The focus of computational geometry is designing for solving geometric problems. These arise in a number of contexts, such as graphics, robotics, medical imaging, and manufacturing. The project's concentrations touch on all these application areas. A number of visibility questions are being examined, including covering regions with floodlights, and the structure of visibility graphs. Several of the problems being explored involve three dimensions: reconstruction from parallel slices (and its application to graphics morphing), computing diameters and centerpoints of sets (with applications to pattern recognition), and motion planning configuration spaces (application to robotics). Fundamental questions in the theory of arrangements are being addressed. Several problems arising from the manufacturing community are being tackled, including that of scheduling a punching tool to create a hole in a sheet of metal of a prescribed shape. Female undergraduate students are engaged in all aspects of the research, and several useful software packages are being produced and distributed.
