Find Out Projection Matrix for Oblique Projection
To find out projection matrix for oblique projection, we want to find out the direction vector d. Because vector PP' and vector d both contain the same direction. Hence, PP'=d
So, x'- 0=d_{1}= f.cosθ
y'- 0=d_{2}= f.sinθ
z'-1=d_{3}
Since z'=0 on the xy-plane, d_{3} = -1,
Because, Oblique projection is a particular case of parallel projection, hence, we can transform the common transformation of parallel projection for Oblique projection as given:
Here, f=foreshortening factor, that is the projected length of the z-axis unit vector. When β is the angle among the Oblique projectors and the plane of projection so,
1/f=tan (β) , that is f= cot(β)
θ=angle among the projected line along with the positive x-axis.