Comment 25 for bug 165780

What Diederik said, but I think you'll need more than 3x3 in general. You need to be able to fill the bounding box of the original pattern rectangle transformed to the new coordinate system. If you imagine a pattern that's 1000px wide and 10px high rotated 45 degrees you'll see that a 3x3 tiling won't work. But it's just basic trig to figure out how big of a box you need.

OTOH, since you know you're tiling the plane can't you just turn off anti-aliasing of the pattern's edges and do what you're doing now?