While the present study focuses on enabling the use of hexagonal halftone through particular geometric rules and suitable spot functions, we recognize that additional work in needed in the realm of characterization. In particular, study is needed on the tone reproduction behavior and on the smoothness appearance. At least three points arise when considering the tone reproduction: (1) packing density differences, (2) sixtouch points vs. four, (3) splitting each hole into two triangles. Concerning smoothness, visual comparisons tend to indicate that hexagonally tiled screens have a smoother appearance than conventional square tiled screensfor monochrome images (see Fig. 21). This may be due to the more complex frequency spectrum providing some level of masking of the periodic structure. A visual model or empirical study will be needed to better understand this potential smoothness effect. A visual comparison of smoothness for a full color image is not immediately compelling. Consider the example of Fig. 22. The right picture was halftoned by a digital simulation of the conventional square-cell-based halftone screens, and the left one was halftoned by a set of hexagonal screens with the following spatial frequencies (in units of cycles/inch): Display FormulaDisplay FormulaDisplay FormulaDisplay FormulaThe frequencies are very low to make the texture apparent in this publication. Empirical print studies are needed to effectively rate the smoothness of these images. The result may be marking process dependent. Another consideration is that many color prints have substantial regions that are primarily monochrome. The hexagonal screen method presented here will allow full color moiré-free printing, with a certain gain in smoothness benefit in the image regions that are predominantly monochrome.