Symbolic Mathematical Laboratory

A large computer program has been developed to aid applied mathematicians in the solution of problems in non-numerical analysis which involve tedious manipulations of mathematical expressions. The mathematician uses typed commands and a light pen to direct the computer in the application of mathematical transformations; the intermediate results are displayed in standard text-book format so that the system user can decide the next step in the problem solution. Three problems selected from the literature have been solved to illustrate the use of the system. A detailed analysis of the problems of input, transformation, and display of mathematical expressions is also presented.

Feature Point Detection and Curve Approximation for Early Processing of Freehand Sketches

Freehand sketching is both a natural and crucial part of design, yet is unsupported by current design automation software. We are working to combine the flexibility and ease of use of paper and pencil with the processing power of a computer to produce a design environment that feels as natural as paper, yet is considerably smarter. One of the most basic steps in accomplishing this is converting the original digitized pen strokes in the sketch into the intended geometric objects using feature point detection and approximation. We demonstrate how multiple sources of information can be combined for feature detection in strokes and apply this technique using two approaches to signal processing, one using simple average based thresholding and a second using scale space.

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.