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.
V olume rendering is a powerful computer graphics technique for visualizing three-dimensional data.l While much visualization creates a rendering only of surfaces-though they may be surfaces of 3D objects-volume rendering lets us also see "inside," beneath the surface of the object being represented. This technique models a volume as cloudlike cells of semitransparent material. Each cell emits light, partially transmits light from other cells, and absorbs some incoming light (see "Volume Rendering" sidebar). For instance, while a surface rendering of the human body might show the skin, a complete volume rendering also shows the bones and internal organs, visible from any side in proper perspective. Volume rendering began with medical visualization but has migrated to other fields, including visualization and graphics for nonscience uses. Objects of visualization need not be tangible; in fact, volume rendering is especially well suited for representing the 3D volumetric scalar and vector fields that frequently arise in computational science and engineering. Volume rendering is a nontrivial technique and can be slow. To effectively use it in studying complex physical and abstract structures, researchers and engineers need a coherent, powerful, easy-to-use visualization tool. This tool should allow for interactive visualization, ideally with support for user-defined "computational steering," that is, the ability to change parameters during simulation. But such a visualization tool presents develapment issues and challenges. First, even with the latest volume-rendering acceleration techniques running on top-of-the-line workstations, it still takes up to several minutes to volume-render an image-far from interactive! The large parallel computers that create the most detailed scientific simulations can generate data sets typically on the order of 32 to 512 megabytes and ranging up to 16 gigabytes. Second, even if rendering time is not a concern, large data sets may be too expensive to store and extremely slow to transfer over network links to typical workstations. This raises the question of whether visualization should be performed directly on the parallel machine generating the simulation data, or sent to a high-performance graphics workstation for postprocessing in the traditional manner. If the visualization and simulation software were integrated, we would need no extra storage, and visual-1070.9924/96/$5.0001996lEEE IEEE COMPUTATIONAL SCIENCE & ENGINEERING Volume Rendering Voxel samples Volume rendering accumulates information from voxels Ray (volumetric "pixels") in a 3D data set to produce a 20 m 4 =-= image, allowing structures in the data to be examined care-Eye fully. The technique models the volumetric data set as cloud-t like material that scatters, emits, and absorbs light.' Several Current sample
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