Topology- and error-driven extension of scalar functions from surfaces to volumes (Articolo in rivista)

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Label
  • Topology- and error-driven extension of scalar functions from surfaces to volumes (Articolo in rivista) (literal)
Anno
  • 2009-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1145/1640443.1640447 (literal)
Alternative label
  • Giuseppe Patane'; Michela Spagnuolo; Bianca Falcidieno (2009)
    Topology- and error-driven extension of scalar functions from surfaces to volumes
    in ACM transactions on graphics; Association Of Computing Machinery (ACM), New York (Stati Uniti d'America)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Giuseppe Patane'; Michela Spagnuolo; Bianca Falcidieno (literal)
Pagina inizio
  • 4-1 (literal)
Pagina fine
  • 4-20 (literal)
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  • This paper, which was published in ACM Transactions on Graphics, 29(1) - 2009, has been invited for presentation at SIGGRAPH 2010, Los Angeles - USA, July 25 - 29, 2010. (literal)
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  • http://dl.acm.org/citation.cfm?doid=1640443.1640447 (literal)
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  • 29 (literal)
Rivista
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  • (December 2009) ACM New York, NY, USA; DOI: http://doi.acm.org/10.1145/1640443.1640447 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 1 (literal)
Note
  • ISI Web of Science (WOS) (literal)
  • Scopu (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Giuseppe Patane' CNR-IMATI, Genova, Italy Michela Spagnuolo CNR-IMATI, Genova, Italy Bianca Falcidieno CNR-IMATI, Genova, Italy (literal)
Titolo
  • Topology- and error-driven extension of scalar functions from surfaces to volumes (literal)
Abstract
  • The behavior of a variety of phenomena measurable on the boundary of 3D shapes is studied by modeling the set of known measurements as a scalar function f:P->R, defined on a surface P. Furthermore, the large amount of scientific data calls for efficient techniques to correlate, describe, and analyze this data. In this context, we focus on the problem of extending the measures captured by a scalar function f , defined on the boundary surface P of a 3D shape, to its surrounding volume. This goal is achieved by computing a sequence of volumetric functions that approximate f up to a specified accuracy and preserve its critical points. More precisely, we compute a smooth map g:R3->R such that the piecewise linear function h:=g|P:P->R, which interpolates the values of g at the vertices of the triangulated surface P, is an approximation of f with the same critical points. In this way, we overcome the limitation of traditional approaches to function approximation, which are mainly based on a numerical error estimation and do not provide measurements of the topological and geometric features of f . The proposed approximation scheme builds on the properties of f related to its global structure, that is, its critical points, and ignores the local details of f, which can be successively introduced according to the target approximation accuracy. (literal)
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