Interactive rendering of dynamic geometry

Fluid simulations typically produce complex threedimensional iso-surfaces whose geometry and topology change over time. The standard way of representing such "dynamic geometry" is by a set of iso-surfaces that are extracted individually at certain time steps. An alternative strategy is to represent the whole sequence as a four-dimensional tetrahedral mesh. The iso-surface at a specific time step can then be computed by intersecting the tetrahedral mesh with a threedimensional hyperplane. This not only allows to animate the surface continuously over time without having to worry about the topological changes, but also enables simplification algorithms to exploit temporal coherence. We show how to interactively render such four-dimensional tetrahedral meshes by improving previous GPU-accelerated techniques and building an out-of-core multi-resolution structure based on quadric-error simplification. As a second application we apply our framework to time-varying surfaces that result from morphing one triangle mesh into another.