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 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...

This document is available in .ps format at our web site (http://miles.cnuce.cnr.it/cg/bibliography.html). This workwas partially founded by the Progetto Coordinato "Modelli multirisoluzione per la visualizzazione di campi scalari multidimensionali" of the Italian National Research Council (CNR). We wish to thank those who have made available on the public domain the datasets used in the evaluation of the proposed techniques. References

In this paper we introduce a scheme for static analysis that allows us to partition large geometric datasets at multiple levels of granularity to achieve both load balancing in parallel computations and minimal access to secondary memory in out-of-core computations. The idea is illustrated and fully exploited for the case of isosurface extraction, but extendible to a class of algorithms based on a small set of algorithm parameters and for which an appropriate static analysis can be performed. 1

For a polyhedral terrain \Sigma, the contour at z-coordinate h, denoted Ch , is defined to be the intersection of the plane z = h with \Sigma. In this paper, we study the contour-line extraction problem, where we want to preprocess \Sigma into a data structure so that given a query z-coordinate h, we can report Ch quickly. This is a central problem that arises in geographic information systems (GIS), where terrains are often stored as Triangular Irregular Networks (TINs). We present an I/O-optimal algorithm for this problem which stores a terrain \Sigma with N vertices using O(N=B) blocks, where B is the size of a disk block, so that for any query h, the contour Ch can be computed using O(log B N + jCh j=B) I/O operations, where jCh j denotes the size of Ch .

The search for intersected cells in isocontouring can be accelerated using suitable range query data structures, such as the interval tree or segment tree. The storage overhead of such search structures can be significantly reduced by searching over a subset of the cells Ë, called a seed set, which contains at least one cell per connected component of every isocontour. We present three algorithms for generating seed sets and compare their time complexity and performance in terms of the number of seed cells generated. The first two algorithms are applicable to both regular and irregular grids of arbitrary dimension, while the third is a specialization for regular grids. The first algorithm produces a nearly optimal seed set, minimizing the storage overhead for the search structure. While the second and third algorithms may produce a larger seed set, they are extremely fast, have the advantage of being suitable for extremely large datasets that cannot be kept in main memory (out-of-core computation), and are amenable to parallelization. In each case the resulting seed sets are orders of magnitude smaller than the total number of cells, while the computational complexity remains optimal. We compare the results of the two new algorithms with previous results and recent new work. 2

This thesis examines two largely unrelated problems in applied algorithmics, motivated by the search for efficient geometric algorithms. In the first part of the thesis, we consider the problem of finding efficient parallel algorithms for heterogeneous parallel computers, i.e., parallel computers in which different processors have different computational potential. To this end, we define a formal computational model for heterogeneous systems and develop algorithms for commonly used communication operations. The result is that many existing parallel algorithms which use these communication operations can be adapted to our model with little or no modifications. In the second part of the thesis we consider the problem of geometric models which allow for varying levels of detail. To this end, we extend the progressive mesh representation introduced by Hoppe. The main technical contribution of this part is an efficient scheme for refining only selected regions of a progressive mesh. Using ...

For large scientific visualization applications, it is often impossible to hold the entire datasets in main memory, even on supercomputers. Previously, we proposed the I/O-filter technique, which is the first I/O-optimal method for the problem of isosurface extraction in scientific visualization. I/O-filter works by indexing and re-organizing the datasets in disk, so that isosurface can be extracted with a very small amount of disk I/O's. The main advantage of this approach is that datasets much larger than main memory can be visualized very efficiently, possibly even on low-end machines. The original I/O-filter technique uses the I/O-optimal interval tree of Arge and Vitter as the indexing data structure, together with the isosurface engine from Vtk (one of the currently best visualization packages). The main shortcoming of this approach was the overheads of the disk scratch space and the preprocessing time necessary to build the data structure, and of the disk space needed to hold th...

A wide variety of techniques have been developed for the visualization of scalar, vector and tensor field data. They range from volume visualization, to isocontouring, from vector field streamlines or scalar, vector and tensor topology, to function on surfaces . This multiplicity of approaches responds to the requirements emerging from an even wider range of application areas such as computational fluid dynamics, chemical transport, fracture mechanics, new material development, electromagnetic scattering/absorption, neuro-surgery, orthopedics, drug design. In this chapter I present a brief overview of the visualization paradigms currently used in several of the above application areas. A major objective is to provide a roadmap that encompasses the majority of the currently available methods to allow each potential user/developer to select the techniques suitable for his purpose. 1.1 Introduction Typically, informative visualizations are based on the combined use of multiple techniques...

Time-varying scalar fields are produced by measurements or simulation of physical processes over time, and must be interpreted with the assistance of computational tools. A useful tool in interpreting the data is graphical visualization, often through level sets, or isocontours of a continuous function derived from the data. In this paper we survey isocontour based visualization techniques for time-varying scalar fields. We focus on techniques that aid selection of meaningful isocontours, and algorithms to extract chosen isocontours.