I am trying to derive the formula for perspective correct texture interpolation on my own while implementing my own software rasterizer (projecting an arbitrarily rotated triangle in camera space on the projection plane and rasterize its texture). Sure, the solution is that one can interpolate the inverse of z in the projection plane (or screen space). However, given the assumption that I do not know that yet, all I came up with so far is the following:
My first step was to formulate the problem (maybe my problem statement is the problem?) and visualize it. Then I tried to find some relations between the variables.
What I am now looking for is some hint / observation that leads to right direction (not the solution).