1. the shape of the light source (L)
2. the shape and the width of the opening of the occluder (W)
3. the orientation of A and B. I've assumed that they are parallel but according to your question that isn't necessary
4. the distance between L and W (d)
5. the distance of the light from the plane of the shadow (D)
I've attached a rough sketch of the (simplified) situation.