Patent ID: 7477421

Claim:
A method for mapping a pixel outside a halftone cell to a point inside the halftone cell, comprising: determining the size of a rectangle which is tiled exactly by the halftone cell, wherein the halftone cell is defined by two rectangular shapes, the first rectangular shape having a width X 1 and a height Y 1 ; and the second rectangular shape having a width X 2 and a height Y 2 ; using a threshold array to render the point when the size of the rectangle size permits; and calculating a plurality of potential solutions for rendering the pixel when the size of the rectangle is too large for a threshold array and selecting one of the plurality of potential solutions based on the locations of the plurality of potential solutions with respect to the halftone cell, wherein calculating the plurality of potential solutions includes calculating a starting point of an enclosing tile in Cartesian coordinates having an x component and a y component, wherein x=x modulo tile size x; and y=y modulo tile size y; and calculating four coefficients wherein wherein the first coefficient, K ⁢ ⁢ 1 = [ X ⁢ ⁢ 1 * y - Y ⁢ ⁢ 2 * x X ⁢ ⁢ 1 * Y ⁢ ⁢ 1 + X ⁢ ⁢ 2 * Y ⁢ ⁢ 2 ] ; wherein the second coefficient, K ⁢ ⁢ 2 = [ x + K ⁢ ⁢ 1 * X ⁢ ⁢ 2 X ⁢ ⁢ 1 ] ; wherein the third coefficient, K ⁢ ⁢ 3 = [ X ⁢ ⁢ 1 * y - Y ⁢ ⁢ 2 * x - ( Y ⁢ ⁢ 1 + Y ⁢ ⁢ 2 ) * X ⁢ ⁢ 1 X ⁢ ⁢ 1 * Y ⁢ ⁢ 1 + X ⁢ ⁢ 2 * Y ⁢ ⁢ 2 ] ; and wherein the fourth coefficient, K ⁢ ⁢ 4 = [ x + K ⁢ ⁢ 2 * X ⁢ ⁢ 2 - max ⁡ ( X ⁢ ⁢ 1 , X ⁢ ⁢ 2 ) X ⁢ ⁢ 1 ] .