Curve Reconstruction with Many Fewer Samples

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dc.contributor.authorOhrhallinger, Stefanen_US
dc.contributor.authorMitchell, Scott A.en_US
dc.contributor.authorWimmer, Michaelen_US
dc.contributor.editorMaks Ovsjanikov and Daniele Panozzoen_US
dc.date.accessioned2016-06-17T14:12:00Z
dc.date.available2016-06-17T14:12:00Z
dc.date.issued2016en_US
dc.description.abstractWe consider the problem of sampling points from a collection of smooth curves in the plane, such that the CRUST family of proximity-based reconstruction algorithms can rebuild the curves. Reconstruction requires a dense sampling of local features, i.e., parts of the curve that are close in Euclidean distance but far apart geodesically. We show that e < 0:47-sampling is sufficient for our proposed HNN-CRUST variant, improving upon the state-of-the-art requirement of e < 13 -sampling. Thus we may reconstruct curves with many fewer samples. We also present a new sampling scheme that reduces the required density even further than e < 0:47-sampling. We achieve this by better controlling the spacing between geodesically consecutive points. Our novel sampling condition is based on the reach, the minimum local feature size along intervals between samples. This is mathematically closer to the reconstruction density requirements, particularly near sharp-angled features. We prove lower and upper bounds on reach r-sampling density in terms of lfs e-sampling and demonstrate that we typically reduce the required number of samples for reconstruction by more than half.en_US
dc.description.number5en_US
dc.description.sectionheadersReconstructionen_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume35en_US
dc.identifier.doi10.1111/cgf.12973en_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages167-176en_US
dc.identifier.urihttps://doi.org/10.1111/cgf.12973en_US
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectI.3.3 [Computer Graphics]en_US
dc.subjectPicture/Image Generationen_US
dc.subjectLine and curve generationen_US
dc.titleCurve Reconstruction with Many Fewer Samplesen_US
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35-Issue 5
SGP16: Eurographics Symposium on Geometry Processing (CGF 35-5)