The focus of computational geometry is designing algorithms for solving geometric problems. These arise in a number of application contexts, including manufacturing, graph drawing, robotics, and graphics. The project's concentrations touch on all these application areas. Research on shortest paths and geodesics on polytopes is relevant to robotics and to texture mapping in graphics. Folding and unfolding of research is connected to a variety of manufacturing concerns. And visibility algorithms see use in graphics and graph drawing. A collection of fundamental open problems in these areas will be pursued, both theoretically and through experimentation with code. Progress on geodesics, on folding, on floodlight illumination, and on visibility graphs can be expected. Female undergraduate students will be engaged in all aspects of the research, and all software developed will be freely distributed on the Internet.
