The Three-Dimensional Solid Design Space is an advanced design workstation for three-dimensional geometric modeling applications, composed of a host computer, a three-dimensional stereoscopic display system, and a state-of-the-art input device capable of sensing the position and orientation of each of the user's fingers. The Design Space smoothly varying complex surface shapes such as car bodies, airplane fuselages, and telephone casings. To support this type of design, a surface representation scheme must be found that is capable of describing either first or second order smooth shapes of arbitrary topology; the surface scheme should be efficiently computable and support successive refinement design. Unfortunately, existing surface representation schemes fail to meet these standards. This research deals with the development of new schemes that possess the characteristics listed above. Such surface schemes will not only enjoy use in interactive three- dimensional design, they will also find important applications in a variety of data fitting problems.
