Design is the art of creating something new and predicting how it will perform before it is ever build. One of the major breakthroughs in the last 25 years is the ability to describe a design as a virtual artifact in a computer, and simulate its physical characteristics accurately to enable designers to make better decisions. The core technology that underlies these mechanical Computer Aided Design and Manufacturing (CAD/CAM) systems is solid modeling, whose theoretical underpinnings are grounded in mathematics.
This talk will cover some of these mathematical concepts, including point set topology, regularized set operations, Constructive Solid Geometry (CSG), representation schemes, algorithms and geometry.
We will cover the impact of solid modeling in industry, and discuss some of the remaining open issues such as the ambiguity between the topological representation and the computed geometric boundary.