Accurate parallel reconstruction of unstructured datasets on rectilinear grids

High performance computing simulations often produce datasets defined over unstructured grids. Those grids allow for the local refinement of the resolution and can accommodate arbitrary boundary geometry. From a visualization standpoint, however, such grids have a high storage cost, require special spatial data structures, and make the computation of high-quality derivatives challenging. Rectilinear grids, in contrast, have a negligible memory footprint and readily support smooth data reconstruction, though with reduced geometric flexibility. The present work is concerned with the creation of an accurate reconstruction of large unstructured datasets on rectilinear grids. We present an efficient method to automatically determine the geometry of a rectilinear grid upon which a low-error data reconstruction can be achieved with a given reconstruction kernel. Using this rectilinear grid, we address the potential ill-posedness of the data fitting problem, as well as the necessary balance between smoothness and accuracy, through a bi-level smoothness regularization. To tackle the computational challenge posed by very large input datasets and high-resolution reconstructions, we propose a block-based approach that allows us to obtain a seamless global approximation solution from a set of independently computed sparse least-squares problems. Results are presented for several 3D datasets that demonstrate the quality of the visualization results that our reconstruction enables, at a greatly reduced computational and memory cost.