%0 Conference Proceedings
%4 sid.inpe.br/sibgrapi@80/2009/08.17.15.26
%2 sid.inpe.br/sibgrapi@80/2009/08.17.15.26.36
%@doi 10.1109/SIBGRAPI.2009.11
%T Hermite Interpolation of Implicit Surfaces with Radial Basis Functions
%D 2009
%A Macędo Júnior, Ives José de Albuquerque,
%A Gois, Joăo Paulo,
%A Velho, Luiz Carlos Pacheco Rodrigues,
%@affiliation IMPA - Instituto Nacional de Matemática Pura e Aplicada
%@affiliation Universidade Federal do ABC
%@affiliation IMPA - Instituto Nacional de Matemática Pura e Aplicada
%E Nonato, Luis Gustavo,
%E Scharcanski, Jacob,
%B Brazilian Symposium on Computer Graphics and Image Processing, 22 (SIBGRAPI)
%C Rio de Janeiro, RJ, Brazil
%8 11-14 Oct. 2009
%I IEEE Computer Society
%J Los Alamitos
%S Proceedings
%K implicit surfaces, Hermite data, radial basis functions, Hermite-Birkhoff interpolation, scattered data approximation, geometric modeling, surface reconstruction.
%X We present the Hermite radial basis function (HRBF) implicits method to compute a global implicit function which interpolates scattered multivariate Hermite data (unstructured points and their corresponding normals). Differently from previous radial basis functions (RBF) approaches, HRBF implicits do not depend on offset points to ensure existence and uniqueness of its interpolant. Intrinsic properties of this method allow the computation of implicit surfaces rich in details, with irregularly spaced points even in the presence of close sheets. Comparisons to previous works show the effectiveness of our approach. Further, the theoretical background of HRBF implicits relies on results from generalized interpolation theory with RBFs, making possible powerful new variants of this method and establishing connections with previous efforts based on statistical learning theory.
%@language en
%3 macedo-HRBFImplicits.pdf