update: July, 12, 2011

Summary

The Diagonal Method (DM) is a “method” of composition that I accidentally discovered in May 2006, doing research in relation to the (in photography known) theory of composition called the “Rule of Thirds”.
The Diagonal Method is not a (contrived) theory, but a discovery. It is not derived from the Golden Section or the Rule of Thirds.

The technical side of Diagonal Method is rather simple: each 90 degree corner of a work of art can be divided into two angles of 45 degrees. This dividing line is actually called the bisection line (a bisection is a line that divides an angle into two equal parts). It appeared that artists were intuitively placing details which they found important, on these lines with a deviation of max. 1 tot 1,5 millimetre.
I called this the Diagonal Method because these lines are also the mathematical diagonals of the two overlapping squares within a rectangle. People seem to look through pictures in the same way as the artist did; they follow the bisection lines or Diagonals. 
 

The difference between the existing theories of composition (the Rule of Thirds and the Golden Section) is that the Diagonal Method is not concerned with making “good” compositions, but with finding details which are important to the artist in a psychological or emotional way. On this level the DM is completely subjective. It has nothing to do with placing lines or shapes in a certain location within a frame with the intention of getting a “better” composition. So we can use the DM to find out what the interests of the artist were. The positioning of these details is done in an unconscious manner. That’s why the DM is so exact.
Of course it is also possible to crop a photograph afterwards in such a way that details which are important to the photographer, are placed somewhere on these Diagonals.

The Diagonal Method

 

The 35 mm photographic frame is a rectangle with a ratio of 2:3. Within this rectangle you can draw two squares that overlap each other (see fig. 1). I discovered that artists like Rembrandt, famous photographers, but also amateur photographers, often were placing details like eyes exactly on these Diagonals.

fig. 1

To test this I used a transparency with just one bisection line (see fig. 2).

Because of the exactness of the DM it is necessary to align the corner of this sheet exactly with the four corners of the work of art that you want to test. (It is not possible to see whether a detail lies on a Diagonal, without such a sheet.)
Any position on the four diagonals could have been used to place details by the artist. The dots on the lines in fig. 3 could be such spots.

fig. 2

Details are often lying on the Diagonals with a accuracy of 1 to 1,5 millimetre on a A4 size picture. Precisely this precision was the decisive factor in my research. If the Diagonal Method would have been just as inaccurate as the Rule of Thirds, then I just would have thrown all my findings in the dust bin.
I searched for a theoretical explanantion of the DM in books of art about composition but I did not find anything useful. Rudolf Arnheim mentions the square and “force lines” and “force fields” in his classic “Art and Visual Perception” but it is rather strange that he does not say a word about rectangular art. He only did research on square works of art.

                                          fig. 3
                               
Brian Thomas tested 98 famous paintings in his work “Geometry in Pictorial Composition” and found a lot of geometric forms in these works but he did not reach a conclusion concerning a particular method which was used more often than others.
My opinion about this kind of research is that it is unlikely that one would find anything conclusive. If I would not have done visual experiments, I also would have found nothing interesting. I did not start with a theory, but with looking and experimenting. Also it was not my goal or intention to look for geometrical forms in art or to find a new compositional method. (The experiment itself will be explained on this website later on.)

For me the important thing was that the DM actually worked, whereas the Rule of Thirds and the Golden Section seemed rather off. (Nevertheless, one can use the Rule of Thirds to avoid placing small and middle sized subjects in the centre of the frame. But there is no exactness. Also, there are no studies in which the theory of the Rule of Thirds is proven.)
The biggest difference between the DM and the Rule of Thirds is that people do not consciously place any details like bricks or lamp posts on certain positions in the frame in the hope that the composition will get better, but unconsciously search for and place emotional and/or pychological important parts and place these (without a conscious intention) on visually strong positions. 

The very first photograph I tested was a portrait made by one of my students (fig. 4), and I was surprised, not to say shocked, that the Diagonal went right through the centre of the pupil of the eye (yellow line).

                                          fig. 4 (the cross point belongs to the Rule of Thirds)

Conclusions 

-  We can discover hidden points of interest in works of arts.

-  All positions on all four diagonals are possible for placing details.

-  In landscapes and architecture there are often no important details so the DM does simply not apply.

-  The DM is mostly found in portraits and social photography.

-  The DM can be used to crop photographs afterwards.

-  Sometimes lines that are formed by things like arms are on or parallel to the  Diagonals.

-  In advertisements small things like watches or the eye of a model are often lying on the Diagonals.

