UC Davis

We review our recent progress on efficient algorithms for generating well-spaced samples of high dimensional data, and for exploring and characterizing these data, the underlying domain, and functions over the domain. To our knowledge, these techniques have not yet been applied to computational topology, but the possible connections are worth considering. In particular, computational topology problems often have difficulty in scaling efficiently, and these sampling techniques have the potential to drastically reduce the size of the data over which these computational topology algorithms must operate. We summarize the definition of these sample distributions; algorithms for generating them in low, moderate, and high dimensions; and applications in mesh generation, rendering, motion planning and simulation.