Interpolation: calculate correction based on 3D table

Question

This is just for my personal interest and a follow-up to question from Linear interpolation: calculate correction based on 2D table

How would calculation look like when line and correction table use three dimensions - what kind of interpolation and formula would have to be used?

Thanks!

Answer 1

It would be the same formula as in the original thread, just three dimensions would be used; the approach would be called tri-linear interpolation, as linear interpolation would be used along all three axes. More information can be found on Wikipedia, where also an illustration visualizes the approach. The underlying formula is basically the same as for two dimensions, except that one additional step of interpolation is used.