Interpolation

In elliptic geometry the mapping shrinks output pixels.
Many output image pixels go to the same input image pixel.

With simple nearest neighbor sampling they all get the same color.
The output image has big pixel blocks.

Bi-linear interpolation gives much better results. Blocks disappear.
Linear artefacts appear at maxima and minima of luminosity.

Bi-cubic interpolation eliminates these linear artefacts. Mitchell-Netravali with a separable kernel is fast. Only the hard mirror lines make some "artificial" lines. Uses 16 input image pixels for one output image pixel. Expensive.

Efficiency

Use the combined Lyapunov coefficient of all three transformations:

- If much larger than 1 use averaging.

- Near 1 use nearest neighbor lookup.

- If much smaller than 1 use bi-linear interpolation.

- If very small use bi-cubic interpolation.