This thesis describes a method of constructing mathematical models r(u, v) of sweep type sculptured surfaces by using coordinate transformations and blending.
The surface modeling scheme is based on the logic of describing sweep surfaces on conventional engineering drawings. A smooth sculptured surface that is best described as a trajectory of cross-section curves swept along profile curves is called a sweep surface. A weep surface is regarded as a tuple consisting of cross-section curves, profile curves, and a sweeping rule.
The sweeping rules considered are parallel sweeping, rotational sweeping, normal sweeping, and synchronized sweeping. For all the sweeping rules, the model r(u,v) of the sweep surface has the same mathematical structure.
The procedures for constructing sweep surface consists of the following steps:(1) Sweeping of a sectional curve along a guide curve according to a given sweeping rule; (2) correction of the swept section curve; (3) blending of two corrected section curves. For variable number of profile curves and section curves, some of the above procedures may be omitted.
The resulting sweep surface can be converted to composite Bezier surface, which makes it easier to evaluate metrical properties of the surface.
