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.
One method of directly rendering a three-dimensional volume of scalar data is to project each cell in a volume onto the screen. Rasterizing a volume cell is more complex than rasterizing a polygon. A method is presented that approximates tetrahedral volume cells with hardware renderable transparent triangles. This method produces results which are visually similar to more exact methods for scalar volume rendering, but is faster and has smaller memory requirements. The method is best suited for display of smoothly-changing data. 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. 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.  In this paper, we address the problem of the interactive volume rendering of unstructured meshes and propose a new hardware-based ray-casting algorithm using partial pre-integration. The proposed algorithm makes use of modern programmable graphics card and achieves rendering rates competitive with full pre-integration approaches (up to 2M tet sec). This algorithm allows the interactive modification of the transfer function and results in high-quality images, since no artifact due to under-sampling the full numerical pre-integration exists. We also compare our approach with implementations of cell-projection algorithm and demonstrate that ray-casting can perform better than cell projection, because it eliminates the high costs involved in ordering and transferring data. 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.