Display of profiled sweep objects

A class of free-form solids called profiled sweep objects is defined by four parametric curves: a 2D contour (cross-section), a 3D trajectory (spine), and two profile curves, which control the scaling of the contour as it moves along the trajectory. Subclasses of this are profiled prisms, which have a linear trajectory, and profiled generalized cylinders, which have an arbitrary 3D trajectory. First an exact definition of profiled sweep object, is presented and their relation with common sweep objects is described. Then a method is given for the construction of planar approximations of these objects that can be used for fast display generation. Finally, ray-tracing algorithms are given that directly use the exact definition for high-quality display.