Computing Smooth Approximations of Scalar Functions with Constraints (Articolo in rivista)

Type
Label
  • Computing Smooth Approximations of Scalar Functions with Constraints (Articolo in rivista) (literal)
Anno
  • 2009-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1016/j.cag.2009.03.014 (literal)
Alternative label
  • Patane' G.; Falcidieno B. (2009)
    Computing Smooth Approximations of Scalar Functions with Constraints
    in Computers & graphics; Pergamon Press, Oxford (Regno Unito)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Patane' G.; Falcidieno B. (literal)
Pagina inizio
  • 399 (literal)
Pagina fine
  • 413 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#altreInformazioni
  • IEEE International Conference on Shape Modelling and Applications 2009 (Beijing, China, 26-28 June 2009). J-H Yong, M. Spagnuolo, W. Wang (eds.). Elsevier, 2009. (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://www.sciencedirect.com/science/article/pii/S0097849309000284 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 33 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#note
  • IEEE International Conference on Shape Modeling and Applications, 2009 (Beijing, China, 26-28 June 2009). H-J Yong, M. Spagnuolo, W. Wang (eds.), Elsiever 2009 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 3 (literal)
Note
  • Scopu (literal)
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Patane' G. Istituto di Matematica Applicata e Tecnologie Informatiche - Consiglio Nazionale delle Ricerche, Genova, Italy Falcidieno B. Istituto di Matematica Applicata e Tecnologie Informatiche - Consiglio Nazionale delle Ricerche, Genova, Italy (literal)
Titolo
  • Computing Smooth Approximations of Scalar Functions with Constraints (literal)
Abstract
  • In engineering, geographical applications, scientific visualization, and bio-informatics, a variety of phenomena is described by a large set of data modeled as the values of a scalar function f:M->R defined on a surface M. A low quality of the discrete representations of the input data, unstable computations, numerical approximations, and noise might produce functions with a high number of critical points. In this context, we propose an algorithmic framework for smoothing an arbitrary scalar function, while simplifying its redundant critical points and preserving those that are mandatory for its description. From our perspective, the critical points of f are a natural choice to guide the approximation scheme; in fact, they usually represent relevant information about the behavior of f or the shape itself. To address the aforementioned aims, we compute a smooth approximation of f whose set of critical points contains those that have been preserved by the simplification process. The idea behind the proposed approach is to combine smoothing techniques, critical points, and spectral properties of the Laplacian matrix. Inserting constraints in the smoothing of f allows us to overcome the traditional error-driven approximation of f, which does not provide constraints on the preserved topological features. Finally, the computational cost of the proposed approach is , where n is the number of vertices of M. (literal)
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