A Hands-On Introduction to Discrete Differential Operators on Polygon Meshes

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dc.contributor.authorWagner, Sven Dominik
dc.contributor.authorBunge, Astrid
dc.contributor.authorBotsch, Mario
dc.date.accessioned2026-04-22T08:18:17Z
dc.date.available2026-04-22T08:18:17Z
dc.date.issued2026
dc.description.abstractMany applications in geometry processing involve the solution of partial differential equations on discrete surface meshes, with the Laplacian undoubtedly being the most ubiquitous operator in this context. Having discrete operators for gradient, divergence, and Laplacian at hand allows to solve many interesting geometry processing problems. Unfortunately, many approaches or implementations require the mesh to be a well-behaved triangle mesh with good-quality elements, and severely degrade or completely fail if these conditions are not met. In this tutorial, we will present how to discretize (and implement) gradient, divergence, and Laplacian operators in a simple, flexible, and robust manner. The presented discrete differential operators can be applied to triangle meshes, quad meshes, or general polygon meshes, they work robustly even for low-quality or degenerate elements, and as such, they allow to generalize many geometry processing algorithms to a much wider range of mesh inputs. We also provide interactive HTML-based course notes at https://graphics.rocks/eg26DDG.
dc.description.sectionheadersTutorials
dc.description.seriesinformationEurographics 2026 - Tutorials
dc.identifier.doi10.2312/egt.20261004
dc.identifier.isbn978-3-03868-267-7
dc.identifier.issn1017-4656
dc.identifier.pages25 pages
dc.identifier.urihttps://doi.org/10.2312/egt.20261004
dc.identifier.urihttps://diglib.eg.org/handle/10.2312/egt20261004
dc.publisherThe Eurographics Association
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectMathematics of computing → Discretization
dc.subjectComputing methodologies → Mesh geometry models
dc.titleA Hands-On Introduction to Discrete Differential Operators on Polygon Meshes
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