Hybrid Sample-based Surface Rendering

The performance of rasterization-based rendering on current GPUs strongly depends on the abilities to avoid overdraw and to prevent rendering triangles smaller than the pixel size. Otherwise, the rates at which highresolution polygon models can be displayed are affected significantly. Instead of trying to build these abilities into the rasterization-based rendering pipeline, we propose an alternative rendering pipeline implementation that uses rasterization and ray-casting in every frame simultaneously to determine eye-ray intersections. To make ray-casting competitive with rasterization, we introduce a memory-efficient sample-based data structure which gives rise to an efficient ray traversal procedure. In combination with a regular model subdivision, the most optimal rendering technique can be selected at run-time for each part. For very large triangle meshes our method can outperform pure rasterization and requires a considerably smaller memory budget on the GPU. Since the proposed data structure can be constructed from any renderable surface representation, it can also be used to efficiently render isosurfaces in scalar volume fields. The compactness of the data structure allows rendering from GPU memory when alternative techniques already require exhaustive paging

Crease surfaces: from theory to extraction and application to diffusion tensor MRI

Crease surfaces are two-dimensional manifolds along which a scalar field assumes a local maximum (ridge) or a local minimum (valley) in a constrained space. Unlike isosurfaces, they are able to capture extremal structures in the data. Creases have a long tradition in image processing and computer vision, and have recently become a popular tool for visualization. When extracting crease surfaces, degeneracies of the Hessian (i.e., lines along which two eigenvalues are equal), have so far been ignored. We show that these loci, however, have two important consequences for the topology of crease surfaces: First, creases are bounded not only by a side constraint on eigenvalue sign, but also by Hessian degeneracies. Second, crease surfaces are not in general orientable. We describe an efficient algorithm for the extraction of crease surfaces which takes these insights into account and demonstrate that it produces more accurate results than previous approaches. Finally, we show that DT-MRI streamsurfaces, which were previously used for the analysis of planar regions in diffusion tensor MRI data, are mathematically ill-defined. As an example application of our method, creases in a measure of planarity are presented as a viable substitute

Lagrangian Coherent Structures with Guaranteed Material Separation

Figure 1: Scalar field on a space-time parameterization of a cylinder flow. All separating structures in space-time are described by this field. The dark lines are 5 different path lines. Given an unsteady flow field, one common way to compute Lagrangian Coherent Structures (LCS) is to extract extremal structures of the Finite Time Lyapunov Exponent (FTLE). Experience has shown that the resulting struc-tures are often close to material structures (i.e., material lines or material surfaces). Moreover, it has been proven that for an integration time converging to infinity, they converge to exact material structures. However, due to the finite integration time in FTLE, they are generally not exact material structures. In this paper we introduce a modification of the FTLE method which is guaranteed to produce separating material structures as features of a scalar field. We achieve this by incorporating the complete available integration time both in forward and backward direction, and by choosing an appropriate definition for separating structures. We apply our method to two test data sets and show the differences to classical FTLE. 1

Description of induced nuclear fission with Skyrme energy functionals: static potential energy surfaces and fission fragment properties

Eighty years after its experimental discovery, a description of induced nuclear fission based solely on the interactions between neutrons and protons and quantum many-body methods still poses formidable challenges. The goal of this paper is to contribute to the development of a predictive microscopic framework for the accurate calculation of static properties of fission fragments for hot fission and thermal or slow neutrons. To this end, we focus on the Pu239(n,f) reaction and employ nuclear density functional theory with Skyrme energy densities. Potential energy surfaces are computed at the Hartree-Fock-Bogoliubov approximation with up to five collective variables. We find that the triaxial degree of freedom plays an important role, both near the fission barrier and at scission. The impact of the parametrization of the Skyrme energy density and the role of pairing correlations on deformation properties from the ground state up to scission are also quantified. We introduce a general template for the quantitative description of fission fragment properties. It is based on the careful analysis of scission configurations, using both advanced topological methods and recently proposed quantum many-body techniques. We conclude that an accurate prediction of fission fragment properties at low incident neutron energies, although technologically demanding, should be within the reach of current nuclear density functional theory

Consistent Approximation of Local Flow Behavior for 2D Vector Fields Using Edge Maps

Abstract not provide

Compression of 2D Vector Fields Under Guaranteed Topology Preservation

In this paper we introduce a new compression technique for 2D vector fields which preserves the complete topology, i.e., the critical points and the connectivity of the separatrices. As the theoretical foundation of the algorithm, we show in a theorem that for local modifications of a vector field, it is possible to decide entirely by a local analysis whether or not the global topology is preserved. This result is applied in a compression algorithm which is based on a repeated local modification of the vector field - namely a repeated edge collapse of the underlying piecewise linear domain. We apply the compression technique to a number of data sets with a complex topology and obtain significantly improved compression ratios in comparison to pre-existing topology-preserving techniques