1. A method performed, at least in part by one or more computers, for generating a multilevel halftone screen, the method comprising the steps of: receiving tile definition data describing a tile definition such tile definition includes a tile shape, a tile angle, screen dot nuclei frequency, and a tile size; generating a tile based at least upon the tile definition data, the tile having a plurality of screen dot nuclei; improving locations of the plurality of screen dot nuclei in the tile; growing peripheral regions around each of the screen dot nuclei in each of a plurality of successive planes of the halftone screen such planes having a shape and a size consistent with the tile shape and the tile size; rotating the plurality of successive planes to zero degrees; generating copies of the plurality of planes; and logically merging the copies of the plurality of planes side-by-side to cover an image to be subjected to halftone processing.