Non-orthogonal lattice line smoothing

This paper investigates smoothing methods for binned data whose bin centers fall on non-orthogonal lattice lines. Smoothing methods such as median polish traditionally assume orthogonal lattice lines. With a mean polish there is a direct connection to simple anova models. However, when binning produces the lattice. the lattice is subject to investigator's discretion. The paper investigates lattice line smoothing for 2-D, 3-D, and 4-D lattices produced by hexagons, truncated-octahedrons, and 24-cell binning. These bin cells have the desirable properties in that they partition space, are as round as possible, and share faces with neighboring cells. Binning sacrifices resolution, but can be advantageous in large data set application where speed is an issue. The smoothing is of direct interest is many applications and applicable as a preprocessing step for variogram estimation.