1.  Field of the Invention
The present invention relates to imaging, and, more particularly, to dot management for an imaging apparatus, such as an ink jet printer. 
2.  Description of the Related Art
An imaging apparatus in the form of an ink jet printer typically forms an image on a print medium by ejecting ink from at least one ink jet printhead to form a pattern of ink dots on the print medium.  Such an ink jet printer includes a reciprocating printhead carrier that transports one or more ink jet printheads across the print medium along a bi-directional scanning path defining a print zone of the printer.  The bi-directional scanning path is oriented parallel to a main scan direction, also commonly referred to as the horizontal direction.  During each scan of the printhead carrier, the print medium is held stationary.  An indexing mechanism is used to incrementally advance the print medium in a sheet feed direction, also commonly referred to as a sub-scan direction, through the print zone between scans in the main scan direction, or after all data intended to be printed with the print medium at a particular stationary position has been completed. 
For a given stationary position of the print medium, printing may take place during unidirectional or bi-directional scans of the printhead carrier.  The height of the printhead generally defines a printing swath as ink is deposited on the print medium during a particular scan of the printhead carrier.  A printing swath is made of a plurality of printing lines traced along imaginary rasters, the imaginary rasters being spaced apart in the sheet feed direction, e.g., vertically.  In order to form the pattern of ink drops on the print medium, a rectilinear array, also known as a matrix, of possible pixel, i.e., drop, locations is defined within the printable boundaries of the print medium.  The closest possible spacing of ink drops in the main scan direction is typically referred to as the horizontal resolution, and the closest possible spacing of ink drops in the sub-scan direction, i.e., between adjacent rasters, is typically referred to as the vertical resolution. 
The quality of printed images produced by an ink jet printer depends in part on the resolution of the printer.  Typically, higher or finer resolutions, where the printed dots are more closely spaced, results in higher quality images.  Increasing the resolution of an ink jet printer increases the number of dots to be printed in a unit area by the product of the increase factor in each dimension in the grid.  For example, doubling the print resolution from 300 dpi (dots, or drops, per inch) to 600 dpi in a matrix results in four times as many dots per unit area. 
Printing quality using an ink jet printer of the type described above can be further improved by using a technique commonly referred to as shingling, or interlaced printing, wherein consecutive printing swaths are made to overlap and only a portion of the ink drops for a given print line, i.e., raster, are applied to the print medium on a given pass of the printhead.  For example, in one known shingling mode using 50% shingling, approximately 50% of the dots for a particular color are placed on any given pass of the printhead, thereby requiring two passes of the printhead to completely print a particular raster.  The candidate dots of the first pass of the printhead may be selected according to a checkerboard pattern.  The remaining 50% of the dots are placed on a subsequent pass of the printhead. 
In typical shingling methods, however, as resolution increases, so does the number of passes of the printhead required to print the image data.  Accordingly, while increasing resolution and using shingling patterns to mask printing defects increases the printing quality, such an approach that significantly increases the number of printing passes may not be optimum from an efficiency standpoint in terms of throughput of the printer. 
What is needed in the art is a printing method that distributes dots among a plurality of passes without increasing the number of passes that are required to print an image at a predetermined resolution.