We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal models. It pre-computes a hierarchical representation of models using tight-fitting oriented bounding box trees (OBBTrees). At runtime, the algorithm traverses two such trees and tests for overlaps between oriented bounding boxes based on a separating axis theorem, which takes less than 200 operations in practice. It has been implemented and we compare its performance with other hierarchical data structures. In particular, it can robustly and accurately detect all the contacts between large complex geometries composed of hundreds of thousands of polygons at interactive rates.

Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that overlap a given search region). More

This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development. The paper puts particular emphasis on the unified exposition of its mathematical and algorithmic properties. Finally, the paper provides the first comprehensive bibliography on Voronoi diagrams and related structures.

The Hausdorff distance measures the extent to which each point of a `model' set lies near some point of an `image' set and vice versa. Thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. In this paper we provide efficient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model. We focus primarily on the case in which the model is only allowed to translate with respect to the image. Then we consider how to extend the techniques to rigid motion (translation and rotation). The Hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived. The method is quite tolerant of small position errors as occur with edge detectors and other feature extraction methods. Moreover, we show how the method extends naturally to the problem of comparing a portion of a model against an i...

The problem of indexing multidimensional objects is considered. First, a classification of existing methods is given along with a discussion of the major issues involved in multidimensional data indexing. Second, a variation to Guttman’s R-trees (R +-trees) that avoids overlapping rectangles in intermediate nodes of the tree is introduced. Algorithms for searching, updating, initial packing and reorganization of the structure are discussed in detail. Finally, we provide analytical results indicating that R +-trees achieve up to 50 % savings in disk accesses compared to an R-tree when searching files of thousands of rectangles. 1

We present an exact and interactive collision detection system, I-COLLIDE, for large-scale environments. Such environments are characterized by the number of objects undergoing rigid motion and the complexity of the mod-els. The algorithm does not assume the objects ’ motions can be expressed as a closed form function of time. The collision detection system is general and can be easily in-terfaced with a variety of applications. The algorithm uses a two-level approach based on pruning multiple-object pairs using bounding boxes and performing exact collision detection between selected pairs of polyhedral models. We demonstrate the performance of the system in walkthrough and simulation environments consisting of a large number of moving objects. In particular, the system takes less than l/20 of a second to determine all the collisions and contacts in an environment consisting of more than a 1000 moving polytopes, each consisting of more than 50 faces on an HP-9000/750. 1

Abstract. A method based on graph theory is investigated for creating global parametrizations for surface triangulations for the purpose of smooth surface fitting. The parametrizations, which are planar triangulations, are the solutions of linear systems based on convex combinations. A particular parametrization, called shape-preserving, is found to lead to visually smooth surface approximations. A standard approach to fitting a smooth parametric curve c(t) through a given sequence of points xi = (xi,yi,zi) ∈ IR 3, i = 1,...,N is to first make a parametrization, a corresponding increasing sequence of parameter values ti. By finding smooth functions x,y,z: [t1,tN] → IR for which x(ti) = xi, y(ti) = yi, z(ti) = zi, an interpolatory curve

The problem of indexing multidimensional objects is considered. First, a classification of existing methods is given along with a discussion of the major issues involved in multidimensional data indexing. Second, a variation to Guttman's R-trees (R -trees) that avoids overlapping rectangles in intermediate nodes of the tree is introduced. Algorithms for searching, updating, initial packing and reorganization of the structure are discussed in detail. Finally, we provide analytical results indicating that R -trees achieve up to 50% savings in disk accesses compared to an R-tree when searching files of thousands of rectangles. 1 Also with University of Maryland Systems Research Center. 2 Also with University of Maryland Institute for Advanced Computer Studies (UMIACS). This research was sponsored partialy by the National Science Foundation under Grant CDR-85-00108. 1. Introduction It has been recognized in the past that existing Database Management Systems (DBMSs) do not ...

Abstract. It is demonstrated that the linear programming problem in d variables and n constraints can be solved in O(n) time when d is fixed. This bound follows from a multidimensional search technique which is applicable for quadratic programming as well. There is also developed an algorithm that is polynomial in both n and d provided d is bounded by a certain slowly growing function of n. Categories and Subject Descriptors: F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems-computations on matrices; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems-geometrical problems and computations; sort-ing and searching; G. 1.6 [Mathematics of Computing]: Optimization-linear programming

Lazy learning methods provide useful representations and training algorithms for learning about complex phenomena during autonomous adaptive control of complex systems. This paper surveys ways in which locally weighted learning, a type of lazy learning, has been applied by us to control tasks. We explain various forms that control tasks can take, and how this affects the choice of learning paradigm. The discussion section explores the interesting impact that explicitly remembering all previous experiences has on the problem of learning to control.