Recirculation Surfaces for Flow Visualization.

We present a formal approach to the visual analysis of recirculation in flows by introducing recirculation surfaces for 3D unsteady flow fields. Recirculation surfaces are the loci where massless particle integration returns to its starting point after some variable, finite integration. We give a rigorous definition of recirculation surfaces as 2-manifolds embedded in 5D space and study their properties. Based on this we construct an algorithm for their extraction, which searches for intersections of a recirculation surface with lines defined in 3D. This reduces the problem to a repeated search for critical points in 3D vector fields. We provide a uniform sampling of the search space paired with a surface reconstruction and visualize results. This way, we present the first algorithm for a comprehensive feature extraction in the 5D flow map of a 3D flow. The problem of finding isolated closed orbits in steady vector fields occurs as a special case of recirculation surfaces. This includes isolated closed orbits with saddle behavior. We show recirculation surfaces for a number of artificial and real flow data sets.

Glyphs for General Second-Order 2D and 3D Tensors.

Glyphs are a powerful tool for visualizing second-order tensors in a variety of scientic data as they allow to encode physical behavior in geometric properties. Most existing techniques focus on symmetric tensors and exclude non-symmetric tensors where the eigenvectors can be non-orthogonal or complex. We present a new construction of 2d and 3d tensor glyphs based on piecewise rational curves and surfaces 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. We apply the glyphs to visualize the Jacobian matrix fields of a number of 2d and 3d vector fields.

Reconstruction of volume data with quadratic super splines.

We propose a new approach to reconstruct nondiscrete models from gridded volume samples. As a model, we use quadratic trivariate super splines on a uniform tetrahedral partition. We discuss the smoothness and approximation properties of our model and compare to alternative piecewise polynomial constructions. We observe, as a nonstandard phenomenon, that the derivatives of our splines yield optimal approximation order for smooth data, while the theoretical error of the values is nearly optimal due to the averaging rules. Our approach enables efficient reconstruction and visualization of the data. As the piecewise polynomials are of the lowest possible total degree two, we can efficiently determine exact ray intersections with an isosurface for ray-casting. Moreover, the optimal approximation properties of the derivatives allow us to simply sample the necessary gradients directly from the polynomial pieces of the splines. Our results confirm the efficiency of the quasi-interpolating method and demonstrate high visual quality for rendered isosurfaces.

Realistic virtual intracranial stenting and computational fluid dynamics for treatment analysis.

In order to support the decisions of medical experts and to develop better stent designs, the availability of a simulation tool for virtual stenting would be extremely useful. An innovative virtual stenting technique is described in this work, which is directly applicable for complex patient-specific geometries. A basilar tip aneurysm provided for the Virtual Intracranial Stenting Challenge 2010 is considered to demonstrate the advantages of this approach. A free-form deformation is introduced for a wall-tight stent deployment. Numerical flow simulations on sufficiently fine computational meshes are performed for different configurations in order to characterize the inflow rate into the aneurysm and the corresponding residence time in the aneurysm sac. A Neuroform and a SILK stent have been deployed at various locations and the computed residence times have been evaluated and compared, demonstrating the advantage associated with a lower stent porosity. It has been found that the SILK stent leads to a large increase in the residence time and to a significant reduction in the maximum wall shear stress in the aneurysm sac. This is only observed when placing the stent in the appropriate position, showing that virtual stenting might be employed for operation support.

Streamline embedding for 3D vector field exploration.

We propose a new technique for visual exploration of streamlines in 3D vector fields. We construct a map from the space of all streamlines to points in IR(n) based on the preservation of the Hausdorff metric in streamline space. The image of a vector field under this map is a set of 2-manifolds in IR(n) with characteristic geometry and topology. Then standard clustering methods applied to the point sets in IR(n) yield a segmentation of the original vector field. Our approach provides a global analysis of 3D vector fields which incorporates the topological segmentation but yields additional information. In addition to a pure segmentation, the established map provides a natural "parametrization" visualized by the manifolds. We test our approach on a number of synthetic and real-world data sets.