If you look at my earlier post “Nautilus” you see that it is difficult to get good results for strongly distorted images. They have regions where the input image is strongly magnified and one input pixel could cover many pixels of the output image.
The output image is strongly pixelized if we do not interpolate and use for its pixels simply the color of the input pixel that lies closest to the transformed coordinates. Here is an example:
This is poor and we get a marked improvement with linear interpolation:
But traces of the pixels stay. We still see some lines at the boundaries of the interpolation segments. With cubic interpolation we can remove these artifacts:
Now the pixels have really disappeared and we get a blurred image as expected from the strong magnification. All artefacts seem to have disappeared. The Mitchell-Netravalli kernel gives a slightly smoother image:
Note that the images here are strongly exaggerated and in practice you would have only small parts of a high resolution print that are magnified like that. But to get high quality we should use cubic interpolation.