## Symmetric Box-splines on the A ∗ n Lattice

Citations: | 1 - 0 self |

### BibTeX

@MISC{Kim_symmetricbox-splines,

author = {Minho Kim and Jörg Peters},

title = {Symmetric Box-splines on the A ∗ n Lattice},

year = {}

}

### OpenURL

### Abstract

Sampling and reconstruction of generic multivariate functions is more efficient on non-Cartesian root lattices, such as the BCC (Body-Centered Cubic) lattice, than on the Cartesian lattice. We introduce a new n × n generator matrix A ∗ that enables, in n variables, for efficient reconstruction on the non-Cartesian root lattice A ∗ n by a symmetric box-spline family M ∗ r. A ∗ 2 is the hexagonal lattice and A ∗ 3 is the BCC lattice. We point out the similarities and differences of M ∗ r to the popular Cartesian-shifted box-spline family Mr, document the main properties of M ∗ r and the partition induced by its knot planes and construct, in n variables, the optimal quasi-interpolant of M ∗ 2. 1.