Mathematical description of an Oblique projection onto xy-plane
In order to expand the transformation for the oblique projection, identify the Figure. This figure explains an oblique projection of the point A (0, 0, 1) to position A'(x',y',0) on the view plane (z=0 plane). The direction of projection i.e. d=(d1,d2,d3). Oblique projections to xy-plane can be identified by a number f and an angle θ. The number f, termed as foreshortening factor, specifies the ratio of projected length OA' of a line to its actual length. Any line L perpendicular to the xy-plane will be foreshortened after projection. θ is the angle that the projected line OA' of a specified line L perpendicular to xy-plane is makes along with the positive x-axis.