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

Lee, Yeon Ju; Yoon, Jungho

Appl. Numer. Math. 60, No. 1-2, 130-141 (2010).

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.

Reviewer: Juan Monterde (Burjasot)

MSC:

65D17	Computer-aided design (modeling of curves and surfaces)
65D10	Numerical smoothing, curve fitting

Keywords:

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

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