Unification of methods for ray tracing a wide class of generalized cylinders with straight line trajectories.

Generalized cylinders of almost most general type but with straight line trajectories are discussed for modeling objects of various kinds. For this kind of generalized cylinders the sweeping cross-section is allowed to change shape, size, and orientation in an arbitrary way as a function of the parameters describing the location of the sweeping cross-section along the trajectory of the generalized cylinder. The sweeping cross-section may not even intersect the trajectory of the generalized cylinder for all or fraction of its range. The only restriction is that the parametric function describing the variation of the sweeping cross-section, as it is swept along the trajectory, should be invertible. This parametric function is a function of the location of the sweeping cross-section along the trajectory as well as the function of the location of the point being transformed in the plane of the initial sweeping cross-section. The objects generated by translational sweep, rotational sweep, pyramids, and cones are all special cases of this kind of generalized cylinders. Our method provides for the unification of these special cases and much more. A complete methodology for calculating and rendering ray traced images of such objects is presented.