Interpolated CMB vs. true value. Distribution of the error in the value given by both naive interpolation on a HealPix mesh and our method for different HealPix resolution. For each line, we represented the distribution of the relative difference between the actual interpolated value and the true value. The green, black, and blue lines correspond to HealPix interpolation at N _side= 2048, N _side= 4096, and N _side= 8192, respectively. The red line corresponds to our method at N _side= 2048.