2D Piecewise Linear Scalar Fields with Invertible Integral Lines

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dc.contributor.authorErxleben, Timm Leon
dc.contributor.authorMotejat, Michael
dc.contributor.authorRössl, Christian
dc.contributor.authorTheisel, Holger
dc.contributor.editorMasia, Belen
dc.contributor.editorThies, Justus
dc.date.accessioned2026-04-17T10:10:25Z
dc.date.available2026-04-17T10:10:25Z
dc.date.issued2026
dc.description.abstractIntegral lines of the gradient flow are standard features in continuously differentiable scalar fields that enjoy some useful properties: They cover the domain densely, do not split, merge, or intersect, and are therefore invertible. For widely used discretizations of scalar fields, the corresponding polygonal approximations of integral lines do not enjoy these properties anymore. We analyze conditions for integral lines in 2D piecewise linear (PL) scalar fields to be invertible by identifying and classifying critical edges in the underlying triangulation. We show that under mild conditions, every 2D PL scalar field can be transformed into an arbitrarily close PL field with invertible integral lines. We present an algorithm that computes this transformation and apply it to a number of test data sets.
dc.description.number2
dc.description.sectionheadersParametric and Structured Geometry
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume45
dc.identifier.doi10.1111/cgf.70340
dc.identifier.issn1467-8659
dc.identifier.pages13 pages
dc.identifier.urihttps://diglib.eg.org/handle/10.1111/cgf70340
dc.identifier.urihttps://doi.org/10.1111/cgf.70340
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.
dc.rightsCC-BY-4.0
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectHuman-centered computing → Scientific visualization
dc.subjectComputing methodologies → Mesh models
dc.title2D Piecewise Linear Scalar Fields with Invertible Integral Lines
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