We propose a fast algorithm for rendering general irregular grids. Our method uses a sweep-plane approach to accelerate ray casting, and can handle disconnected and nonconvex (even with holes) unstructured irregular grids with a rendering cost that decreases as the “disconnectedness” decreases. The algorithm is carefully tailored to exploit spatial coherence even if the image resolution differs substantially from the object space resolution. In this paper, we establish the practicality of our method through experimental results based on our implementation, and we also provide theoretical results, both lower and upper bounds, on the complexity of ray casting of irregular grids.

Abstract—Lazy Sweep Ray Casting is a fast algorithm for rendering general irregular grids. It is based on the sweep-plane paradigm, and it is able to accelerate ray casting for rendering irregular grids, including disconnected and nonconvex (even with holes) unstructured irregular grids with a rendering cost that decreases as the “disconnectedness ” decreases. The algorithm is carefully tailored to exploit spatial coherence even if the image resolution differs substantially from the object space resolution. Lazy Sweep Ray Casting has several desirable properties, including its generality, (depth-sorting) accuracy, low memory consumption, speed, simplicity of implementation, and portability (e.g., no hardware dependencies). We establish the practicality of our method through experimental results based on our implementation, which is shown to be substantially faster (by up to two orders of magnitude) than other algorithms implemented in software. We also provide theoretical results, both lower and upper bounds, on the complexity of ray casting of irregular grids.

Very large irregular-grid data sets are represented as tetrahedral meshes and may incur significant disk I/O access overhead in the rendering process. An effective way to alleviate the disk I/O overhead associated with rendering large tetrahedral mesh is to reduce the I/O bandwidth requirement through compression. Existing tetrahedral mesh compression algorithms focus only on compression efficiency and cannot be readily integrated into the mesh rendering process, and thus demand that a compressed tetrahedral mesh be decompressed before it can be rendered into a 2D image. This paper presents an integrated tetrahedral mesh compression and rendering algorithm called Gatun, which allows compressed tetrahedral meshes to be rendered incrementally as they are being decompressed, thus leading to an efficient irregular grid rendering pipeline. Both compression and rendering algorithms in Gatun exploit the same local connectivity information among adjacent tetrahedra, and thus can be tightly int...

We present the Circular Incident Edge Lists (CIEL), a new data structure and a high-performance algorithm for generating a series of iso-surfaces in a highly unstructured grid. Slicing-based volume rendering is also considered. The CIEL data structure represents all the combinatorial information of the grid, making it possible to optimize the classical propagation from local minima paradigm. The usual geometric structures are replaced by a more efficient combinatorial structure. An active edges list is maintained, and iteratively propagated from an iso-surface to the next one in a very efficient way. The intersected cells incident to each active edge are retrieved, and the intersection polygons are generated by circulating around their facets. This latter feature enables arbitrary irregular cells to be treated, such as those encountered in certain computational fluid dynamics (CFD) simulations. Since the CIEL data structure solely depends on the connections between the cells, it is possible to take into account dynamic changes in the geometry of the mesh and in property values, which only requires the sorted extrema list to be updated. Experiments have shown that our approach is significantly faster than classical methods. The major drawback of our method is its memory consumption, higher than most classical methods. However, experimental results show that it stays within a practical range.

Summary. Volumetric datasets obtained from scientific simulation and partial differential equation solvers are typically given in the form of non-rectilinear grids. The splatting technique is a popular direct volume rendering algorithm, which can provide high quality rendering results, but has been mainly described for rectilinear grids. In splatting, each voxel is represented by a 3D kernel weighted by the discrete voxel value. While the 3D reconstruction kernels for rectilinear grids can be easily constructed based on the distance among the aligned voxels, for irregular grids the kernel construction is significantly more complicated. In this paper, we propose a novel method based on a 3D Delaunay triangulation to create 3D elliptical Gaussian kernels, which then can be used by a splatting algorithm for the rendering of irregular grids. Our method does not require a resampling of the irregular grid. Instead, we use a weighted least squares method to fit a 3D elliptical Gaussian centered at each grid point, approximating its Voronoi cell. The resulting 3D elliptical Gaussians are represented using a convenient matrix representation, which allows them to be seamlessly incorporated into our elliptical splatting rendering system. 1

Volume visualization has become more and more important in modern world due to its wide applicability. Numerous techniques have been developed to render data sets in the form of regular grids (voxel data) and irregular grids. As the volume data sets grow bigger and bigger, data compression algorithms are required to reduce the disk storage size, and potentially the memory size during rendering as well. This paper surveys several techniques of volume visualization and volume compression, together with their integration or interaction. In general the strategies include: decompression the whole data set before rendering, on-the-fly rendering during decompression, on-the-fly decompression during rendering, and rendering in the compression domain.

Very large irregular-grid volume data sets are typically represented as tetrahedral mesh and require substantial disk I/O and rendering computation. One effective way to reduce this demanding resource requirement is compression. Previous research showed how rendering and decompression of a losslessly compressed irregular-grid data set can be integrated into a one-pass computation. This work advances the state of the art one step further by showing that a losslessly compressed irregular volume data set can be simplified while it is being decompressed and that simplification, decompression, and rendering can again be integrated into a pipeline that requires only a single pass through the data sets. Since simplification is a form of lossy compression, the on-the-fly volume simplification algorithm provides a powerful mechanism to dynamically create versions of a tetrahedral mesh at multiple resolution levels directly from its losslessly compressed representation, which also corresponds to the finest resolution level. In particular, an irregulargrid volume renderer can exploit this multi-resolution representation to maintain interactivity on a given hardware/software platform by automatically adjusting the amount of rendering computation that could be afforded, or performing so called time-critical rendering. The proposed tetrahedral mesh simplification algorithm and its integration with volume decompression and rendering has been successfully implemented in the Gatun system. Performance measurements on the Gatun prototype show that simplification only adds less than 5% of performance overhead on an average and with multi-resolution pre-simplification the end-to-end rendering delay indeed decreases in an approximately linear fashion with respect to the simplification ratio.