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The primary purpose of this 3-year DOE-funded research effort, now completed, was to develop consistent, theoretical foundations of computations on discrete geometry, to realize the promise of predictive and scalable management of large geometric datasets as handled routinely in applied sciences. Geometry (be it simple 3D shapes or higher dimensional manifolds) is indeed a central and challenging issue from the modeling and computational perspective in several sciences such as mechanics, biology, molecular dynamics, geophysics, as well as engineering. From digital maps of our world, virtual car crash simulation, predictive animation of carbon nano-tubes, to trajectory design of space missions, knowing how to process and animate digital geometry is key in many cross-disciplinary research areas

Final Report for the grant "Applied Geometry" (DOE DE-FG02-04ER25657)