Symmetric box-splines on the A*n lattice

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 An by a symmetric box-spline family M r . A2 is the hexagonal lattice and A3 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 .