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

✍ Scribed by D. Barrera; M.A. Fortes; P. González; M. Pasadas

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
906 KB
Volume
218
Category
Article
ISSN
0377-0427

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✦ Synopsis

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.

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✍ D. Barrera; M.A. Fortes; P. González; M. Pasadas 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 706 KB

In this paper we present two different methods for filling in a hole in an explicit 3D surface, defined by a smooth function f in a part of a polygonal domain D ⊂ R 2 . We obtain the final reconstructed surface over the whole domain D. We do the filling in two different ways: discontinuous and conti