Symmetric box-splines on the An* 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 x n generator matrix A* that enables, in n variables, 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* with respect 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-r*. (C) 2010 Elsevier Inc. All rights reserved.