Extensions of sweep surface constructions

Sweeping is a very important, powerful, and widespread method in geometric modelling. In this paper, we consider only sweep surfaces, generated by sweeping one curve (cross-section) along the other curve (trajectory), and their existing construction methods: the Frenet frame method, the discrete approach, the offset method, and the projection technique. All these methods are extended so that they now include non-homogeneous scaling and twisting of the cross-section, which enable the generation of complex twisted-profiled sweep surfaces.