I have a hopefully rather simple question: I want to experiment with different geometries of flowlines and equipotential lines in a 2-Dimensional space in order to fit experimental data. Flow lines and equipotential lines are always orthogonal to each other, and hence form a basic rectangular grid in their most simple setup. I know want to transform this simple, basic rectangular grid to different shapes while preserving the angles between flow lines and equipotential lines. A bit like this, imagine the vertical lines in the non-transformed image are equipotential lines, while the horizontal ones are flow lines:
My online research so far has led me to the so-called 'conformal mapping' which seems to do exactly what I want, i.e. transforming the structure of the rectangular grid while preserving the angles between the grid lines.
The topic appears to be quite complex, however, so before I potentially invest days to learn the mechanisms behind it only to find out that it will not solve my problem, I wanted to ask you, who are most likely more familiar with this technique, whether what I have in mind is actually mathematically feasible:
Is it possible to find the underlying equation/transformation mechanisms for conformal mapping of all points in the grid, if I know the old cartesian coordinates and define their respective new cartesian coordinates of the four edge points of this rectangular grid?
edit: Mind, I do not require you to solve the issue, this would probably lead too far. I just want to know whether it is generally possible.