Robust Discrete Differential Operators for Wild Geometry

dc.contributor.authorWagner, Sven Dominiken_US
dc.contributor.authorBotsch, Marioen_US
dc.contributor.editorEgger, Bernharden_US
dc.contributor.editorGünther, Tobiasen_US
dc.date.accessioned2025-09-24T10:38:13Z
dc.date.available2025-09-24T10:38:13Z
dc.date.issued2025
dc.description.abstractMany geometry processing algorithms rely on solving PDEs on discrete surface meshes. Their accuracy and robustness crucially depend on the mesh quality, which oftentimes cannot be guaranteed - in particular when automatically processing geometries extracted from arbitrary implicit representations. Through extensive numerical experiments, we evaluate the robustness of various Laplacian implementations across geometry processing libraries on synthetic and ''in-the-wild'' surface meshes with degenerate or near-degenerate elements, revealing their strengths, weaknesses, and failure cases. To improve numerical stability, we extend the recently proposed tempered finite elements method (TFEM) to meshes with strongly varying element sizes, to arbitrary polygonal elements, and to gradient and divergence operators. Our resulting differential operators are simple to implement, efficient to compute, and robust even in the presence of fully degenerate mesh elements.en_US
dc.description.sectionheadersGeometry, Simulation, and Optimization
dc.description.seriesinformationVision, Modeling, and Visualization
dc.identifier.doi10.2312/vmv.20251242
dc.identifier.isbn978-3-03868-294-3
dc.identifier.pages9 pages
dc.identifier.urihttps://doi.org/10.2312/vmv.20251242
dc.identifier.urihttps://diglib.eg.org/handle/10.2312/vmv20251242
dc.publisherThe Eurographics Associationen_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectCCS Concepts: Mathematics of computing → Discretization; Computing methodologies → Mesh geometry models
dc.subjectMathematics of computing → Discretization
dc.subjectComputing methodologies → Mesh geometry models
dc.titleRobust Discrete Differential Operators for Wild Geometryen_US
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