In numerical analysis hierarchical techniques for local refinement became more and more popular in the last years, because they lead to more reliable results and allow one to simulate more complex phenomena. A special scheme is Adaptive Mesh Refinement (AMR), introduced by M. Berger in the 1980's. In this approach a hierarchy of nested regular axis-aligned subgrids is generated, representing relevant regions of the computational domain on different levels of resolution. The data are usually stored as separate overlapping subgrids.

This numerical technique is applied in many domains like hydrodynamics, meteorology and in particular in astrophysics. Despite of its popularity there exists only very little work on visualization for AMR data. In this project we develop interactive visualization techniques to interpret and analyze AMR simulation data. Both, 2D analysis to quantitatively convey the information within single slices and a 3D representation to quickly grasp the overall structure, especially of time-dependent data are being developed. Further the feasibility of AMR data structures to accelerate the rendering of large scalar data is examined.

In the recent years the advent of powerful graphics hardware with programmable pixel shaders enabled interactive raycasting implementations on low-cost commodity desktop computers. Unlike slice-based volume rendering approaches GPU-assisted raycasting does not suffer from rendering artifacts caused by varying sample distances along different ray-directions or limited frame-buffer precision. It further supports direct implementations of many sophisticated acceleration techniques and lighting models.

We presented a GPU-assisted raycasting approach for data that consists of volumetric fields defined on computational grids as well as unstructured point sets. We avoid resampling the point data onto proxy grids by directly encoding the point data in a GPU-octree data structure. This allows to efficiently access the (semi-transparent) point data during ray traversal and correctly blend it with the grid data, yielding interactive, high-quality rendering results. We discuss approaches to accelerate the rendering performance for larger point sets and give real world application examples to demonstrate the usefulness of our approach.

Data courtesy: T. Abel (KIPAC)

In the recent years the advent of powerful graphics hardware with flexible, programmable fragment shaders enabled interactive raycasting implementations which perform the ray-integration on a per-pixel basis. Unlike slice-based volume rendering these approaches do not suffer from rendering artifacts caused by varying sample distances along different ray-directions or limited frame-buffer precision. They further allow a direct realization of sophisticated optical models.

We investigate the applicability of GPU-assisted raycasting to block-structured, locally refined grids. We present an interactive algorithm for artifact-free, high-quality rendering of data defined on this type of grid structure and apply it to render data of time-dependent, three-dimensional galaxy and star formation simulations. We use a physically motivated emission-absorption model to map the computed temperature and density fields to color and opacity.

Data courtesy: T. Abel (KIPAC)

Analysis of phenomena that simultaneously occur on different spatial and temporal scales requires adaptive, hierarchical schemes to reduce computational and storage demands. Adaptive Mesh Refinement (AMR) schemes support both refinement in space that results in a time-dependent grid topology, as well as refinement in time that results in updates at higher rates for refined levels.

Visualization of AMR data requires generating data for absent refinement levels at specific time steps. We describe a solution starting from a given set of ``key frames" with potentially different grid topologies. The presented work was developed in a project involving several research institutes that collaborate in the field of cosmology and numerical relativity. AMR data results from simulations that are run on dedicated compute machines and is thus stored centrally, whereas the analysis of the data is performed on the local computers of the scientists. We built a distributed solution using remote procedure calls (RPC). To keep the application responsive, we split the bulk data transfer from the RPC response and deliver it asynchronously as a binary stream. The number of network round-trips is minimized by using high level operations. In summary, we provide an application for exploratory visualization of remotely stored AMR data.

Data courtesy: R. Takahashi (LSU)

Direct volume rendering is a popular technique for visualizing volumetric scalar data. The underlying idea is to map the data field to physical quantities like absorption and emission coefficients and to compute the intensity distribution of light traveling through this semi-transparent medium in the image plane. Nowadays volume rendering approaches leverage the powerful texture units of modern graphics hardware, which perform fast bi-, resp. tri-linear interpolation of texture samples and thereby allow interactive frame rates even on standard consumer PC systems.

We developed a texture-based direct volume-rendering algorithm for AMR Data that allows interactive frame rate even for highly resolved hierarchies. The algorithm was applied for rendering time-dependent AMR simulations, among them one of the most complex AMR simulation ever carried out, containing up to 27 levels of resolution.

Resulting images appeared on the cover of the February 2003 issue of "National Geographic Magazine" , were nominated as finalist entries in the "Science and Engineering Visualization" contest 2003, sponsored by the National Science Foundation (NSF) and have been chosen as "NASA Astronomy Picture of the Day" in June 2003.

