Hex-splines: a novel spline family for hexagonal lattices

摘要: This paper proposes a new family of bivariate, nonseparable splines, called hex-splines, especially designed for hexagonal lattices. The starting point the construction is indicator function Voronoi cell, which used to define in natural way first-order hex-spline. Higher order hex-splines are obtained by successive convolutions. A mathematical analysis this bivariate spline presented. In particular, we derive closed form hex-spline arbitrary order. We also discuss important properties, such as their Fourier transform and fact they Riesz basis. highlight approximation For conventional rectangular lattices, revert classical separable tensor-product B-splines. Finally, some prototypical applications experimental results demonstrate usefulness handling hexagonally sampled data.