Minimal energy Cr-surfaces on uniform Powell-Sabin-type meshes for noisy data

Authors:
D. Barrera;M. A. Fortes;P. González;M. Pasadas
Affiliations:
Departamento de Matemática Aplicada, Universidad de Granada, Edificio Politécnico, C/Severo Ochoa, s/n, 18071 Granada, Spain;Departamento de Matemática Aplicada, Universidad de Granada, Edificio Politécnico, C/Severo Ochoa, s/n, 18071 Granada, Spain;Departamento de Matemática Aplicada, Universidad de Granada, Edificio Politécnico, C/Severo Ochoa, s/n, 18071 Granada, Spain;Departamento de Matemática Aplicada, Universidad de Granada, Edificio Politécnico, C/Severo Ochoa, s/n, 18071 Granada, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Minimal energy Cr-surfaces on uniform Powell-Sabin type meshes

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Multiresolution analysis for minimal energy Cr-surfaces on Powell-Sabin type meshes

MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces

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Abstract

In this paper we present a method to obtain for noisy data, a C^r-surface, for any r=1, on a polygonal domain which approximates a Lagrangian data set and minimizes a quadratic functional that contains some terms associated with Sobolev semi-norms weighted by some smoothing parameters. The minimization space is composed of bivariate spline functions constructed on a uniform Powell-Sabin-type triangulation of the domain. We prove a result of almost sure convergence and we choose optimal values of the smoothing parameters by adapting the generalized cross-validation method. We finish with some numerical and graphical examples.