I thought I’d muscle in on Swans on Tea’s turf for a post and discuss an interesting optical illusion that is based just as much on optics as on the idiosyncrasies of the eye itself. While stumbling through StumbleUpon.com, I found an interesting collection of images at 2Loop.com showing ‘3D Painted Rooms’. An example of this is shown below the fold, from 2Loop…

The first image shows the room as it is actually painted, a rather seemingly scattered collection of curved lines. When looked at from a particular point in the room, however, the lines ‘magically’ appear to form a collection of circles suspended in midair!

The images on 2Loop are referred to as ‘3D Painted Rooms’, though the title is a little misleading, since the images are not three-dimensional; rather, the illusion is created because our eyes only take two dimensional projections of things we see. Depth is only determinable by seeing the same scene from slightly different positions, allowing one to deduce distance by parallax. For humans and other creatures with binocular vision, parallax is automatically provided by the presence of two eyes, each of which gives a slightly different image. Our eyes can be fooled, however, when at a particular point of view objects at different distances superimpose to make an image of a single recognizable object.

These images immediately brought to mind an artist named Gillian Brown, who has made much more sophisticated pictures than the simple geometric shapes shown above. An example of Gillian’s work, taken from her website, is shown below (“Untitled (Classroom)“):

The photo on the left shows the illusion as it appears from its one ‘special’ observation point. The photo on the right shows how the actual image is painted across the walls, floor and real (three-dimensional) desk.

This particular art form is known as anamorphosis, and developed from early artistic studies of perspective, which in turn were realized through the development of the camera obscura.*

A camera obscura is simply a dark box or chamber which possesses a small hole in one wall. If the hole is sufficiently small, an inverted image of the outside of the box will appear on the wall opposite the hole. This can be readily understood using geometrical optics: the pinhole in the box only allows one light ray from any point on an object outside the box to penetrate inside. The result is a 1:1 mapping of ‘object points’ on the outside of the box to ‘image points’ on the inside, as illustrated below:

This image-forming behavior has been observed and understood since at least 1020 A.D., when Ibn al-Haitham of Egypt performed experiments with the camera obscura, though basic observations go back to the time of Aristotle and perhaps further.

One can see that a similar process actually goes on inside a person’s eye, with its small pupil, though the inner workings of the eye are far more complicated. However, the rays of light that we see from an object necessarily converge on the pupil in the same manner that they converge on a camera obscura. Because of this, if we were to somehow record the image on the inside of the camera and then look through the pinhole used to generate it, we would see an image that would have the proper perspective of a three-dimensional object!

In 1425, Renaissance architect and engineer Filippo Brunelleschi developed just this technique for creating paintings with proper visual perspective. He created paintings with a pinhole in them which, when viewed through a mirror, reproduced exactly a scene as viewed from a particular location. Others developed this idea into proper camera obscuras. A number of artists created ‘peep show’ boxes, in which light was allowed into the box through the ‘peep hole’, creating an inverted image in the box. The artist could paint the image as it appeared on the inside of the box, and then patrons could view the ‘three-dimensional’ image through the peep hole. (A little shout-out to the Dutch: one maker of such boxes was Samuel Van Hoogstraten, a contemporary of Vermeer.)

It is to be noted that the image does not have to be projected on a flat surface! All walls inside the camera obscura, as well as the bottom and top of the box, will be illuminated, and all those surfaces will contribute to the image. The next logical step is to ‘project’ an image on an irregular or angled surface, and this is exactly what is done by Gillian Brown. Leonardo da Vinci is credited with the first anamorphic drawing, a child’s face which must be viewed from an extreme angle. Other artists incorporated the technique; Holbein’s painting The Ambassadors, for instance, contains a highly distorted skull which must be viewed from an extreme lower right corner to see it in proper perspective.

So how does one create an anamorphic image? We’ve already mentioned one method: use a camera obscura to project an image onto a surface, and paint the surface. If one views the image from the original obscura hole position, the image will appear as the original.

Another technique was used by artist Fra Andrea Pozzo in his painting of the curved ceiling in the church of St. Ignazio in Rome. Starting with a small flat preliminary painting, he ‘scaled up’ by making grid lines across the small picture. He hung a net flat across the length of the curved ceiling, and ran strings from the ‘fixed point’ (obscura hole) through the net to points in the ceiling. This allowed him to ‘map’ the flat picture to the curved ceiling.

I’m thinking of trying to make a small-scale anamorphosis, now that I’ve been researching this. I’ll keep people informed if I succeed! In the meantime, I should note that free software exists for performing transformations on your favorite pictures.

One more artist should be looked at for his amazing anamorphic designs: street artist Julian Beever. My favorite is depicted below:

Remember, you’re looking at a flat surface that has been drawn on!

Update: A little historical note: Camera obscuras were apparently popular in the 1870s in the U.S., and numerous parks constructed camera obscura buildings, which are now lost.

*For a good discussion of the history of one point perspective and camera obscura, see the magnificent book, Pinhole Photography, by Eric Renner, and his wonderful website. Much of my understanding of this subject comes from these sources.