Since the images of points following this parametrization travel at constant speed, we can now find the vanishing point of the images. You can see a particle at A' moving down at A'-B' units per second and a particle at C' moving down at C'-D' units per second by clicking "Animate Points" in the applet. These particles reach their common vanishing point at the same time. Since we have found the vanishing point for horizontal lines, we know the vertical position of the artist's viewpoint. You can display the principal vanishing point V by clicking on "Show Vanishing Point".
At the same time, we can find the viewing distance. The image of a diagonal of the square is given by the line segment from C' to B'. We already know the value of t0, since we know how long it took the previous particles to meet. The image of a point starting at C' and moving along the diagonal of the square will take the same amount of time to reach its vanishing point. Imagine a particle moving up from C' at a constant speed of B'-C' units per second - after t0 seconds, that particle reaches its vanishing point as shown on the applet. You can display this vanishing point W by clicking on "Show Viewing Distance".
We now know the artist stood facing V at a distance from the canvas equal to the distance between V and W. If you click "Show Subject and Viewpoint", you will see a circle centered at V passing through W with the artist's viewpoint shown in black. You will also see how the original square room can be recreated from the painting and the viewpoint.