This investigation will have three major impacts: (1) Add new algorithms and methodologies to the repertoire of computational geometry techniques, including new approximation methods and new algorithms that are simpler and easier to implement than existing ones; (2) Formulate precise algorithmic versions of a large body of geometric problems from allied fields, in such a way that the methods of computational geometry can be applied successfully and so that the community of largely theoretical computational geometers can be properly exposed to the more practical applications of the field (allied fields include cartography, computer vision, computer-aided design, graphics, manufacturing, etc); and (3) Disseminate methodologies of computational geometry to applied researchers who work in allied fields but who have been largely unaware of progress in computational geometry, particularly since it has been construed as a primarily theoretical instrument. This third impact will be made through discussions of research directions with contacts in industrial research labs and through publishing papers for conferences and in journals whose readership includes a breadth of engineering disciplines.
