ABSTRACT
This chapter looks at the application of blue-noise halftoning to hexagonal sampling grids; where hexagonal grids differ from rectangular in that every other row is offset one-half a pixel period. Hexagonal sampling grids also increase the robustness to changes in aspect ratio. The best case for rectangular grids occurs for square grids, but what is particularly interesting is the wide range of aspect ratios where hexagonal grids outperform this best case. In contrast, minority pixels must begin to cluster as the gray-level approaches 1/2 on a hexagonal grid, which lead R. Ulichney to write that hexagonal sampling grids do not support blue-noise. Hexagonal grid, blue-noise halftoning should, therefore, be able to achieve higher principal frequencies for the same gray-levels as rectangular grids and, therefore, should achieve lower visual costs. A regular hexagonal sampling lattice is characterized by samples placed a horizontal distance apart equal to some sample period Dx and a vertical distance apart of 32Dx.
