Modelling volumes bounded by b-spline surfaces

A dichotomy between modelling systems using "sculptured surface" techniques, and those using "constructive solid geometry" has existed since these two distinct approaches emerged. To gain the shape representational power of sculptured surfaces, such as B-splines, it has been necessary to give up the facility to combine objects via set operations. Conversely, systems that build complex assemblies from combinations of simpler volume elements have been restricted to a small class of primitives. By using a more complex but uniform boundary representation, this work makes it possible to unify these two approaches to design with a single method. The "primitives" are solids bounded by B-spline surfaces. Furthermore, systems providing set operation require that the objects being combined have closed boundaries. The B-spline boundaries of this method need not be closed, but must only satisfy a weak completion criterion.