In this dissertation is presented a practical approach of the Projected Tetrahedra’s (PT) algorithm for interactive volume rendering of unstructured data using programmable graphics cards. Unlike similar works reported earlier, the proposed method employs two fragment shaders, one for computing the tetrahedra projections and another for rendering the volume. The proposed algorithm achieve interactive rates by storing the model in texture memory and avoiding redundant projections of the earlier implementations using vertex shaders. The algorithm is capable of rendering over 2 millions tetrahedra per second on current graphics hardware, making it competitive with recent ray casting approaches, while occupying a substantially smaller memory footprint. 1.

Computational simulations frequently generate solutions defined over very large tetrahedral volume meshes containing many millions of elements. Furthermore, such solutions may often be expressed using non-linear basis functions. Certain solution techniques, such as discontinuous Galerkin methods, may even produce non-conforming meshes. Such data is difficult to visualize interactively, as it is far too large to fit in memory and many common data reduction techniques, such as mesh simplification, cannot be applied to non-conforming meshes. We introduce a point-based visualization system for interactive rendering of large, potentially non-conforming, tetrahedral meshes. We propose methods for adaptively sampling points from non-linear solution data and for decimating points at run time to fit GPU memory limits. Because these are streaming processes, memory consumption is independent of the input size. We also present an order-independent point rendering method that can efficiently render volumes on the order of 20 million tetrahedra at interactive rates.

Figure 1. Our novel point-based volume rendering technique is faster than the current state of the art while still generating high quality images. Left to right: baseline image rendered at full quality; our method with unshaped footprints, circular footprints and ellipsoidal footprints, respectively. The lower half (our method) shows the difference to the baseline exact image. Notice the increasing level of fidelity. Unstructured volume grids are ubiquitous in scientific computing, and have received substantial interest from the scientific visualization community. In this paper, we take a point-based approach to rendering unstructured grids. In particular, we present a novel method of approximating these irregular elements with point-based primitives amenable to existing hardware acceleration techniques. To improve interactivity to large datasets, we have adapted a level-of-detail strategy. We use a well-known quantitative metric to analyze the image quality achieved by the final rendering. 1.

Figure 1: Three images of the Lawrence-Livermore National Laboratory (LLNL) simulation of a Richtmyer-Meshkov instability (time step 270; iso-value 16) at different level-of-detail (LOD) levels. While data is loaded asynchronously in the background it is possible to fully interact with the scene. A kd-tree based LOD structure is used to bridge loading times while allowing interactive ray tracing of up to four frames per second on a custom PC. The visualization of iso-surfaces from gridded volume data is an important tool in many scientific applications. Today, it is possible to ray trace high-quality iso-surfaces at interactive frame rates even on commodity PCs. However, current algorithms fail if the data set exceeds a certain size either because they are not designed for out-of-core data sets or the loading times are too high because there is too much overhead involved in the out-ofcore (OOC) techniques. We propose a kd-tree based OOC data structure that allows to ray trace iso-surfaces of large volumetric data sets of may giga bytes at interactive frame rates on a single PC. A LOD technique is used to bridge loading times of data that is fetched asynchronously in the background. Using this framework we are able to ray trace iso-surfaces between 2 and 4 fps on a single dual-core Opteron PC at 640×480 resolution and an in-core memory footprint that is only a fraction of the entire data size. Categories and Subject Descriptors (according to ACM CCS): I.3.2 [Graphics Systems]: Stand-alone systems; I.3.6 [Methodology and Techniques]: Graphics data structures and data types; I.3.7 [Three-Dimensional Graphics and

The amount of data available from simulation and measurement is growing at an incredible rate. A major challenge for the visualization community is to develop methods that allow users to explore these data interactively. For three-dimensional scalar fields, direct volume rendering has become an important technique in research and commercial settings. Interactive volume rendering requires the efficient use of available computational resources to keep pace with the disparity, resolution, and complexity of the volumes that are commonly produced from simulations (e.g., computational fluid dynamics or structural mechanics) and measurements (e.g., environmental observation and forecasting systems). For structured grids, direct volume rendering is well-studied and sufficiently straightforward with modern graphics hardware. This is not the case with unstructured volumes, because the elements that compose the mesh do not so easily map to current hardware. These datasets may be extremely large and contain more than a single static instance. Therefore, advanced solutions are required to achieve interactive visualization of this type of data. The goal of this dissertation is to provide several new techniques to facilitate the visualization of disparate unstructured meshes. Two new methods are proposed to accelerate volume rendering

Computational simulations frequently generate solutions defined over very large tetrahedral volume meshes containing many millions of elements. Furthermore, solutions over these meshes may often be expressed using non-linear basis functions. Certain solution techniques, such as discontinuous Galerkin finite element methods, may even produce non-conforming meshes. Such data is difficult to visualize interactively, as it is far too large to fit in memory and many common data reduction techniques, such as mesh simplification, cannot be applied to non-conforming meshes. Common linear interpolation method cannot faithfully and accurately evaluate the non-linear solutions. To provide accurate visualization, in the first part of this dissertation, we introduce a method for pixel-exact evaluation of higher order solution data on the GPU. We demonstrate the importance of per-pixel rendering versus simple linear interpolation for producing high quality visualizations. We also show that our system can accommodate reasonably large datasets—spacetime meshes containing up to 20 million tetrahedra. To provide interactive visualization, in the second part, we introduce a point-based visualization system for interactive rendering of large, potentially non-conforming, tetrahedral meshes. We propose methods for adaptively sampling points from non-linear solution data and for decimating points at run time to fit GPU memory limits. Because these are streaming processes, memory consumption is independent of the input size. We also present an order-independent point rendering method that can efficiently render volumes on the order of 20 million tetrahedra at interactive rates.