How to implement point interpolation in 3D?

Question

Mathematics

The point is that I'm a little confused and would be very grateful to those who will help me with this problem :D
There are various methods for interpolating points in a two-dimensional coordinate system.
That is, if the input data are the coordinates of points on the X and Y plane, then one of the methods can be used to interpolate these points:
1. Piecewise linear interpolation.
2. Piecewise-quadratic interpolation.
3. Cubic splines.
4. Lagrange polynomial.
... And so on ...
Now imagine that the input is three-dimensional coordinates X, Y and Z.
As far as I understand correctly, there are three main methods of interpolation.
1. Nearest neighbor method.
2. Bilinear interpolation.
3. Bicubic interpolation.
That is, if three-dimensional coordinates are given, one can use, for example, bicubic interpolation in order to obtain some intermediate values ​​of the function f(x, y).
However, here is the question. Recently I came across an article about "Trilinear interpolation", link here
The question is, what does this type of interpolation do? As I understand it, this is an interpolation for the four-dimensional case ... Is this true?
Many thanks in advance for your replies!

Answer 1

Asking the right question is half the answer

Interpolation is done for a function over a certain set of its values ​​​​and arguments (often used when either the definition of the function is not known or its calculation is more expensive than obtaining a certain value with sufficient accuracy).
This method of "Trilinear interpolation" can be used, for example, to obtain the color (or any other numerical characteristic) of a point in three-dimensional space.