Van De Ville, DimitriDimitriVan De VilleTHIERRY BLUUnser, MichaelMichaelUnserPhilips, WilfriedWilfriedPhilipsLemahieu, IgnaceIgnaceLemahieuVan de Walle, RikRikVan de Walle2024-03-082024-03-082004-06-0110577149https://scholars.lib.ntu.edu.tw/handle/123456789/640636This paper proposes a new family of bivariate, nonseparable splines, called hex-splines, especially designed for hexagonal lattices. The starting point of the construction is the indicator function of the Voronoi cell, which is used to define in a natural way the first-order hex-spline. Higher order hex-splines are obtained by successive convolutions. A mathematical analysis of this new bivariate spline family is presented. In particular, we derive a closed form for a hex-spline of arbitrary order. We also discuss important properties, such as their Fourier transform and the fact they form a Riesz basis. We also highlight the approximation order. For conventional rectangular lattices, hex-splines revert to classical separable tensor-product B-splines. Finally, some prototypical applications and experimental results demonstrate the usefulness of hex-splines for handling hexagonally sampled data.enApproximation theory | Bivariate splines | Hexagonal lattices | Sampling theoryjournal article10.1109/TIP.2004.827231156488672-s2.0-2942566485https://api.elsevier.com/content/abstract/scopus_id/2942566485