Abstract
Abstract In this paper, we propose a family of non-stationary combined ternary ( 2 m + 3 ) \left(2m+3) -point subdivision schemes, which possesses the property of generating/reproducing high-order exponential polynomials. This scheme is obtained by adding variable parameters on the generalized ternary subdivision scheme of order 4. For such a scheme, we investigate its support and exponential polynomial generation/reproduction and get that it can generate/reproduce certain exponential polynomials with suitable choices of the parameters and reach 2 m + 3 2m+3 approximation order. Moreover, we discuss its smoothness and show that it can produce C 2 m + 2 {C}^{2m+2} limit curves. Several numerical examples are given to show the performance of the schemes.
Highlights
Subdivision schemes are an efficient tool to design smooth curves and surfaces from a given initial polyline/ polyhedral mesh
Subdivision schemes have become of interest in biomedical imaging applications and isogeometric analysis (IgA), a modern computational approach that integrates finite element analysis into conventional CAD systems
One of the important capabilities of non-stationary schemes is the reproduction of exponential polynomials. Such schemes may be useful for the processing of families of oscillatory signals that are well approximated by combinations of exponential polynomials, such as speech signals, and narrowband signals in general
Summary
Subdivision schemes are an efficient tool to design smooth curves and surfaces from a given initial polyline/ polyhedral mesh. To generate and reproduce more general exponential polynomials, we propose a family of non-stationary combined ternary (2m + 3)-point subdivision schemes based on the generalized ternary scheme of order 4 proposed in [22]. For such a scheme, we investigate its properties, including the support, exponential polynomial generation/reproduction, approximation order and smoothness.
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