This project considers both theoretical and applied aspects of computational geometry. The geometric structure of, and efficient algorithms for, problems in a variety of areas are being investigated. Some particular areas of interest are: applications of Davenport- Schinzel sequences, generalized Voronoi diagrams, probabilistic techniques, and triangulations. This work has implications for robot motion planning, graphics, solid modeling and computer vision. A major emphasis is on the cross-fertilization between the basic research in computational geometry and the various applications areas.