Fractional distance residuals—(estimated-true)/true—per HEALpixel for the constant number sample in the mock catalog. The top row shows the median fractional residual (the bias); the bottom row shows the median absolute fractional residual (the scatter). The left column is for geometric estimates, and the right column is for kinegeometric estimates. The color bars span the full common range in each of the top and bottom rows. The top row uses a bilinear color bar (separate scales for negative and positive values): The dominance of red HEALpixels over blue ones at high latitudes is because the positive red scale extends to smaller values than the negative blue scale; the absolute biases are more or less the same overall.