-  Details which are important to the artist are lying almost always within 1 mm on one or more Diagonals

 
Photographs and paintings


Photograph by Spencer Platt, World Press 2006 winning photo

                            Four Diagonals are crossing the eyes of the four persons in the car.

On the right is a photograph by Rankin ("Feeling Hungry") with a skinny girl, in fact so skinny that her clothes have to be held together with clamps. It is not impossible that she suffers from anorexia. It is therefore strange that she is about to eat a gigantic slab of chocolate. (You could also say that she has not eaten for a couple of days and that she is now "feeling very hungry". But chocolate would not be the first thing you would eat except when you have no choice.)
The moment of eating is nevertheless important and is emphasized by the Diagonal from the top left corner: the Diagonal is exactly crossing the point between her teeth and the chocolate slab. Notice that the Diagonal is not crossing her left eye: the distance between her eye and the Diagonal is 5 millimetre. Often the Diagonal is crossing right through the pupil of an eye, but not in this photograph because the eye is not the most important part. The exactness of the
Diagonal Method is stunning.


Photograph by Rankin (Courtesy by Rankin Photography)

 

 Diagonal Method                                                       Rule of Thirds
 
Above: Nicolas Cage in an advertisement for Mont Blanc watches. On the left we see the Diagonal method: the Diagonal from the top left corner is crossing his eye and the Diagonal from the bottom right corner is crossing the centre of his watch. Apparently Nicolas Cage is as important here as the watch.


 Diagonal Method                                       Rule of Thirds

Above: in these photographs, the person is not important, only the camera is important.
The Diagonal from the bottom right corner is crossing the centre of the lens of the camera, so attracting attention.




Diagonal Method                                                   Rule of Thirds

In the etching on the left by Rembrandt, "The Tax Receiver" (or "Weigher of Gold"), we can see three Diagonals crossing the three most important details:
1. One from the top left is crossing the little bag with money),
2. One from the top right is crossing the right eye of the main figure,
3. One from the bottom right is crossing the forefinger and thumb holding the pen.

 

 Diagonal, Rule of Thirds and the Golden Section          Diagonal method

Left: the painting "Ginevra Benci" by Leonardo da Vinci, with three methods:

1. The Diagonal Method (blue line that crosses the left eye).
2. The Golden Section (yellow lines).
3. The Rule of Thirds (green dotted lines).

On the right (above), the Mona Lisa by Leonardo da Vinci.
The Diagonal is crossing the lips. That's what we would expect in the Mona Lisa painting because the smile
is more important than the eyes.

Some conclusions after four years of research: a new way of looking at pictures:

         When working with the Rule of Thirds and the Golden Section we have the habit of thinking that the composition would get better when we place certain objects or lines on particular spots within the frame.
This vision leads to two problems: a. this theory is not proven and 2. many photographs that are considered as very good by the public in general do not follow this theory.
The Diagonal Method cannot be viewed in the same manner because it is not a theory of composition. One important difference is that (when taking the photograph) the DM is used unconsciously (that is why it is so accurate: within one millimetre from the lines). Another difference is that the way artists choose and place details (on the DM lines) is very subjective: it is the result of their whole character and way of living. (Apparently both artists and viewers of works of art are looking at frames and pictures along the bisection lines (the DM lines), that is why the DM works.) 

       To view this as a matter of composition only, would mean that we are trying to put the theory of composition on the Diagonal Method. But first of all the DM gives us insight in the interests, character and motives of the artist (see also the article by Fleur Jongepier: Articles and bibliography).
This is a new vision because only certain subjects are interesting or important. In the old way, any line or detail from any subject could or should be placed on a particular spot, to get a better composition. But with the DM, a better composition is not the goal or purpose. Details on the DM lines become more important but this is not the same as a better composition. So we have to change our view towards the concept of reading pictures and photographs in a psychological way, and away from the concept of objective and fixed matrixes with lead to good or bad compositions.

         At the same time, having said this, people apparently see, notice, details along the bisection lines sooner than details in other places of a photograph, painting or drawing. This means that when more important details (in general, people would agree that for instance, eyes are more important than bricks in a wall) do not lie on the bisection lines, that work of art would seem "not right", confusing. That is when cropping comes "into the picture". While cropping, one can of course choose which detail must be important and which not. So the subjective aspect remains. I received reactions from different persons who said that after cropping, their photographs looked more "pleasing". (Alls this applies mostly to works that have persons in it and where the framing of the bigger subject is not more important than placing the details, as is said before.)

Edwin Westhoff

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The Diagonal Method is registered on October 23, 2006 in Washington (Library of Congress) under
number Txu-328-140 and in Amsterdam (Merkplaats) under number 4.620517.1, June, 23, 2006.

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