Ability to create, convert between, and to maintain consistency of distinct representations of mechanical parts is a major technological barrier that undermines the usefulness and reliability of commercial geometric modeling systems. Current research efforts focus on eliminating ambiguity in communicating engineering specifications, dealing with errors and uncertainty in geometric modeling and CAD systems, formal modeling of parametric families of mechanical parts, and investigating novel methods and computational techniques in support of design and manufacturing.

Today mechanical forms, functions, and fabrication processes cannot be described combinatorially, in terms of discrete, simple, and interacting primitives; this apparent lack of combinatorial structure is a major roadblock for competitive design and manufacturing of mechanical systems. In collaboration with industry, the present research deals with theoretical, practical, and computational aspects of mechanical design and seeks to establish a formal basis for making mechanical design and manufacturing of parts more systematic and competitive, and for smooth integration of mechanical form modeling with other engineering activities.

Geometric models contain only part of the information needed to capture the desired physical behavior of an artifact, and the processes used to manufacture it. Historically, physical and geometric modeling has followed independent paths, resulting in incompatible models and representations, difficult integration problems, as well as expensive representation conversions (such as meshing). Current research focuses on devising improved methods for describing physical artifacts using geometric and topological languages, and for simulating physical models using new meshfree technology. The broader efforts are focused on development of new engineering languages and computer algorithms for systematic specification, modeling, simulation, analysis, and optimization of physical objects and systems.