Volume rendering is a technique for visualizing 3D arrays of sampled data. It has applications in areas such as medical imaging and scientific visualization, but its use has been limited by its high computational expense. Early implementations of volume rendering used brute-force techniques that require on the order of 100 seconds to render typical data sets on a workstation. Algorithms with optimizations that exploit coherence in the data have reduced rendering times to the range of ten seconds but are still not fast enough for interactive visualization applications. In this thesis we present a family of volume rendering algorithms that reduces rendering times to one second. First we present a scanline-order volume rendering algorithm that exploits coherence in both the volume data and the image. We show that scanline-order algorithms are fundamentally more efficient than commonly-used ray casting algorithms because the latter must perform analytic geometry calculations (e.g. intersecting rays with axis-aligned boxes). The new scanline-order algorithm simply streams through the volume and the image in storage order. We describe variants of the algorithm for both parallel and perspective projections and

We examine various simple algorithms that exploit homogeneity and accumulated opacity for tracing rays through shaded volumes. Most of these methods have error criteria which allow them to trade quality for speed. The time vs. quality tradeoff for these adaptive methods is compared to fixed step multiresolution methods. These methods are also useful for general light transport in volumes. 1 Introduction We are interested in speeding volume ray tracing computations. We concentrate on the one dimensional problem of tracing a single ray, or computing the intensity at a point from a single direction. In addition to being the kernel of a simple volume ray tracer, this computation can be used to generate shadow volumes and as an element in more general light transport problems. Our data structures will be view independent to speed the production of animations of preshaded volumes and interactive viewing. In [11] Levoy introduced two key concepts which we will be expanding on: presence accel...

We present a brute-force ray tracing system for interactive volume visualization. The system runs on a conventional (distributed) shared-memory multiprocessor machine. For each pixel we trace a ray through a volume to compute the color for that pixel. Although this method has high intrinsic computational cost, its simplicity and scalability make it ideal for large datasets on current high-end parallel systems. To gain efficiency several optimizations are used including a volume bricking scheme and a shallow data hierarchy. These optimizations are used in three separate visualization algorithms: isosurfacing of rectilinear data, isosurfacing of unstructured data, and maximum-intensity projection on rectilinear data. The system runs interactively (i.e., several frames per second) on an SGI Reality Monster. The graphics capabilities of the Reality Monster are used only for display of the final color image.

Figure 1: All images show tetrahedral meshes consisting of 125K to 190K cells rendered with our hardware-based ray casting algorithm. The algorithm exploits the programmable fragment unit of the ATI Radeon 9700 graphics chip and runs at several frames per second in a 512 × 512 viewport. The left image shows multiple shaded isosurfaces, the middle and right images are rendered with a full density-emitter model. 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 preintegration tables.

This paper describes a volume rendering system for unstructured data, especially finite element data, that creates images with very high accuracy. The system will currently handle meshes whose cells are either linear or quadratic tetrahedra. Compromises or approximations are not introduced for the sake of efficiency. Whenever possible, exact mathematical solutions for the radiance integrals involved and for interpolation are used. The system will also handle meshes with mixed cell types: tetrahedra, bricks, prisms, wedges, and pyramids, but not with high accuracy. Accurate semitransparent shaded isosurfaces may be embedded in the volume rendering. For very small cells, subpixel accumulation by splatting is used to avoid sampling error. A revision to an existing accurate visibility ordering algorithm is described which includes a correction and a method for dramatically increasing its efficiency. Finally, hardware assisted projection and compositing are extended from tetrahedra to arbit...

We present a simple new algorithm that performs fast and memory-efficient cell projection for (exact) rendering of unstructured datasets. The main idea of the "ZSweep" algorithm is very simple; it is based on sweeping the data with a plane parallel to the viewing plane, in order of increasing z, projecting the faces of cells that are incident to vertices as they are encountered by the sweep plane. The efficiency arises from the fact that the algorithm exploits the implicit (approximate) global ordering that the z-ordering of the vertices induces on the cells that are incident on them. The algorithm projects cells by projecting each of their faces, with special care taken to avoid double projection of internal faces and to assure correctness in the projection order. The contribution for each pixel is computed in stages, during the sweep, using a short list of ordered face intersections, which is known to be correct and complete at the instant that each stage of the computation is comple...

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.

A general volume rendering technique is described that efficiently produces images of excellent quality from data defined over irregular grids having a wide variety of formats. Rendering is done in software, eliminating the need for special graphics hardware, as well as any artifacts associated with graphics hardware. Images of volumes with about one million cells can be produced in one to several minutes on a workstation with a 150 MHz processor. A significant advantage of this method for applications such as computational fluid dynamics is that it can process multiple intersecting grids. Such grids present problems for most current volume rendering techniques. Also, the wide range of cell sizes (by a factor of 10,000 or more), which is typical of such applications, does not present difficulties, as it does for many techniques. A spatial hierarchical organization makes it possible to access data from a restricted region efficiently. The tree has greater depth in regions of greater detail, determined by the number of cells in the region. It also makes it possible to render useful "preview" images very quickly (about one second for one-million-cell grids) by displaying each region associated with a tree node as one cell. Previews show enough detail to navigate effectively in very large data sets. The algorithmic techniques include use of a k-d tree, with prefixorder partitioning of triangles, to reduce the number of primitives that must be processed for one rendering, coarse-grain parallelism for a shared-memory MIMD architecture, a new perspective transformation that achieves greater numerical accuracy, and a scanline algorithm with depth sorting and a new clipping technique.

A visibility ordering of a set of objects, from a given viewpoint, is a total order on the objects such that if object a obstructs object b,thenb precedes a in the ordering. Such orderings are extremely useful for rendering volumetric data. We present an algorithm that generates a visibility ordering of the cells of an unstructured mesh, provided that the cells are convex polyhedra and nonintersecting, and that the visibility ordering graph does not contain cycles. The overall mesh may be nonconvex and it may have disconnected components. Our technique employs the sweep paradigm to determine an ordering between pairs of exterior (mesh boundary) cells which can obstruct one another. It then builds on Williams' MPVO algorithm [33] which exploits the ordering implied by adjacencies within the mesh. The partial ordering of the exterior cells found by sweeping is used to augment the DAG created in Phase II of the MPVO algorithm. Our method thus removes the assumption of the MPVO algorithm t...

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.