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Analysis of phenomena that simultaneously occur on quite different spatial and temporal scales require adaptive, hierarchical schemes to reduce computational and storage demands. For data represented as grid functions, the key are adaptive, hierarchical, time-dependent grids that resolve spatio-temporal details without too much redundancy. Here, so-called AMR grids gain increasing popularity. For visualization and feature identification/tracking, the underlying continuous function has to be faithfully reconstructed by spatial and temporal interpolation. Well designed interpolation methods yield better results and help to reduce the amount of data to be stored. We address the problem of temporal interpolation of AMR grid data, e.g.\ for creation of smooth animations or feature tracking. Intermediate grid hierarchies are generated by merging the cells on all refinement levels that are present in the key frames considered. Utilizing a clustering algorithm a structure of nested grids is induced on the resulting collection of cells. The grid functions are mapped to the intermediate hierarchy, thus allowing application of appropriate interpolation techniques.

\noindent The size of data sets produced on remote supercomputer facilities frequently exceeds the processing capabilities of local visualization workstations. This phenomenon increasingly limits scientists when analyzing results of large-scale scientific simulations. That problem gets even more prominent in scientific collaborations, spanning large virtual organizations, working on common shared sets of data distributed in Grid environments. In the visualization community, this problem is addressed by distributing the visualization pipeline. In particular, early stages of the pipeline are executed on resources closer to the initial (remote) locations of the data sets. \noindent This paper presents an efficient technique for placing the first two stages of the visualization pipeline (data access and data filter) onto remote resources. This is realized by exploiting the ``extended retrieve'' feature of GridFTP for flexible, high performance access to very large HDF5 files. We reduce the number of network transactions for filtering operations by utilizing a server side data processing plugin, and hence reduce latency overhead compared to GridFTP partial file access. The paper further describes the application of hierarchical rendering techniques on remote uniform data sets, which make use of the remote data filtering stage.

Fast Volume Rendering of Sparse High-Resolution Datasets Using Adaptive Mesh Refinement Hierarchies
(2001)

In this paper we present an algorithm that accelerates 3D texture-based volume rendering of large and sparse data sets. A hierarchical data structure (known as AMR tree) consisting of nested uniform grids is employed in order to efficiently encode regions of interest. The hierarchies resulting from this kind of space partitioning yield a good balance between the amount of volume to render and the number of texture bricks -- a prerequisite for fast rendering. Comparing our approach to an octree based algorithm we show that our algorithm increases rendering performance significantly for sparse data. A further advantage is that less parameter tuning is necessary.

Many phenomena in nature and engineering happen simultaneously on rather diverse spatial and temporal scales, i.e.\ exhibit a multi-scale character. Therefore various hierarchical data structures and numerical schemes have been devised to represent quantitatively such phenomena. A special numerical multilevel technique, associated with a particular hierarchical data structure, is so-called Adaptive Mesh Refinement (AMR). This scheme achieves locally very high spatial and temporal resolutions. Due to its popularity, many scientists are in need of interactive visualization tools for AMR data. In this article we present a 3D texture-based volume rendering algorithm for AMR data, that directly utilizes the hierarchical structure. Thereby interactive rendering even for large data sets is achieved. In particular the problems of interpolation artifacts, opacity corrections, and texture memory limitations are addressed. The algorithm's value in practice is demonstrated with simulation and image data.

Multi-scale phenomena are abundant in many application fields. Representing and numerically simulating such processes is a challenging task since quite different scales have to be resolved, which often requires enormous amounts of storage and computational power. An important strategy in this context is adaptivity, i.e. local adjustment of the spatio-temporal resolution to the details to be resolved. A standard representation therefore are hierarchical, locally refined grids. A specific adaptive approach for solving partial differential equations, usually called AMR (Adaptive Mesh Refinement), was introduced in 1984. The basic idea is to combine the simplicity of structured grids and the advantages of local refinement. In this numerical scheme the computations are started on a set of coarse, potentially overlapping structured grids, that cover the computational domain. Local error criteria are applied to detect regions that require higher resolution. These are covered by subgrids with decreasing mesh spacing, which do not replace, but rather overlap the refined regions of the coarser patches. The equations are advanced on the finer subgrids and the refinement procedure recursively continues until all cells fulfill the considered error criteria, giving rise to a hierarchy of nested levels of refinement. In 1989 a variant of this scheme, called Structured Adaptive Mesh Refinement (SAMR), which reduces some of the complexity of the original approach, was proposed. While the separate subgrids in the AMR scheme could be rotated against each other, in SAMR they are aligned with the major axes of the coordinate system, which for example simplifies the computation of fluxes of (conserved) quantities through the cell faces. SAMR has become more and more popular in the last decade, and nowadays it is applied in many domains like hydrodynamics, meteorology and in particular in cosmology and relativistic astrophysics. Due to this growing popularity, an increasing number of scientists is in need of appropriate interactive visualization techniques to interpret and analyze AMR simulation data. Tools for both, 2D analysis to quantitatively convey the information within single slices and 3D representations to apprehend the overall structure are required. In this thesis we develop direct and indirect volume visualization algorithms for scalar fields that are defined on structured Adaptive Mesh Refinement (SAMR) grids. In particular algorithms for planar slicing and the display of height fields, C0-continuous isosurface extraction, software-, and hardware-based direct volume rendering and temporal interpolation for cell-, and vertex-centered data on unrestricted SAMR grids are proposed. Additionally we investigate the applicability of SAMR data structures for accelerated software-, and hardware-based volume rendering of large 3D scalar data.