Building on the smooth setting, we present a set of natural properties for Laplace operators on discrete surface meshes. We point out an important theoretical limitation: discrete Laplacians cannot satisfy all of these properties on general unstructured triangle meshes; retroactively, this explains the diversity of existing discrete Laplacians found in the literature. Furthermore, building on insights that date back to James Clerk Maxwell, we provide a characterization of those triangle meshes that do allow for "perfect" Laplacians. Finally, we present a principled construction that extends discrete Laplacians from triangle meshes to arbitrary polygonal surface meshes.
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Research Seminar Announcement
We would like to invite everyone interested to join us. The research seminar will take place on Friday 22.06.2018, 13:15 in G29-R335.