HalfLine to draw lines "to infinity"

Question

I'd like to draw a simple figure illustrating geometric perspective (so-called "central-point perspective") in which perspective lines on two cubes are extended "to infinity," where they meet.

Here is my first attempt:

Graphics3D[
 {
  Translate[Cuboid[], {-3/2, 0, 0}],
  Translate[Cuboid[], {1/2, 0, 0}],
  Red, Thickness[0.02],
  Line[{{-1/2, 0, 1}, {-1/2, 20, 1}}],
  Line[{{-1/2, 0, 0}, {-1/2, 20, 0}}],
  Line[{{1/2, 0, 1}, {1/2, 20, 1}}],
  Line[{{1/2, 0, 0}, {1/2, 20, 0}}]},
 Boxed -> False,
 ViewPoint -> {0, -.9, .05},
 PlotRegion -> {{0, 2}, {0, 50}, {0, 2}},
 ViewAngle -> 20 \[Degree]]

As you can see the red lines (by design) only extend a finite distance back. (I even had difficulty drawing them longer and re-setting the PlotRange.)

I'd like to draw HalfLine which, in theory, should extend to infinity, where all four red lines meet at the vanishing point.

Alas, I can't seem to make that work.

Answer 1

I think you would like something like this:

Graphics3D[{Translate[Cuboid[],{-3/2,0,0}],Translate[Cuboid[],
{1/2,0,0}],Red,Thickness[0.02],
HalfLine[{{-1/2,0,1},{-1/2,20,1}}],
HalfLine[{{-1/2,0,0},{-1/2,20,0}}],
HalfLine[{{1/2,0,1},{1/2,20,1}}],
HalfLine[{{1/2,0,0},{1/2,20,0}}]},Boxed->False,ViewVector->{{0,-5,1+1/2},
{0,-1,0.5}},ViewAngle->40Degree,PlotRange->{{-150,150},{-150,150},{-150,150}}]

giving:

Note the use of ViewVector which is in coordinates of the plot, rather than using ViewPoint which is in non-dimensional units based on the dimensions of the plot. Furthermore, note that PlotRegion is changed to PlotRange.