Example of our covering of the sphere with overlapping patches based on HEALPix neighborhoods for N_side = 128 and patch width q = 8 (note that in our numerical experiments, N_side = 2048 and the patch width is either q = 8 or q = 12). Several randomly selected patches on the sphere are also represented in color. The plotted value in gray indicates the number of overlapping patches including each pixel. Because the patch width is usually small with respect to the number of pixels per face, the number of overlapping patches varies in small regions around the pixels that only have seven neighbors.