Definitions

To compute the projection we need only project each vertex of the polygon projecting the shadow.

Vertex s = [s_x s_y s_z 1]^T casts a shadow from light source l = [l_x l_y l_z l_w]^T onto the shadow projection plane P at the point p = [x y z w]^T. The equation of P is ax+by+cz+d=0.