US Patent 7477421 Halftoning system

A method for mapping a point (pixel) outside a halftone cell to a point inside the halftone cell by determining the size of a rectangle which is tiled exactly by the halftone cell. If the size of the rectangle permits, a threshold array is employed to render the pixel. Otherwise, the pixel is rendered by calculating four potential solutions and selecting one of the four potential solutions based on the where the four potential solutions are located with respect to the halftone cell.