9312932 Storti The goal of this project is to create a robust conceptual design system in which solids are described by a single potential function (rather than approximated by a multitude of faces, volume elements, or surface patches as in conventional modelers). This formulation of geometric design, called implicit solid modeling (ISM), offers three distinct advantages: (1) A straightforward approach to solid modeling which is intuitive and easy to learn. (2) All of the basic data which defines the shape of a solid is specified and manipulated using exact, rational arithmetic which guarantees that geometric property evaluation tests performed are robust and reliable. (3) Point/solid classification (determining whether a point lies inside, on the surface of, or outside a given solid), the fundamental geometric test traditionally used in solid modeling, reduces to simply evaluating the potential function and comparing its value to a specified threshold level. Moverover, evaluation of the potential function inherently provides (at no additional computational cost) a measure of the distance from the given point to the surface of the solid, which is exactly the information needed for intelligent engineering design. During the course of this research, an effective ISM conceptual design system based on exact computation is created and used to explore ways in which the distance measure provided by the ISM potential function can be used to develop improved engineering design tools. The underlying exact computations are achieved using a computer algebra system, and swept solids (essential for modeling offset surfaces and path planning) are created using tech niques from algebraic geometry including envelope theory and elimination theory. A polygonizer is incorporated to provide capability for rapid visualization on standard graphics hardware and availability of a suitable output format so that the ISM system can serve as a conceptual preprocessor for conventional solid modeling systems and rapid prototyping systems based on stereolithography. While the primary implications of this research involve advances in traditional areas of engineering design such as sculptured surface description, optimal layout, packaging, and motion planning, an additional goal of this project involves broadening the scope of engineering design research through enhanced interaction with investigators in the fields of computer algebra and algebraic geometry. ***
