Window's Vista

This week, Futility Closet had a post about the Vista Paradox. The paradox is connected to an effect I discussed before, where the angular nature of our vision causes objects to move in unexpected ways. In this case, we're viewing a distant tower through a window. As we approach the window, the window takes up proportionately more of our vision that the tower, causing it to appear to shrink. I tried making an animation of this to test my understanding:

As expected, the tower (red) changes very little, while the closer window (blue) expands rapidly. Initially, I was concerned with how the window's proportions appear to change, but I checked with my mother Sally, and she gets the same expression I did. There still may be an error in my implementation though.

After reading the Futility Closet post, I was reminded of an effect often used in filmmaking called a Dolly Zoom: The camera moves forward (backward) while zooming out (in), causing the edges of the frame to stay where they are, but the center to contract (expand). The scene that always comes to my mind for this is one from Fellowship of the Ring:

makeagif

Using the same framework as above, I plotted a series of rings at different distances, but the same size. Then I moved the camera toward them, while fixing the edges of the plot to the nearest ring:

This effect makes the center appear to shrink, the opposite of the motion in the film, but exactly the same technique. It's neat to see this artifact of human perception appear in both architecture and filmmaking!