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 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 .

• Type: Journal
• Year: 2010
• Where: JAT
• Authors: Minho Kim, Jörg Peters
• Keywords: Box-spline Family, JAT 2010, Non-cartesian Root Lattice, Root Lattice A∗