Riemannian manifolds with a metric induced by an embedding space may be represented by a point set instead of cell complex or other fixed-topology data structures in the embedding space. For modelling and simulation applications we are particularly interested in manifolds embedded in low-dimensional Euclidean spaces, but this project is not necessarily limited to this. The point sets may be generated for an already well-characterised manifold (e.g. via an atlas) or they may represent results from measuring a manifold (e.g. a dense 3D point set or an algebraic complex).
Point-based representations have been used for rendering and meshless simulations with some success; in particular for manifolds with complex topology or geometry. This project will investigate generating suitable point set representations for well-characterised manifolds, differential operators, modelling operations and simulations on these point sets.
Simulation,http://www.langbein.org/research/points/simulation by Frank C Langbein [15/October/2008, 17:49].
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