As the application of computers to the physical world widen, there is an ever increasing need for computational tools to deal with the physical attributes of objects, such as their geometry. The field of Computational Geometry has made impressive strides in the last twenty years in providing an algorithmic foundation for the solution to many geometric problems in computer graphics, computer vision, robotics and manufacturing, and many other application areas. The purpose of this proposal is to develop a set of novel geometric representations and algorithmic techniques that will make computational geometry more useful in modeling physical-world objects and processes. The aim is not to obtain universal, domain-independent solutions --- such as a complete solution to robustness concerns in geometric computing. Instead the focus will be on certain key issues, such as scale- sensitivity, shape variability, and motion, that arise in many of the important uses of geometry in modeling physical objects and systems. Geometric models that properly capture certain key aspects of the uncertainty or variability in models of physical objects and processes will be investigated, and efficient algorithms for manipulating these models effectively will be developed. It is expected that this set of research directions will generate new mathematical and algorithmic problems that will be interesting and worthy of study on their own right, in addition to producing geometric tools that are well-tailored to physical world applications. ***
