Given set of points in $3D$ ( $X = (x_1, x_2, x_3)$, $Y = (y_1, y_2, y_3)$ ), how can I fit transformation from $X$ to $Y$?
As far as I know this is called projective transformation. Here is example of $X$ and $Y$. Blue and red lines in $X$ are parallel, but they are not parallel in $Y$.