Spectral Coarsening with Hodge Laplacians

Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The utility of a coarsening algorithm depends on both, the choice of representation as well as the specific processing algorithm or operator. e.g. simulation using the Finite Element Method, calculating Betti numbers, etc. We propose a novel method that can coarsen triangle meshes, tetrahedral meshes and simplicial complexes. Our method allows controllable preservation of salient features from the high-resolution geometry and can therefore be customized to different applications.