Data courtesy: T. Abel (KIPAC)

In the AMR approach the subgrid structure generally changes after each update, due to a regridding procedure that aims to place grids in regions where higher resolution is required. The update frequency usually doubles between two consecutive levels of refinement, i.e. increases exponentially.For realistic AMR simulations, which often contain dozens of refinement levels, and typically evolve several scalar and vector quantities, storing all intermediate subgrids would result in huge amounts of data. AMR simulation packages therefore often dump data only for time steps that correspond to root level updates. Generating smooth animations of time-dependent data requires dense output. If the frequency of data dumps is too coarse, dense output is usually obtained by some sort of temporal interpolation between the given key-frames. Creation of dense output from a given set of time-steps via interpolation is problematic for AMR data, due to the change of the underlying grid topology and the fact that usually not all generated subgrids are available.

We developed an approach that generates intermediate grid hierarchies from a given set of key frames dumped by the simulation. It allows the application of standard interpolation schemes like linear and hermite interpolation. The resulting algorithms is fast and thus enable on-the-fly generation of smooth animations for AMR data.

Data courtesy: T. Abel (KIPAC)

Due to the enormous rate of increase in resolution of datasets, which are for example generated by 3D imaging devices or numerical simulations, volume rendering performance is still an issue even when utilizing highly specialized graphics hardware. The performance limiting factors are the fill rate of the hardware, i.e. the number of pixels that can be generated per time unit, the available texture memory, and the I/O bandwidth.

We investigate approaches that accelerate texture-based volume rendering for the frequently occurring case of large, but sparse data, i.e. highly resolved data where only a small fraction of the voxels contains relevant information. The binary relevance criterion might for example be given by voxel transparency or by choosing material subsets of segmented data. The strategy is to circumvent the limitations of the graphics hardware mentioned above by restricting most of the rendering work to the relevant parts of the volume. In order to benefit from the strength of texture hardware, the resulting coverage should consist of few axis-aligned, non-overlapping regions, and further allow for a view-consistent order for each viewpoint.

Hierarchical data structures based on recursive space partition via axis-aligned planes meet these criteria. We present an adaptive approach, where the regions are arranged in subvolumes that result from partitioning the data domain in a variant of a kd-tree. The tree is constructed by hierarchical clustering of cells that contain relevant data. This approach yields a good balance between the size of the resulting volume to render and the number of texture bricks and results in significant performance gains if compared to the octree scheme.

Data courtesy:
R. Menzel (FU-Berlin)

• R. Kaehler, T. Abel, H.-C. Hege. Simultaneous GPU-Assisted Raycasting of Unstructured Point Sets and Volumetric Grid Data. Proc. of IEEE/EG Symposium on Volume Graphics 2007, p. 49–56, Prague, Czech Republic, 2007.
• R. Kaehler, J. Wise, T. Abel, H.-C. Hege. GPU-Assisted Raycasting of Cosmological Adaptive Mesh Refinement Simulations. Proc. of Volume Graphics 2006, p. 103–110, Boston, USA, 2006.
• R. Kaehler, S. Prohaska, A. Hutanu, H.-C. Hege. Visualization of Time-Dependent Remote Adaptive Mesh Refinement Data. Proc. IEEE Visualization 2005, p. 175-182, Minneapolis, USA, 2005.
• Ralf Kaehler. Accelerated Volume Rendering on Structured Adaptive Meshes. Ph.D. thesis,Freie Universität Berlin, Fachbereich Mathematik und Informatik (P. Deuflhard), 2005.
• S. Prohaska, A. Hutanu, R. Kaehler, H.-C. Hege. Interactive Exploration of Large Remote Micro-CT Scans. Proc. IEEE Visualization '04, p. 345–352, 2004.
• S. Alonso, Ralf Kaehler, A. S. Mikhailov,, F. Sagues. Expanding scroll rings and negative tension turbulence in a model of excitable media. Physical Review E, APS Journals(70), 2004.
• H.-C. Hege, A. Hutanu, R. Kaehler, A. Merzky, T. Radke, E. Seidel, B. Ullmer. Progressive Retrieval and Hierarchical Visualization of Large Remote Data. Proc. 2003 Workshop on Adaptive Grid Middleware, p. 60–72, September 2003.
• R. Kaehler, M. Simon, H.-C. Hege. Fast Volume Rendering of Sparse Datasets using Adaptive Mesh Refinement. IEEE Transactions on Visualization and Computer Graphics, 9(3):341–351, 2003.
• R. Kaehler, H.-C. Hege. Visualization of Time-Dependent Adaptive Mesh Refinement Data. ZIB Preprint 03-16, 2003.
• R. Kaehler, H.-C. Hege. Texure-based Volume Rendering of Adaptive Mesh Refinement Data. The Visual Computer, 18(8):481–492, 2002.
• R. Kaehler, D. Cox, R. Patterson, S. Levy, H.-C. Hege, T. Abel. Rendering the First Star in the Universe - A Case Study. Proceedings of IEEE Visualization, IEEE Computer Society Press:537–540, 2002.
• H.-C. Hege, R. Kaehler, E. Seidel, T. Radke. GriKSL zeigt Live-Demos auf der iGrid2002. DFN-Mitteilungen, Heft 60, p. 21–22, 2002.