Anamorphic projection onto the corner of a room

Question

I want to use a router to carve anamorphic projections of polyhedron wireframes onto two adjacent walls of my office. Like this:

In order to do this I need to transfer the positions of the vertices and edges onto my walls. Ideally I would end up with values for the positions expressed as (x,z) and (y,z) that I can transfer directly onto the wall.

Obviously, this question is related to the Rubik's cube illusion and QRcode/shopping trolley questions. However, I found it difficult to translate these examples to my current problem. Perhaps I just need the methodology explained more succinctly and/or in a more general way.

Update

I have managed to define a polyhedron in terms that will work in Dr belisarius' answer,

polyh = Map[
         Polygon, 
         PolyhedronData["RhombicDodecahedron", "VertexCoordinates"][[#]] & /@
         PolyhedronData["RhombicDodecahedron", "FaceIndices"], {1}]

The transform looks like

lin[cam_, obj_][t_] := cam t + (1 - t) obj
s[cam_, obj_] := First@Solve[lin[cam, obj][t][[3]] == 0, t];
tr[cam_, obj_] := lin[cam, obj][t] /. s[cam, obj] // FullSimplify

Graphics3D[
    polyh /. Polygon[x_] :> Polygon[tr[{10, -10, 10}, #] & /@ x], 
      Lighting -> "Neutral", ViewVector -> {{10, -10, 10}, {0, 3, 0}}, 
      Boxed -> True]

(Not quite sure why bounding box is 3D...?)

to create a printable projection,

Framed@Graphics[
   {EdgeForm[{Thick, Blue}], FaceForm[],
   polyh /. (Polygon[x_] :> Polygon[tr[{10, -10, 10}, #] & /@ x]) /. 
    Polygon[x_] :> Polygon[Most /@ x]}]

Progress... also, need to define two planes (x,z) and (y,z) rather than (x,y) in transform to emulate the room corner.

Not yet sure how to get from here to marking lines on my wall ready for routing...