The Diagonal Method is discovered by Edwin Westhoff
The Diagonal Method (DM) is a “method” of composition that was accidentally discovered in May 2006 by the Dutch photographer and teacher of photography Edwin Westhoff, while 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 milimetre. 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 concerning content. Such a detail can be meaningful in a narrative, 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. The positioning of the detail itself, (and the reconizing of these by the onlooker), is more objective, meaning that this is done in a purely visual or "automatic" manner.
So the conclusion is that the Diagonal Method is a combination of subjective and objective factors (although both are done unconsciously).
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. Sometimes people tell me that their work of art or photograph has become better, using the Diagonal Method, but this does not necessarily mean (just) the composition, but rather the whole impact and purpose of the picture, because the onlooker immediately sees the most important details or parts of the photograph or picture, as intended by the artist.
There is a most important difference between the DM and the Rule of Thirds. Concerning the Rule of Thirds, people do consciously place subjects like horizons and lampposts on the lines of the Rule of Thirds. I know, because many of my students tell me that they do this. Most of the time these parts are not particularly important, concerning content. On the other hand, photographers (unconsciously) place details on the lines of the Diagonal Method which have an important meaning in the narrative of the photograph, or are important to the photographer in a psychological or emotional way (and are immediately seen by the viewer). This is the least understood aspect of the Diagonal Method, but at the same time the most important one.
It is, like someone from Vietnam told me, a "new paradigm in composition". Using the Diagonal Method, one can detect for instance, things in which the artist was interested in or, see in a quick glance the most important details of a photograph or painting. This means that compositional arrangements are linked with content. This is new. The Rule of Thirds and the Golden Section are theories, and the theory is that the composition will get better if you place subjects on certain lines or cross points. Clearly, the narrow definition of the word "composition" is meant in these cases (see the section below). In addition,
I found in my research that the Rule of Thirds and the Golden Section "do not work", meaning that one can place subjects on certain lines, but this does not necessarily lead to a better composition (in most cases, it leads to a worse composition, because the overall intuitive framing of the picture is violated by a rational decision. The theories of the Rule of Thirds and the Golden Section are contradictory to rule No. 1 in composition: "The overall intuitive framing of a picture is always more important then the placement of details".
With the Diagonal Method, the overall intuitive framing and the placement of details are done at the same time, because both are done unconsciously. So rational manipulation cannot destroy the total composition. (Rational manipulation is sometimes necessary but the combination of intuition/feeling and thinking is always paramount in getting good compositions.) Therefore it is important that the placement of details is done unconsciously, as is the case with the Diagonal Method. (Of course, when a detail is just one milimetre "off", one can use the cropping tool "Diagonal" in Lightroom to correct this.