Fitting of several 1D density profiles using the sinc family of kernels with constant and self-adaptive indexes. The upper left panel shows a Gaussian, mountain-like, profile. The exact (e) analytical value is shown in red, the result with the variable (v) kernel index, constant n = 5 and n = 3 in green, blue, and pink, respectively. The light blue line shows the profile of the smoothing-length normalized to its highest value (achieved just at the limits of the system, x = 0 and x = 1). The orange line shows the profile of the kernel index n associated with the green line. The same applies to the upper right (valley), the bottom left (wall), and the bottom right (cliff) profiles.