Lets assume we are mapping one face of earth. we place a plane touching the earth at 0 lattitude and 0 longitude. Now we take the plane of projection. suppose that we expand the projection unevenly. The small projectional area of a certain lattitude and longitude is expanded by a factor which is the function of it's lattitude abd longitude. Evidently we won't get a circular projection. But how do i find the shape/equation of the projection if i know the expansion factor as a function of lattitude and longitude?