In the last decades cosmological N-body dark matter simulations have enabled ab initio studies of the formation of structure in the Universe. Gravity amplified small density fluctuations generated shortly after the Big Bang, leading to the formation of galaxies in the cosmic web. These calculations have led to a growing demand for methods to analyze time-dependent particle based simulations. Rendering methods for such N-body simulation data usually employ some kind of splatting approach via point based rendering primitives and approximate the spatial distributions of physical quantities using kernel interpolation techniques, common in SPH (Smoothed Particle Hydrodynamics)-codes. This paper proposes three GPU-assisted rendering approaches, based on a new, more accurate method to compute the physical densities of dark matter simulation data. It uses full phase-space information to generate a tetrahedral tessellation of the computational domain, with mesh vertices defined by the simulation's dark matter particle positions. Over time the mesh is deformed by gravitational forces, causing the tetrahedral cells to warp and overlap. The new methods are well suited to visualize the cosmic web. In particular they preserve caustics, regions of high density that emerge, when several streams of dark matter particles share the same location in space, indicating the formation of structures like sheets, filaments and halos. We demonstrate the superior image quality of the new approaches in a comparison with three standard rendering techniques for N-body simulation data.
There has also been extensive work on the visualization of data on tetrahedral grids. Cell-projection methods usually employ the Projected Tetrahedra (PT) algorithm, that decomposes each tetrahedron into a set of triangles and assigns scalar values for the entry and exit points of the viewing rays to each vertex @cite_22 . A GPU-assisted method for decomposing the tetrahedra into triangles using the PT algorithm was presented by Wylie et al. @cite_29 . An artifact-free PT rendering approach using a logarithmically scaled pre-integration table was proposed by Kraus et al. @cite_11 . Maximo et al. developed a hardware-assisted PT approach using CUDA for visibility sorting @cite_3 . GPU-assisted raycasting methods for tetrahedral grids have, for example, been discussed by Weiler et al. @cite_21 and Espinha et al. @cite_6 .
@cite_22 @cite_29 @cite_21 @cite_3 @cite_6 @cite_11
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Projective methods for volume rendering currently represent the best approach for interactive visualization of unstructured data sets. We present a technique for tetrahedral projection using the programmable vertex shaders on current generation commodity graphics cards. The technique is based on Shirley and Tuchman's Projected Tetrahedra (PT) algorithm and allows tetrahedral elements to be volume scan converted within the graphics processing unit. Our technique requires no pre-processing of the data and no additional data structures. Our initial implementation allows interactive viewing of large unstructured datasets on a desktop personal computer. Hardware-accelerated direct volume rendering of unstructured volumetric meshes is often based on tetrahedral cell projection, in particular, the Projected Tetrahedra (PT) algorithm and its variants. Unfortunately, even implementations of the most advanced variants of the PT algorithm are very prone to rendering artifacts. In this work, we identify linear interpolation in screen coordinates as a cause for significant rendering artifacts and implement the correct perspective interpolation for the PT algorithm with programmable graphics hardware. We also demonstrate how to use features of modern graphics hardware to improve the accuracy of the coloring of individual tetrahedra and the compositing of the resulting colors, in particular, by employing a logarithmic scale for the pre-integrated color lookup table, using textures with high color resolution, rendering to floating-point color buffers, and alpha dithering. Combined with a correct visibility ordering, these techniques result in the first implementation of the PT algorithm without objectionable rendering artifacts. Apart from the important improvement in rendering quality, our approach also provides a test bed for different implementations of the PT algorithm that allows us to study the particular rendering artifacts introduced by these variants. In this paper we introduce a novel parallel and interactive SPH simulation and rendering method on the GPU using CUDA which allows for high quality visualization. The crucial particle neighborhood search is based on Z-indexing and parallel sorting which eliminates GPU memory overhead due to grid or hierarchical data structures. Furthermore, it overcomes limitations imposed by shading languages allowing it to be very flexible and approaching the practical limits of modern graphics hardware. For visualizing the SPH simulation we introduce a new rendering pipeline. In the first step, all surface particles are efficiently extracted from the SPH particle cloud exploiting the simulation data. Subsequently, a partial and therefore fast distance field volume is rasterized from the surface particles. In the last step, the distance field volume is directly rendered using state-of-the-art GPU raycasting. This rendering pipeline allows for high quality visualization at very high frame rates. We present the first implementation of a volume ray casting algorithm for tetrahedral meshes running on off-the-shelf programmable graphics hardware. Our implementation avoids the memory transfer bottleneck of the graphics bus since the complete mesh data is stored in the local memory of the graphics adapter and all computations, in particular ray traversal and ray integration, are performed by the graphics processing unit. Analogously to other ray casting algorithms, our algorithm does not require an expensive cell sorting. Provided that the graphics adapter offers enough texture memory, our implementation performs comparable to the fastest published volume rendering algorithms for unstructured meshes. Our approach works with cyclic and or non-convex meshes and supports early ray termination. Accurate ray integration is guaranteed by applying pre-integrated volume rendering. In order to achieve almost interactive modifications of transfer functions, we propose a new method for computing three-dimensional pre-integration tables.