Non-uniform interpolatory subdivision via splines
نویسندگان
چکیده
We present a framework for deriving non-uniform interpolatory subdivision algorithms closely related to non-uniform spline interpolants. Families of symmetric non-uniform interpolatory 2n-point schemes of smoothness C are presented for n = 2, 3, 4 and even higher order, as well as a variety of non-uniform 6-point schemes with C continuity.
منابع مشابه
Non-uniform Interpolatory Subdivision Based on Local Interpolants of Minimal Degree
This paper presents new univariate linear non-uniform interpolatory subdivision constructions that yield high smoothness, C and C, and are based on least-degree spline interpolants. This approach is motivated by evidence, partly presented here, that constructions based on high-degree local interpolants fail to yield satisfactory shape, especially for sparse, non-uniform samples. While this impr...
متن کاملCurvature of Approximating Curve Subdivision Schemes
The promise of modeling by subdivision is to have simple rules that avoid cumbersome stitching-together of pieces. However, already in one variable, exactly reproducing a variety of basic shapes, such as conics and spirals, leads to non-stationary rules that are no longer as simple; and combining these pieces within the same curve by one set of rules is challenging. Moreover, basis functions, t...
متن کاملComputation of interpolatory splines via triadic subdivision
We present an algorithm for computation of interpolatory splines of arbitrary order at triadic rational points. The algorithm is based on triadic subdivision of splines. Explicit expressions for the subdivision symbols are established. These are rational functions. The computations are implemented by recursive filtering.
متن کاملTernary interpolatory Subdivision Schemes Originated from splines
A generic technique for construction of ternary interpolatory subdivision schemes, which is based on polynomial and discrete splines, is presented. These schemes have rational symbols. The symbols are explicitly presented in the paper. This is accompanied by a detailed description of the design of the refinement masks and by algorithms that verify the convergence of these schemes. In addition, ...
متن کاملInterpolatory Subdivision Schemes Induced by Box Splines
This paper is devoted to a study of interpolatory refinable functions. If a refinable function φ on Rs is continuous and fundamental, i.e., φ(0) = 1 and φ(α) = 0 for α ∈ Zs\{0}, then its corresponding mask b satisfies b(0) = 1 and b(2α) = 0 for all α ∈ Zs\{0}. Such a refinement mask is called an interpolatory mask. We establish the existence and uniqueness of interpolatory masks which are induc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Computational Applied Mathematics
دوره 240 شماره
صفحات -
تاریخ انتشار 2013