Interpolatory subdivision schemes and wavelets
Journal of Approximation Theory
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Polynomial generation and quasi-interlpolation in stationary non-uniform subdivision
Computer Aided Geometric Design
A non-stationary uniform tension controlled interpolating 4-point scheme reproducing conics
Computer Aided Geometric Design
Polynomial reproduction by symmetric subdivision schemes
Journal of Approximation Theory
Journal of Computational and Applied Mathematics
Full length article: Polynomial reproduction for univariate subdivision schemes of any arity
Journal of Approximation Theory
Generalized Daubechies Wavelet Families
IEEE Transactions on Signal Processing
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
Advances in Computational Mathematics
Non-uniform non-tensor product local interpolatory subdivision surfaces
Computer Aided Geometric Design
A generalized surface subdivision scheme of arbitrary order with a tension parameter
Computer-Aided Design
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We present an accurate investigation of the algebraic conditions that the symbols of a non-singular, univariate, binary, non-stationary subdivision scheme should fulfill in order to reproduce spaces of exponential polynomials. A subdivision scheme is said to possess the property of reproducing exponential polynomials if, for any initial data uniformly sampled from some exponential polynomial function, the scheme yields the same function in the limit. The importance of this property is due to the fact that several curves obtained by combinations of exponential polynomials (such as conic sections, spirals or special trigonometric and hyperbolic functions) are considered of interest in geometric modeling. Since the space of exponential polynomials trivially includes standard polynomials, this work extends the theory on polynomial reproduction to the non-stationary context. A significant application of the derived algebraic conditions on the subdivision symbols is the construction of new non-stationary subdivision schemes with specific reproduction properties.