Accurate solid modeling using polyhedral approximations

Although curved-surface solid modeling systems achieve a higher level of accuracy than faceted systems, they also introduce a host of topological, geometric, and numerical complications. A method for calculating accurate boundary representations of solid models is introduced that reduces the impact of these complications. The method uses a pair of bounding polyhedral approximations to enclose the boundary of each object. A structural analysis automatically determines where to make adaptive refinements to the polyhedrons to assure the topological validity of the results. Potential singularities are localized. The implementation is an experimental extension to the Geometric Design Processor (GDP) solid modeling system.<>