Multivariate Compactly Supported Fundamental Re nable Functions
نویسندگان
چکیده
For a given continuous compactly supported reenable function that is fundamental (that means, () =), this paper presents several methods to construct, directly from , compactly supported fundamental reenable functions with higher regularity. Asymptotic regularity analyses of the constructions are given. These constructions immediately provide multivariate interpolatory subdivision schemes that generate highly smooth surfaces. These constructions also lead directly to constuctions of a pair of dual reenable functions with high regularity in any number of variables. Combined with the biorthogonal wavelet construction algorithm for a pair of dual reenable functions given in RiS2], we obtain symmetric multivariate biorthogonal wavelets with arbitrarily high regularity.
منابع مشابه
Fundamental Re nable Functions , Duals and Biorthogonal
In areas of geometric modeling and wavelets, one often needs to construct a compactly supported reenable function with suucient regularity which is fundamental for interpolation (that means, (0) = 1 and () = 0 for all 2 Z s nf0g). Low regularity examples of such functions have been obtained numerically by several authors and a more general numerical scheme was given in RiS1]. This paper present...
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