A pixel center position that is not covered by a primitive covering a portion of the pixel is displaced to lie within a fragment formed by the intersection of the primitive and the pixel. X,y coordinates of a pixel center are adjusted to displace the pixel center position to lie within the fragment, affecting actual texture map coordinates or barycentric weights. Alternatively, a centroid sub-pixel sample position is determined based on coverage data for the pixel and a multisample mode. The centroid sub-pixel sample position is used to compute pixel or sub-pixel parameters for the fragment.