pixel memory storing up to a predetermined number of fragment tuples, each stored fragment tuple being associated with a fragment that is visible in the pixel; each fragment tuple including a color value, a center Z (depth) value, and a pair of Z gradient values;

a pipeline processing circuit for processing a new fragment tuple representing a fragment added to the pixel, the pipeline processing circuit including a sequence of pipeline stage circuits, the pipeline stage circuits including:

a fragment ordering pipeline stage for ordering the new fragment tuple and the fragment tuples stored in the pixel memory so as to generate a sequence of fragment tuples ordered with respect to Z value;

a subpixel ordering pipeline stage for determining if successive fragments in the sequence of fragments are out of order with respect to Z value at any of a predefined set of subpixel positions, including:

subpixel Z value generation circuitry for determining a Z value for two successive fragments tuples in the sequence of fragment tuples at each subpixel sample position, if any, covered by both of the two fragments represented by the two fragment tuples, based on the center Z value and pair of Z gradient values for each of the two fragments tuples; and

subpixel Z value comparison circuitry for comparing the determined Z values and generating swap values indicating whether the fragments are out of order with respect to Z value at each of the predefined subpixel sample positions; and

a merge pipeline stage that uses the swap values to produce a modified sequence of fragment tuples, the merge pipeline stage merging two of the fragment tuples in the modified sequence of fragment tuples, when the sequence of fragment tuples includes more fragment tuples than said predetermined number, so as to generate a merged fragment tuple, the merge pipeline including subpixel merge circuitry for merging color values for the two fragment tuples at each of the predefined subpixel sample positions, if any, that is covered by both of the two fragments represented by the two fragment tuples being merged, the color values being merged at each such subpixel sample position in an order specified by a corresponding one of the swap values.