Consider a uniform 2D grid, where each $(x,y)$ value on this grid has a corresponding value. So, if I want to find the value, $v$ (unknown) of a point that exists at some arbitrary co-ordinate $(x,y)$ (known) that exists between grid values, then I can use bilinear interpolation to find $v$, using say, the 4 closest grid points to the point $(x,y)$.
However, what if I am given $(x,y)$ as before, AND also given $v$, but I now want to "interpolate" the value of $v$, INTO the 4 closest points on the grid. That is, I want to simply figure out how much $v$ contributes into the 4 grid points closest to it.
What is that called? Is it also called "interpolation", or does this go by another name?
This only makes sense if there is a unique $z=x+iy$ corresponding to a given $v$, and then it is interpolation of the inverse (complex or vector-valued) function.