(*^

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          Looking at a Three Dimensional World with Two Dimensional Eyes

The following cell illustrates Mathematica  notation for vectors and the dot product and how the magnitude of a vector can be defined using the dot product.  Evaluate it now.
;[s]
6:0,1;72,0;105,2;116,0;232,3;247,0;249,-1;
4:3,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,0,0,0;1,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
Clear[U, V]

U := {1, 2, 3}
V := {3, 4, 5}

U.V

Mag[x_] := Sqrt[x.x]

Mag[U]
:[font = special1; inactive; preserveAspect; ]
The following cell illustrates how Mathematica  can be used to find the point where two lines "intersect" even when they don't exactly intersect because of measurement error.  Evaluate it now.
;[s]
5:0,0;35,1;46,0;176,2;191,0;193,-1;
3:3,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
Clear[V, G, L, S, Ft, Fs, P, answer]

V = {0, 0, 105};       (* Viewpoint                   *)
G = {3.20, 4.20, 0};   (* apparent location on ground *)
L = {-105, 0, 105};    (* Light source                *)
S = {8.3, 4.3, 0};     (* Shadow                      *)

(* The next lines define the function f(s, t)         *)

P[s_, t_] = t L + (1 - t) S - (s V + (1 - s) G);

F[s_, t_] = P[s, t] . P[s, t];

Ft[s_, t_] = D[F[s, t], t];  (* partial F / partial t *)
Fs[s_, t_] = D[F[s, t], s];  (* partial F / partial s *)

(* The next line find the values of s and t that make *)
(* both partial derivatives zero.                     *)

answer = 
   Solve[{Ft[s, t] == 0, Fs[s, t] == 0}, {s, t}];
   
(* The next line finds the point half-way between the *)
(* closest points on the two lines.  This is the      *)
(* that we seek.                                      *)

0.5 * (t L + (1 - t) S + s V + (1 - s) G) /. answer
;[s]
19:0,0;61,1;94,0;118,1;151,0;175,1;208,0;232,1;265,0;267,1;324,0;436,1;463,0;493,1;520,0;522,1;635,0;701,1;871,0;925,-1;
2:10,12,10,Courier,1,12,0,0,0;9,12,10,Courier,1,12,0,0,65535;
:[font = special1; inactive; preserveAspect; ]
In the next cell we first define the points and rods for the pyramid used as an example in this module.  Then we define a procedure  LookAt  that draws the picture taken by a camera from a particular viewpoint.  Evaluate the next cell now and then look at this pyramid from various different points-of-view.  Then use the same ideas to draw the pictures taken by a camera looking at your Tinkertoy house from various points-of-view.  Use your own measurments.
;[s]
5:0,0;133,2;139,0;212,1;458,0;460,-1;
3:3,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,65535,0,0;1,13,9,Times,1,12,0,0,0;
:[font = input; preserveAspect; ]
Clear[AA, BB, CC, DD, TT, Points, Rods]

AA = {-1,  0,  0};
BB = { 1,  0,  0};
CC = { 0,  1,  0};
DD = { 0, -1,  0};
TT = { 0,  0,  1};

Points = {AA, BB, CC, DD, TT};

Rods = {{AA, CC}, {CC, BB}, {BB, DD}, {DD, AA},
        {AA, TT}, {BB, TT}, {CC, TT}, {DD, TT}};

LookAt[theta_, R_, H_] :=
  Block[{u = {-Sin[theta], Cos[theta], 0},
         v = {-H Cos[theta]/Sqrt[H^2 + R^2],
              -H Sin[theta]/Sqrt[H^2 + R^2],
               R/Sqrt[H^2 + R^2]}},
        Show[Graphics[{PointSize[0.02],
         Join[
          Table[Point[{u . Points[[k]],
                       v . Points[[k]]}],
                      {k, 1, Length[Points]}],
          Table[Line[{{u . Rods[[k]][[1]],
                       v . Rods[[k]][[1]]},
                      {u . Rods[[k]][[2]],
                       v . Rods[[k]][[2]]}}], 
                     {k, 1, Length[Rods]}]
         ]}],
          AspectRatio -> Automatic]]
          
LookAt[Pi/8, 100, 75]                                      
^*)