a well-founded theory to prove the efficiency of the presented algorithm via
convergence analysis. We, therefore, compare the convergence behavior of our method against uniform subdivisions
and a refinement scheme that was presented in the context of CPU volume ray-casting. Minimizing
the number of sampling points is of interest for rendering large datasets where each evaluation might need an expensive
decompression. Furthermore, with increasing screen resolutions high-resolution images are created more
efficiently with our method.