We believe that navigation in information spaces is best supported by tapping into our natural spatial and geographic ways of thinking. To this end, we are developing a new computer interface model called Pad. The ongoing Pad project uses a spatial metaphor for computer interface design. It provides an intuitive base for the support of such applications as electronic marketplaces, information services, and on-line collaboration. Pad is an infinite two-dimensional information plane that is shared among users, much as a network file system is shared. Objects are organized geographically; every object occupies a well defined region on the Pad surface. For navigation, Pad uses "portals" - magnifying glasses that can peer into and roam over different parts of this single infinite shared desktop; links to specific items are established and broken continually as the portal's view changes. Portals can recursively look onto other portals. This paradigm enables the sort of peripheral activity generally found in real phy...

This paper describes a general-purpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task to provide a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than those that do not use it. We believe that this technique will become a standard tool in writing geometric software.

A kinetic data structure (KDS) maintains an attribute of interest in a system of geometric objects undergoing continuous motion. In this paper we develop a conceptual framework for kinetic data structures, propose a number of criteria for the quality of such structures, and describe a number of fundamental techniques for their design. We illustrate these general concepts by presenting kinetic data structures for maintaining the convex hull and the closest pair of moving points in the plane; these structures behavewell according to the proposed quality criteria for KDSs.

We define the notion of a well-separated pair decomposition of points in d-dimensional space. We then develop efficient sequential and parallel algorithms for computing such a decomposition. We apply the resulting decomposition to the efficient computation of k-nearest neighbors and n-body potential fields.

For many KDD applications, such as detecting criminal activities in E-commerce, finding the rare instances or the outliers, can be more interesting than finding the common patterns. Existing work in outlier detection regards being an outlier as a binary property. In this paper, we contend that for many scenarios, it is more meaningful to assign to each object a degree of being an outlier. This degree is called the local outlier factor (LOF) of an object. It is local in that the degree depends on how isolated the object is with respect to the surrounding neighborhood. We give a detailed formal analysis showing that LOF enjoys many desirable properties. Using realworld datasets, we demonstrate that LOF can be used to find outliers which appear to be meaningful, but can otherwise not be identified with existing approaches. Finally, a careful performance evaluation of our algorithm confirms we show that our approach of finding local outliers can be practical.

Abstract—Collision detection is of paramount importance for many applications in computer graphics and visualization. Typically, the input to a collision detection algorithm is a large number of geometric objects comprising an environment, together with a set of objects moving within the environment. In addition to determining accurately the contacts that occur between pairs of objects, one needs also to do so at real-time rates. Applications such as haptic force-feedback can require over 1,000 collision queries per second. In this paper, we develop and analyze a method, based on bounding-volume hierarchies, for efficient collision detection for objects moving within highly complex environments. Our choice of bounding volume is to use a “discrete orientation polytope” (“k-dop”), a convex polytope whose facets are determined by halfspaces whose outward normals come from a small fixed set of k orientations. We compare a variety of methods for constructing hierarchies (“BV-trees”) of bounding k-dops. Further, we propose algorithms for maintaining an effective BV-tree of k-dops for moving objects, as they rotate, and for performing fast collision detection using BV-trees of the moving objects and of the environment. Our algorithms have been implemented and tested. We provide experimental evidence showing that our approach yields substantially faster collision detection than previous methods. Index Terms—Collision detection, intersection searching, bounding volume hierarchies, discrete orientation polytopes, bounding boxes, virtual reality, virtual environments. 1

We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyper-strips (resp. hyper-cylinders) so that the maximum width of a hyper-strip (resp., the maximum diameter of a hyper-cylinder) is minimized. Let w be the smallest value so that S can be covered by k hyper-strips (resp. hyper-cylinders), each of width (resp. diameter) at most w : In the plane, the two problems are equivalent. It is NP-Hard to compute k planar strips of width even at most Cw ; for any constant C ? 0 [50]. This paper contains four main results related to projective clustering: (i) For d = 2, we present a randomized algorithm that computes O(k log k) strips of width at most 6w that cover S. Its expected running time is O(nk 2 log 4 n) if k 2 log k n; it also works for larger values of k, but then the expected running time is O(n 2=3 k 8=3 log 4 n). We also propose another algorithm that computes a c...

In manufacturing, it is often necessary to orient parts prior to packing or assembly. We say that a planar part is polygonal if its convex hull is a polygon. We consider the following problem: given a list of n vertices describing a polygonal part whose initial orientation is unknown, find the shortest sequence of mechanical gripper actions that is guaranteed to orient the part up to symmetry in its convex hull. We show that such a sequence exists for any polygonal part by giving an O#n log n# algorithm for finding the sequence. Since the gripper actions do not require feedback, this result implies that any polygonal part can be oriented without sensors.

Query optimization is an integral part of relational database management systems. One important task in query optimization is selectivity estimation, that is, given a query P , we need to estimate the fraction of records in the database that satisfy P . Many commercial database systems maintain histograms to approximate the frequency distribution of values in the attributes of relations. In this paper, we present a technique based upon a multiresolution wavelet decomposition for building histograms on the underlying data distributions, with applications to databases, statistics, and simulation. Histograms built on the cumulative data distributions give very good approximations with limited space usage. We give fast algorithms for constructing histograms and using them in an on-line fashion for selectivity estimation. Our histograms also provide quick approximate answers to OLAP queries when the exact answers are not required. Our method captures the joint distribution of multiple attri...

This paper describes an efficient algorithm for computing the distance between non-convex objects. Objects are modeled as the union of a set of convex components. From this model we construct a hierarchical bounding representation based on spheres. The distance between objects is determined by computing the distance between pairs of convex components using preexisting techniques. The key to efficiency is a simple search routine that uses the bounding representation to ignore most of the possible pairs of components. The efficiency can further be improved by accepting a relative error in the returned result. Several empirical trials are presented to examine the performance of the algorithm. 1. Introduction Computing the distance between objects is a common problem in robotics. Using a mathematical model of two objects, we find a point on each object such that the distance between the points is minimized. If one object is a robot and the other object is the union of all the obstacles i...