I-TANGO: Intersections --- Topology, Accuracy and Numerics for Geometric Objects (in Computer Aided Design)

University Of Connecticut, Storrs CT

Investigators

Abstract

DMS-0138098 Thomas J. Peters The investigators will define new representations for intersecting spline surfaces within computer-aided design (CAD) geometric objects. They will also create algorithms to compute error bounds for approximated intersections representing topological boundaries. Many modeling techniques for geometric design depend upon reliable intersection algorithms. Intersection algorithms will be designed to deliver spline-based CAD geometric models that can be robustly used within a variety of engineering calculations. These intersection representations and error bounds will significantly improve robustness between engineering design and computational applications for stress analysis, fluid dynamics and electromagnetics. No single intersection representation or method will be appropriate for all intersection problems, similar to the mature view taken in computational linear algebra relative to matrix inversion. There, a matrix is first analyzed as to whether it is singular, ill-conditioned (as in the case of a Hilbert matrix), positive-definite, etc. For these approximated spline intersections, new guaranteed error bounds will be developed, as well as corresponding new criteria for semantic consistency of the intersection boundaries formed within spline-based geometric models. For example, the significant improvements to approximated spline models from this project will provide clear benefits to science, industry, and defense. The delivery of the Boeing 777 airplane has been hailed in the popular press as the first production of a 'paperless' airplane, meaning that computerized models supplanted the traditional paper drawings of the engineering design room. While an impressive milestone, the next ambitious step is to eliminate many of the physical prototypes used for destructive testing and engineering analyses prior to releasing an airplane. These tests on physical prototypes are expensive. An appealing, cost-effective alternative is to reliably simulate the complex behavior of turbulence, stress and strain on computerized geometric models of these aircraft. Progress towards that goal has been delayed by inaccuracies introduced in the geometric input to these simulations, specifically along intersection boundaries, and improvement of such intersections is the primary focus of this project. This project will ensure relevance to these contemporary aeronautical design problems by the participation of Boeing scientists and engineers.