Examples of linear multi-box splines

Scattered data interpolation by box splines

Given scattered data in IR, interpolation from a dilated box spline space SM (2 ·) is always possible for a fine enough scaling. For example, for the Lagrange function of a point θ one could take any shifted dilate M(2 · −j) which is nonzero at θ and zero at the other interpolation points. However, the resulting interpolant, though smooth (and local), will consist of a set of “bumps”, and so by...

Interpolatory 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...

Symmetric box-splines on root lattices

Root lattices are efficient sampling lattices for reconstructing isotropic signals in arbitrary dimensions, due to their highly symmetric structure. One root lattice, the Cartesian grid, is almost exclusively used since it matches the coordinate grid; but it is less efficient than other root lattices. Box-splines, on the other hand, generalize tensor-product B-splines by allowing non-Cartesian ...

Box-like Splines With Nonuniform Stepsize

We construct a polynomial spline similar to the box spline, except that we relax the condition that its knots are spaced uniformly in each direction. The recurrence relation for this spline is a generalization of the recurrence relations for the box spline and univariate B-spline. The construction generalizes to exponential-polynomial splines [5]. §

Exponential box - like splines on nonuniform