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
In the course of the Visual Computing research seminar Dr. Evgeny Gladilin from the Leibniz Institute of Plant Genetics and Crop Plant Research (IPK) Gatersleben will give a talk with subsequent discussion about the topic Aufgaben der Bildanalyse in quantitativer Pflanzenforschung.
We would like to invite everyone interested to join us. The research seminar will take place in on Friday 21.04.2017, 13:00 c.t. in G29-R335.