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We present an algorithm for adaptively extracting and rendering isosurfaces from compressed time-varying volume data sets. Tetrahedral meshes defined by longest edge bisection are used to create a multiresolution representation of the volume in the spatial domain that is adapted overtime to approximate the time-varying volume. The reextraction of the isosurface at each time step is accelerated with the vertex programming capabilities of modern graphics hardware. A data layout scheme which follows the access pattern indicated by mesh refinement is used to access the volume in a spatially and temporally coherent manner. This data layout scheme allows our algorithm to be used for out-of-core visualization.