An O(N) Algorithm for Three-Dimensional N-Body Simulations

We develop an algorithm that computes the gravitational potentials and forces on N point-masses interacting in three-dimensional space. The algorithm, based on analytical techniques developed by Rokhlin and Greengard, runs in order N time. In contrast to other fast N-body methods such as tree codes, which only approximate the interaction potentials and forces, this method is exact ?? computes the potentials and forces to within any prespecified tolerance up to machine precision. We present an implementation of the algorithm for a sequential machine. We numerically verify the algorithm, and compare its speed with that of an O(N2) direct force computation. We also describe a parallel version of the algorithm that runs on the Connection Machine in order 0(logN) time. We compare experimental results with those of the sequential implementation and discuss how to minimize communication overhead on the parallel machine.

Assembly Guidance in Augmented Reality Environments Using a Virtual Interactive Tool

The application of augmented reality (AR) technology for assembly guidance is a novel approach in the traditional manufacturing domain. In this paper, we propose an AR approach for assembly guidance using a virtual interactive tool that is intuitive and easy to use. The virtual interactive tool, termed the Virtual Interaction Panel (VirIP), involves two tasks: the design of the VirIPs and the real-time tracking of an interaction pen using a Restricted Coulomb Energy (RCE) neural network. The VirIP includes virtual buttons, which have meaningful assembly information that can be activated by an interaction pen during the assembly process. A visual assembly tree structure (VATS) is used for information management and assembly instructions retrieval in this AR environment. VATS is a hierarchical tree structure that can be easily maintained via a visual interface. This paper describes a typical scenario for assembly guidance using VirIP and VATS. The main characteristic of the proposed AR system is the intuitive way in which an assembly operator can easily step through a pre-defined assembly plan/sequence without the need of any sensor schemes or markers attached on the assembly components.