Research in three broad areas of computational geometry will be conducted. These areas cover the spectrum from practical considerations which arise when implementing and debugging geometric algorithms to theoretical questions arising in algorithm design and lower bound proofs. They include design and analysis of algorithms, concentrating mostly on problems involving nonlinear surfaces in dimensions higher than two, in particular, hidden surface removal, triangulations of real-algebraic varieties, and multidimensional searching, building an environment for implementing geometric algorithms and tools which can ultimately be used by researchers to produce and share geometric software, and design of robust geometric algorithms which entails tackling problems arising from finite precision arithmetic as well as the degeneracy of common real world geometric data.
