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 present the "Near Optimal IsoSurface Extraction" (NOISE) algorithm for rapidly extracting isosurfaces from structured and unstructured grids. Using the span space, a new representation of the underlying domain, we develop an isosurface extraction algorithm with a worst case complexity of O( p n + k) for the search phase, where n is the size of the data set and k is the number of cells intersected by the isosurface. The memory requirement is kept at O(n) while the preprocessing step is O(n log n). We utilize the span space representation as a tool for comparing isosurface extraction methods on structured and unstructured grids. We also present a fast triangulation scheme for generating and displaying unstructured tetrahedral grids. Keywords---Isosurface extraction, unstructured grids, span space, kd-trees I. Introduction Isosurface extraction is a powerful tool for investigating scalar fields within volumetric data sets. The position of an isosurface, as well as its relation to ...

This paper describes a new method for contouring a signed grid whose edges are tagged by Hermite data (exact intersection points and normals). This method avoids the need to explicitly identify and process "features" as required in previous Hermite contouring methods. We extend this contouring method to the case of multi-signed functions and demonstrate how to model textured contours using multi-signed functions. Using a new, numerically stable representation for quadratic error functions, we develop an octree-based method for simplifying these contours and their textured regions. We next extend our contouring method to these simplified octrees. This new method imposes no constraints on the octree (such as being a restricted octree) and requires no "crack patching". We conclude with a simple test for preserving the topology of both the contour and its textured regions during simplification.

We present an isocontouringalgorithm which is near-optimal for real-time interaction and modification of isovalues in large datasets. A preprocessing step selects a subset S of the cells which are considered as seed cells. Given a particular isovalue, all cells in S which intersect the given isocontour are extracted using a high-performance range search. Each connected component is swept out using a fast isocontour propagation algorithm. The computational complexity for the repeated action of seed point selection and isocontour propagation is O(logn 0 + k), where n 0 is the size of S and k is the size of the output. In the worst case, n 0 = O(n), where n is the number of cells, while in practical cases, n 0 is smaller than n by one to two orders of magnitude. The general case of seed set construction for a convex complex of cells is described, in addition to a specialized algorithm suitable for meshes of regular topology, including rectilinear and curvilinear meshes. Keyword...

The Marching Cubes (MC) algorithm is a commonly used method for generating isosurfaces. The MC algorithm also generates an excessively large number of triangles to represent an isosurface. Generating many triangles increases the rendering time which is directly proportional to the number of triangles. This paper presents a decimation method to reduce the number of triangles generated by the MC algorithm. Decimation is carried out within the framework of the MC algorithm before creating a large number of triangles. Four major steps comprise the reported implementation of the algorithm: a) surface tracking, b) merging, c) crack patching, and d) triangulation. Surface tracking is an enhanced implementation of the MC algorithm. Starting from a seed point, the surface tracker visits only those cells likely to compose part of the desired isosurface. This results in up to approximately 80% computational saving The cells making up the extracted surface are stored in an octree that is further p...

The interval tree is an optimally efficient search structure proposed by Edelsbrunner [5] to retrieve intervals of the real line that contain a given query value. We propose the application of such a data structure to the fast location of cells intersected by an isosurface in a volume dataset. The resulting search method can be applied to both structured and unstructured volume datasets, and it can be applied incrementally to exploit coherence between isosurfaces. We also address issues about storage requirements, and operations other than the location of cells, whose impact is relevant in the whole isosurface extraction task. In the case of unstructured grids, the overhead due to the search structure is compatible with the storage cost of the dataset, and local coherence in the computation of isosurface patches is exploited through a hash table. In the case of a structured dataset, a new conceptual organization is adopted, called the chess-board approach, wich exploits the regular str...

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.

A popular technique for rendition of isosurfaces in sampled data is to consider cells with sample points as corners and approximate the isosurface in each cell by one or more polygons whose vertices are obtained by interpolation of the sample data. That is, each polygon vertex is a point on a cell edge, between two adjacent sample points, where the function is estimated to equal the desired threshold value. The two sample points have values on opposite sides of the threshold, and the interpolated point is called an intersection point. When one cell face has an intersection point ineach of its four edges, then the correct connection among intersection points becomes ambiguous. An incorrect connection can lead to erroneous topology in the rendered surface, and possible discontinuities. We show that disambiguation methods, to be at all accurate, need to consider sample values in the neighborhood outside the cell. This paper studies the problems of disambiguation, reports on some solutions, and presents some statistics on the occurrence of such ambiguities. A natural way to incorporate neighborhood information is through the use of calculated gradients at cell corners. They provide insight into the behavior of a function in well-understood ways. We introduce two gradient-consistency heuristics that use calculated gradients at the corners of ambiguous faces, as well as the function values at those corners, to disambiguate at a reasonable computational cost. These methods give the correct topology on several examples that caused problems for other methods we examined.

We present two beneficial rendering extensions to the Projected Tetrahedra (PT) algorithm by Shirley and Tuchman. These extensions are compatible with any cell sorting technique, for example the BSP-XMPVO sorting algorithm for unstructured meshes.

Recent advances in the technology of 3D sensors and in the performance of numerical simulations result in the generation of volume data at ever growing size. In order to allow real-time exploration of even the highest resolution data sets, adaptive techniques benefiting from the hierarchical nature of multi-resolution representations have gained special attention. In this paper we propose an adaptive approach to the fast reconstruction of iso-surfaces from regular volume data at arbitrary levels of detail. The algorithm has been designed to enable real-time navigation through complex structures while providing user-adjustable resolution levels. Since adaptive on-the-fly reconstruction and rendering is performed from a hierarchical octree representation of the volume data, the method does not depend on pre-processing with respect to a specific iso-value thus allowing the user to interactively browse through the pencil of iso-surfaces. Special attention is paid to the fixing of cracks in...