The approximation power of moving least-squares
Mathematics of Computation
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Barycentric rational interpolation with no poles and high rates of approximation
Numerische Mathematik
A class of general quartic spline curves with shape parameters
Computer Aided Geometric Design
Short kernel fifth-order interpolation
IEEE Transactions on Signal Processing
Complete parameterization of piecewise-polynomial interpolation kernels
IEEE Transactions on Image Processing
Non-uniform non-tensor product local interpolatory subdivision surfaces
Computer Aided Geometric Design
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This paper presents a general framework for the construction of piecewise-polynomial local interpolants with given smoothness and approximation order, defined on non-uniform knot partitions. We design such splines through a suitable combination of polynomial interpolants with either polynomial or rational, compactly supported blending functions. In particular, when the blending functions are rational, our approach provides spline interpolants having low, and sometimes minimum degree. Thanks to its generality, the proposed framework also allows us to recover uniform local interpolating splines previously proposed in the literature, to generalize them to the non-uniform case, and to complete families of arbitrary support width. Furthermore it provides new local interpolating polynomial splines with prescribed smoothness and polynomial reproduction properties.