Subdivision Surface Based One-Piece Representation

University Of Kentucky Research Foundation, Lexington KY

Investigators

Abstract

DMS-0310645 Fuhua (Frank) Cheng This is a CARGO incubation award made under solicitation http://www.nsf.gov/pubs/2002/nsf02155/nsf02155.htm. This grant provides funding for the development of necessary mathematical theories and geometric algorithms to support subdivision surface based one-piece representation, i.e., representing the final object in a design process with only one subdivision surface, no matter how complicated the object's topology or shape. Hence, the number of parts in the final representation is always the minimum: one. The research requires studies in three areas: representation refinement, representation conversion and representation joining. The aim for representation refinement is to develop new vertex generation schemes and topological structures that allow local refinement of a subdivision surface's control mesh while preserving the crack-free property of the refining process. The aim for representation conversion is to develop conversion algorithms for subdivision surfaces of different type or subdivision surfaces of the same type but whose control meshes are of different topology. The aim for representation joining is to develop direct and indirect joining techniques that can be iteratively applied to join different component surfaces of an object into a single surface. If successful, the results of this research will significantly shorten the construction process of a free-from surface because one-piece representation makes Boolean operations more efficient and, consequently, increase the productivity of a design engineer. Actually, in addition to their roles in one-piece representation, the results in the first area will also significantly improve the current art of subdivision surface theory. They would not only include current refinement techniques as special cases, but also provide more powerful mesh refining rules which allow both local and adaptive refinement of subdivision surfaces. The results in the second area will also make it possible for a CAD/CAM system to include subdivision surfaces as a new and yet more general free-form surface modeling tool because B-splines and NURBS are special cases of subdivision surfaces.