On the Shape of a Set of Points and Lines in the Plane

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dc.contributor.authorKreveld, Marc vanen_US
dc.contributor.authorLankveld, Thijs vanen_US
dc.contributor.authorVeltkamp, Remco C.en_US
dc.contributor.editorMario Botsch and Scott Schaeferen_US
dc.date.accessioned2015-02-27T15:03:25Z
dc.date.available2015-02-27T15:03:25Z
dc.date.issued2011en_US
dc.description.abstractDetailed geometric models of the real world are in increasing demand. LiDAR data is appropriate to reconstruct urban models. In urban scenes, the individual surfaces can be reconstructed and connected to form the scene geometry. There are various methods for reconstructing the free-form shape of a point sample on a single surface. However, these methods do not take the context of the surface into account. We present the guided a-shape: an extension of the well known a-shape that uses lines (guides) to indicate preferred locations for the boundary of the shape. The guided a-shape uses (parts of) these lines as boundary where the points suggest that this is appropriate. We prove that the guided a-shape can be constructed in O((n+m) log(n+m)) time, from an input of n points and m guides. We apply guided a-shapes to urban reconstruction from LiDAR, where neighboring surfaces can be connected conveniently along their intersection lines into adjacent surfaces of a 3D model. We analyze guided a-shapes of both synthetic and real data and show they are consistently better than a-shapes for this application.en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.identifier.issn1467-8659en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2011.02029.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltd.en_US
dc.subjectComputer Graphics [I.3.5]en_US
dc.subjectComputational Geometry and Object Modelingen_US
dc.subjectBoundary representationsen_US
dc.subjectComputer Graphics [I.3.5]en_US
dc.subjectComputational Geometry and Object Modelingen_US
dc.subjectGeometric algorithmsen_US
dc.subjectlanguagesen_US
dc.subjectand systemsen_US
dc.titleOn the Shape of a Set of Points and Lines in the Planeen_US
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SGP11: Eurographics Symposium on Geometry Processing