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Non-stationary subdivision schemes for surface interpolation based on exponential polynomials. (English) Zbl 1195.65015

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.

##### MSC:
 65D17 Computer aided design (modeling of curves and surfaces) 65D10 Smoothing, curve fitting