Walking down a corridor

eye = {0, 0, 0};
screen = {1, 0, 0};
screenU = {0, 1, 0}; screenV = {0, 0, 1};
screenDim = {1, 1};
Project[p_] := Module[{u, v, n},
  n = Norm[screen - eye]/(Abs[(screen - eye).p] + 0.001);
  u = p.screenU*n;
  v = p.screenV*n;
  If[Abs[u] < screenDim[[1]]/2 && Abs[v] < screenDim[[2]]/2 &&
    p.(screen - eye) > Norm[screen - eye],
   {u, v}
   ,
   False
   ]
  ];
move[p_, t_] := p + {-t, 0.05 Sin[2 Pi t], 0.2 Cos[2 Pi t]};
Manipulate[
 corridor =
  Table[Map[{i, 0, 0} + # &, {{0, -1, 2}, {0, -1, -1}, {0, 1, -1}, {0,
       1, 2}, {0, -1, 2}}], {i, -10, 100}];
 beams = Table[
   Map[{i, 0, 0} + # &, {{0.5, -1, 1.5}, {0.5, 1, 1.5}}], {i, -10,
    100}];
 proj = Select[Map[Project[move[#, t]] &, corridor, {2}],
   And @@ (VectorQ /@ #) &];
 projbeams =
  Select[Map[Project[move[#, t]] &, beams, {2}],
   And @@ (VectorQ /@ #) &];
 Graphics[{
   Table[{GrayLevel[i/100], Line[proj[[i]]]}, {i, Length@proj}],
   Table[{GrayLevel[i/100], Line[projbeams[[i]]]}, {i,
     Length@projbeams}]
   }, PlotRange -> 0.5],
 {t, 0.01, 1}]