Geodesic
Stable multiresolution analysis on triangles for surface compression
Electronic transactions on numerical analysis, Tome 25 (2006), pp. 224-258.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Recently we developed multiscale spaces of piecewise quadratic polynomials on the Powell- $\textcent $###$\sterling $Sabin 6-split of a triangulation relative to arbitrary polygonal domains . These multiscale bases are weakly $$###$$§$$###$\copyright \ddot $ stable with respect to the norm. In this paper we prove that these multiscale spaces form a multiresolution analysis for the Banach space and we show that the multiscale basis forms a strongly stable Riesz basis for $\textcent $###$ \sterling $ the Sobolev spaces with . In other words, the norm of a function can be determined $$###$$ "! )0!1 $$###$$2 $#\\%(' from the size of the coefficients in the multiscale representation of . This property makes the multiscale basis ) suitable for surface compression. A simple algorithm for compression is proposed and we give an optimal a priori error bound that depends on the smoothness of the input surface and on the number of terms in the compressed approximant.$$
Classification : 41A15, 65D07, 65T60, 41A63
Keywords: hierarchical bases, powell-sabin splines, wavelets, stable approximation by splines, surface compression 
@article{ETNA_2006__25__a16,
     author = {Maes, Jan and Bultheel, Adhemar},
     title = {Stable multiresolution analysis on triangles for surface compression},
     journal = {Electronic transactions on numerical analysis},
     pages = {224--258},
     publisher = {mathdoc},
     volume = {25},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__25__a16/}
}
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Maes, Jan; Bultheel, Adhemar. Stable multiresolution analysis on triangles for surface compression. Electronic transactions on numerical analysis, Tome 25 (2006), pp. 224-258. http://geodesic.mathdoc.fr/item/ETNA_2006__25__a16/