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Zbl 1195.65015
Lee, Yeon Ju; Yoon, Jungho
Non-stationary subdivision schemes for surface interpolation based on exponential polynomials. (English)
[J] Appl. Numer. Math. 60, No. 1-2, 130-141 (2010). ISSN 0168-9274

A subdivision scheme for generating curves and surfaces from a finite set of control points is proposed. The main fact is that the subdivision scheme is non-stationary: the mask used to compute the new points changes from level to level. The definition of the mask at each level goes as follows: Given some finite set of exponential polynomials (functions of the type $x^\alpha e^{\beta x}$) the mask is the one fitting a kind of butterfly-shaped stencil for the set of exponential polynomials. Thus, the computation of the mask at each level is equivalent to solve a linear system. Examples of how the algorithm works for parametric surfaces as torus and spheres are shown. A careful analysis of the convergence and of the smoothness of the subdivision scheme is done proving that these non-stationary schemes have the same smoothness and approximation order as the classical butterfly interpolatory scheme.
[Juan Monterde (Burjasot)]

MSC 2000:: *65D17 Computer aided design (modeling of curves and surfaces)
65D10 Smoothing

Keywords: non-stationary subdivision; exponential polynomial; interpolation; asymptotical equivalence; smoothness; approximation order; curves; surfaces; control points; fitting; torus; spheres; convergence

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Zentralblatt MATH Berlin [Germany]