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We present a collection of new techniques for designing and analyzing eecient external-memory algorithms for graph problems and illustrate how these techniques can be applied to a wide variety of speciic problems. Our results include: Proximate-neighboring. We present a simple method for deriving external-memory lower bounds via reductions from a problem we(More)
In this paper we give I/O-optimal techniques for the extraction of isosurfaces from volumetric data, by a novel application of the UO-optimal interval tree of Arge aud Vitter. The main idea is to prepm-cess the dataset once anal for all to build au efficient search strut-ture in disk, aud then each time we want to extract au isosurface, we perform au(More)
In this paper, we present a novel out-of-core technique for the interactive computation of isosurfaces from volume data. Our algorithm minimizes the main memory and disk space requirements on the visualization workstation, while speeding up isosurface extraction queries. Our overall approach is a two-level indexing scheme. First, by our meta-cell technique,(More)
Contour trees are used when high-dimensional data are preprocessed for efficient extraction of isocontours for the purpose of visualization. So far, efficient algorithms for contour trees are based on processing the data in sorted order. We present a new algorithm that avoids sorting of the whole dataset, but sorts only a subset of so-called(More)
We consider the two-point query version of the fundamental geometric shortest path problem: Given a set h of polygonal obstacles iu the plane, having a total of n vertices, build a data structure such that for any two query points s and t we can efficiently determine the length, d(s,t), of an Euclidean shortest obstacle-avoiding path, *(s,t), from s to t.(More)
We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map M with n vertices, and apply it to the development of a uniied dynamic data structure that supports point-location, ray-shooting, and shortest-path queries in M. The space requirement is O(n logn). Point-location queries take time O(log n).(More)
We propose to design new algorithms for motion planning problems using the well-known Domain Subdivision paradigm, coupled with "soft" predicates. Unlike the traditional exact predicates in computational geometry, our primitives are only exact in the limit. We introduce the notion of resolution-exact algorithms in motion planning: such an algorithm has an(More)
We present a fully dynamic data structure for point location in a monotone sub­ division, based on the trapezoid method. The operations supported are insertion and deletion of vertices and edges, and horizontal translation of vertices. Let n be the current number of vertices of the subdivision. Point location queries take O(log n) time, while updates take(More)
This course will focus on describing techniques for handling datasets larger than main memory in scientific visualization and computer graphics. Recently, several external memory techniques have been developed for a wide variety of graphics and visualization problems, including surface simplification, volume rendering , isosurface generation, ray tracing,(More)