BOOLE: A Boundary Evaluation System for Boolean Combinations of Sculptured Solids

In this paper we describe a system, BOOLE, that generates the boundary representations (B-reps) of solids given as a CSG expression in the form of trimmed B ezier patches. The systemmakes use of techniques from computational geometry, numerical linear algebra and symbolic computation to generate the B-reps. Given two solids, the system rst computes the intersection curve between the two solids using our surface intersection algorithm. Using the topological information of each solid, it computes various components within each solid generated by the intersection curve and their connectivity. The component classi cation step is performed by ray-shooting. Depending on the Boolean operation performed, appropriate components are put together to obtain the nal solid. We also present techniques to parallelize this system on shared memory multiprocessor machines. The system has been successfully used to generate B-reps for a number of large industrial models including parts of a notional submarine storage and handling room (courtesy Electric Boat Inc.) and Bradley ghting vehicle (courtesy Army Research Labs). Each of these models is composed of over 8000 Boolean operations and is represented using over 50,000 trimmed B ezier patches. Our exact representation of the intersection curve and use of stable numerical algorithms facilitate an accurate boundary evaluation at every Boolean set operation and generation of topologically consistent solids.