gnuplot 5.4 regression(?): smooth acsplines w filledcurves
As far as I could check it (withouth comparison to analytical calculations), it now looks qualitatively right (isotropic). Compared to http://www.gnuplot.info/demo/dgrid3d.3.png the gnu-valley demo also lost its spurious groove in the middle. Difficult to compare with analytical results, but let's face it, interpolation is a dirty business anyway (-: Thank you!
See attached. In pm3d map view, the Manhattan ridges are clearly visible for the non-binary-exponent cases 15, 17, in case of the square as ridges wrongly radiating out of the central domain, and, more dramatically with the triangle, where domain boundaries are aligned onto a Cartesian grid. The cases with qnorm exponent 16 are isotropic as they should be. You might also plot the circular plateau with qnorm 1 in normal 3d mode to see how the central tip looks like a pyramid with four sharp edges...
dgrid3d: Mathematical error in the metric computation plot3d.c:qnorm()
dgrid3d: Mathematical error in the metric computation plot3d.c:qnorm()