A geometric modeling system is a basic building block in any computer-aided design system for discrete products based on mechanical engineering. A number of such systems have been developed. However, it is not yet possible to use them effectively for establishing tolerances on dimensions of parts. This problem will be addressed in three phases. In the first phase, tolerances will be defined in mathematical terms. In the second phase, algorithms which verify dimensional correctness will be developed. In the third phase, experiments will be conducted to demonstrate that the tolerances can indeed be verified, and that verification for assembly can be performed using machine vision inspection.
