# Fisheye pictures

In a room in Pembroke College, Cambridge, hangs a round picture in a square frame.

On another wall of the room I found a similarly curious picture:

(We were able to stay for a couple of nights in this room because I was once a student at this college.)

The first picture seems to be of a green lawn surrounded by buildings and then by sky; the other, its converse, sky surrounded by buildings and then by grass.

It took a little studying to be sure that the buildings are those surrounding the Old Court of the college.  I could discern the great hall, the chapel, and other features.  The lawn, closely mown in the fashion of ancient colleges, is in fact square; its corners are obtusified by the perspective.  The pictures are of the same space, looking down and up, vertically.  In one, the center is the nadir, the point below you; in the other, the view is straight up, to the zenith, or point overhead.  In both, the field of view is more than 90 degrees in radius (more than 180 degrees in diameter).  Here’s my crude cross-section of the upward view:

For the downward view, flip the blue outline.

The views are like those of a super-fisheye camera, taking in a bit more than a hemisphere.  If the field of view were only 180 degrees, the upward-looking eye would see the upper parts of the buildings but not the lowest parts or any of the grass.  (With the peripheral vision of both eyes included, I have a slightly more than 180° field.)

The pictures bore only a small indecipherable monogram.  I was later able to find out that they, together with similar paired pictures of the Ivy Court and the Library Lawn, had been offered to the college in 2007 by Edward Hill, and I was amazed to find that he is only yards from where I at present live, and I have yet to visit his gallery.  Also to ask him whether he based his drawings of the buildings on photography or sketching.

I was interested in the pictures because they reminded me of the projections I use for plotting astronomical charts. Here is one way of showing the sky,

centered on the zenith for a certain place and time (latitude 45 north, sidereal hour 6 to put Orion on the meridian, though it doesn’t really matter).

The chart’s radius is 90 degrees from the zenith to the horizon, with another 10 degrees to show “grass” on the planet.  It’s simplified in that I’ve shown only few stars and no Milky Way or ecliptic or other details, but have included the constellation boundaries because they serve to give you a feel of how shapes get transformed by the mapping projection one chooses to use.  I want to remark on mapping projections, but they need an irreducible minimum of explanation and I will do so in a further post.

The chart and the “up” picture of the college courtyard correspond: the one could have old buildings around its circumference, the other could have constellations instead of clouds across the middle.  And with the same projection, centered on the nadir instead of the zenith, one could map the starry sky as a band around a shrunken Earth.

Indeed you’ve seen pictures like this.  Some (I’ve seen charming elaborate examples though I can’t remember where) are of gardens and other scenery on which the viewer is looking down from a modest height, and the landscape spreads out with foreshortening, perhaps to an encircling sea and then the encircling horizon.  But others are photographs from nearby space, of our whole planet.  All are like charts, from increasing height, centered on the nadir.

And then there are Escher’s woodcuts of “planetoids.”

## 5 thoughts on “Fisheye pictures”

1. Hilary Naylor says:

obtusified! That’s a new one for me.
thanks
Hilary

1. To quote my reply to a friend who also raised an eyebrow at “obtusified”: “I’ve given way to letting myself coin neologisms when I see they’re the shortest way to be clear.”

I could have written: “The lawn… is in fact square, but as you look out at a low angle toward its corners they are changed by perspective from right angles to angles that are extremely obtuse, that is, close to 180 degrees, thus almost forming parts of a circle.” But I felt it not only saves verbiage, but even is more quickly understandable, to invent a word that possibly the language needs and say that the corners are “obtusified”.

By the way, for those who don’t know Hilary, she’s the most useful and patient contributor to an Amnesty International online discussion group, and she always ends her remarks with “Thanks”, thus doing her best to keep the temperature cool.

2. These pictures look very similar to what I think are called “little planet” views. A google image search of the term “little planet perspective” shows many examples. Although I’m not sure, I thought the views were achieved not with an expensive fish-eye lens, but via image manipulation software of many normal digital images stitched together. Several of them have been showcased as the Astronomy Picture of the Day from time to time. They are very captivating!

3. Anthony Barreiro says:

Hmm, an interesting coincidence. My recent interest in celestial navigation led to the realization that in order to understand celestial navigation in particular I would need to learn about navigation in general. I’ve just started reading the encyclopedic Bowditch, The American Practical Navigator, and I’ve just finished reading the long early chapter about various chart (map) projections; the advantages, disadvantages, and common uses of each; and the inescapable fact that you cannot make a flat chart or map of a round surface that portrays both angular relationships and proportional areas accurately. Also, some charts and maps will show lines of latitude and/or longitude as straight lines while distorting the lines of shortest distances between two points (a very important consideration in navigation!), while other charts and maps will show those shortest great circle routes as straight lines while distorting longitude and most if not all lines of latitude. I’ll never remember all the details, but it has impressed on me the necessity of understanding whichever chart or map projection you’re using.

1. Anthony Barreiro says:

Whoops. Charts that show great circle routes as straight lines will distort latitude and most if not all lines of longitude. Like I said, I’ll never keep all the details straight in my head!