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dc.contributor.authorBremer, Peer-Timoen_US
dc.contributor.authorHart, John C.en_US
dc.contributor.editorMarc Alexa and Szymon Rusinkiewicz and Mark Pauly and Matthias Zwickeren_US
dc.date.accessioned2014-01-29T16:31:42Z
dc.date.available2014-01-29T16:31:42Z
dc.date.issued2005en_US
dc.identifier.isbn3-905673-20-7en_US
dc.identifier.issn1811-7813en_US
dc.identifier.urihttp://dx.doi.org/10.2312/SPBG/SPBG05/047-054en_US
dc.description.abstractRecently, point set surfaces have been the focus of a large number of research efforts. Several different methods have been proposed to define surfaces from points and have been used in a variety of applications. However, so far little is know about the mathematical properties of the resulting surface. A central assumption for most algorithms is that the surface construction is well defined within a neighborhood of the samples. However, it is not clear that given an irregular sampling of a surface this is the case. The fundamental problem is that point based methods often use a weighted least squares fit of a plane to approximate a surface normal. If this minimization problem is ill-defined so is the surface construction. In this paper, we provide a proof that given reasonable sampling conditions the normal approximations are well defined within a neighborhood of the samples. Similar to methods in surface reconstruction, our sampling conditions are based on the local feature size and thus allow the sampling density to vary according to geometric complexity.en_US
dc.publisherThe Eurographics Associationen_US
dc.titleA Sampling Theorem for MLS Surfacesen_US
dc.description.seriesinformationEurographics Symposium on Point-Based Graphics (2005)en_US


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