The diagonally swapped image will be referred to as O d . Two masks are created, there are many alternatives but the example shown below is a radial linear ramp from black to white. Other masks can be used, the requirement is that the mask tends smoothly to pure white at the image boundary. The second mask on the right is diagonal swapped version of the mask on the left. The mask shall be referred to as M .
M d is calculated as for O d above.
The following two images are created by multiplying the two original images by their respective masks. And finally, the tilable image on the left is created by averaging the two images above. On the right is a reduced 2x2 tiling of the tile on the left showing the absence of any discontinuities. The average of the two tiles above. A 2x2 tiling of the tile on the left.