Symmetric box-splines on the image lattice Original Research Article

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×nn×n generator matrix View the MathML sourceA∗ that enables, in nn variables, efficient reconstruction on the non-Cartesian root lattice View the MathML sourceAn∗ by a symmetric box-spline family View the MathML sourceMr∗. View the MathML sourceA2∗ is the hexagonal lattice and View the MathML sourceA3∗ is the BCC lattice. We point out the similarities and differences of View the MathML sourceMr∗ with respect to the popular Cartesian-shifted box-spline family MrMr, document the main properties of View the MathML sourceMr∗ and the partition induced by its knot planes and construct, in nn variables, the optimal quasi-interpolant of View the MathML sourceM2∗.