Reconstructing Curves from Sparse Samples on Riemannian Manifolds

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dc.contributor.authorMarin, Dianaen_US
dc.contributor.authorMaggioli, Filippoen_US
dc.contributor.authorMelzi, Simoneen_US
dc.contributor.authorOhrhallinger, Stefanen_US
dc.contributor.authorWimmer, Michaelen_US
dc.contributor.editorHu, Ruizhenen_US
dc.contributor.editorLefebvre, Sylvainen_US
dc.date.accessioned2024-06-20T07:55:04Z
dc.date.available2024-06-20T07:55:04Z
dc.date.issued2024
dc.description.abstractReconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive attention, primarily relying on human assistance, and where not, limited by very strict sampling conditions. In this work, we formally improve on the state-of-the-art requirements and introduce an innovative algorithm capable of reconstructing closed curves directly on surfaces from a given sparse set of sample points. We extend and adapt a state-of-the-art planar curve reconstruction method to the realm of surfaces while dealing with the challenges arising from working on non-Euclidean domains. We demonstrate the robustness of our method by reconstructing multiple curves on various surface meshes. We explore novel potential applications of our approach, allowing for automated reconstruction of curves on Riemannian manifolds.en_US
dc.description.number5
dc.description.sectionheadersParametrization and Curves
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume43
dc.identifier.doi10.1111/cgf.15136
dc.identifier.issn1467-8659
dc.identifier.pages14 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.15136
dc.identifier.urihttps://diglib.eg.org/handle/10.1111/cgf15136
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectCCS Concepts: Mathematics of computing → Paths and connectivity problems; Graph algorithms; Computing methodologies → Mesh geometry models
dc.subjectMathematics of computing → Paths and connectivity problems
dc.subjectGraph algorithms
dc.subjectComputing methodologies → Mesh geometry models
dc.titleReconstructing Curves from Sparse Samples on Riemannian Manifoldsen_US
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