Nederlandse versie                                                                                                                           text updated: May 24, 2009 (section 9)
                                                                                                                                                                photographs updated: Sept. 15, 2008


Contents:
Section 1: information about the Rule of Thirds and the Diagonal Method
Section 2: Diagonal Method in Adobe Photoshop Lightroom 
Section 3: examples of cropping with the DM
Section 4: publication of the article in Focus Magazine
Section 5: links to relevant websites about the Diagonal Method
Section 6: examples of the DM in photographs, etchings and paintings
Section 7: original text on Wikipedia English + discussion page (by Eddy Speeder)
Section 8: Article by Fleur Jongepier: "Westhoff's Diagonal Method: Unraveling Photography"
Section 9: Composition in general and the Golden Ratio (under construction) (NEW) 
                1. The problem with using "rules of composition".
                2. The Golden Ratio
             3. Leonardo da Vinci's "Vitruvian Man" and the Golden Ratio (to be continued)
             4. Bottom-up and Top-down perception and the Diagonal Method (under construction).
             5. The problem with "Beauty" (under construction).
Section 10: Quotes from the internet 
Section 11: testsheet with DM
Section 12: bibliography

Summary

The Diagonal Method is a "method" of composition that I discovered in 2006, doing research and experiments in relation to the (in photography existing) rule of composition called the "Rule of Thirds" (see the explanation in section 1). The Diagonal Method is rather simple: each 90 degree corner of a picture is divided in two angles of 45 degrees. The dividing line is called the bissectrice and is also the diagonal of the two overlapping squares in a rectangular picture. It appeared that artists intuitively were placing details which they find important, on these bissectrice lines . People who look at pictures follow the same bissectrice lines and so can see which details the artist found interesting or important. The exactitude of the DM is important: details have to lie on the Diagonals within 1 mm (or at most 2 mm) on a A4 size picture. The DM is not a method which can be applied consciously while taking photographs because artists place details which are interesting to them, on the Diagonals by means of pure feeling and intuition. So there are mainly two applications for the DM: cropping when the photograph is already taken and analyzing photographs and understanding artists better, concerning their motives and interests. 
The DM has no theorethical basis and is not scientifically proven (though several universities are doing research now around the validity of the DM). The DM is discovered solely out of experimental research.

Section 1
Information about the Rule of Thirds and the Diagonal Methode

In almost every book about photography or photographic composition we find the "Rule of Thirds". The 35 mm frame is divided in nine equal parts by drawing lines on one third from every side (see fig. 2). The Rule of Thirds is said to be derived from the Golden Section, actually the Golden Rectangle, since the Golden Section is nothing more than the ratio of 1:1,6180339. In the Golden Rectangle (fig. 1) you can see two horizontal and two vertical lines placed according to the Golden Section from each corner of the rectangle. The Golden Rectangle is more oblong (see dotted line in fig. 2) than the 35 mm frame with a ratio of 2:3,236. 

On the left we see the Golden Rectangle with the four lines drawn
according to the Golden Section ratio of 1:1,618 or 2:3,236.
From the top left corner one diagonal is drawn of the left square.
(see also fig. 3)


fig. 1



In fig. 2 we see the 35 mm frame divided in thirds. The ratio is 2:3,0.



fig. 2



Because the Golden rectangle is more oblong, it does not fit in the 35 mm frame. Apparently the Golden Rectangle (including the four lines) was abandoned and a new ratio was contrived: the Rule of Thirds, which fitted neatly in the 35 mm frame. The construction of horizontal and vertical lines in the Rule of Thirds looks somewhat similar to the lines in the Golden Rectangle, but George Bush and Pamela Anderson also look similar to each other, provided that you don't look too close.

The Rule of Thirds can of course be applied in a very rough way, as a simple method to prevent placing subjects in the middle of the frame.

Analysis of famous photographs and paintings showed however that important details are lying besides the cross points of the Rule of Thirds and not on the crosspoints. I discovered this a few years ago. While designing a new course about composition in the year 2006, I had to know why the Rule of Thirds is so inaccurate so I did some visual experiments. Intuitively I drew four dots somewhere in the corners of empty 35 mm frames, to see whether there was any system to it. To my surprise I found that these dots were on the diagonals of the squares in the frame, which divided each corner of 90 degrees in two parts of 45 degrees. I think that this equal division of 45 degrees is more harmonious than the division you get by drawing the diagonals from corner to corner (because when you use the real diagonals from corner to corner, you will get an unequal division of each corner.)
I called this the "Diagonal Method", but you have to know of course that the diagonals of the squares are meant, and not of the rectangle (you could call it the "Bisection Method", but I thought that this would be a too difficult name).
(Therefore, the diagonals of the Diagonal Method are written as "Diagonals" with a capital D, meaning that the diagonals of the squares are meant (the bisection lines) and not the normal diagonals from corner to corner.)

I tested dozens of photographs and paintings by famous photographers and masters like Rembrandt, most of them depicting people. It turned out that important details like eyes, hands and important objects (like knives, books, cigarettes and so on) were lying on one or more diagonals of the squares within the rectangle or 35 mm frame.

The Diagonal Method works as follows: in the 35 mm frame you can draw two overlapping squares. In each square you can draw two diagonals (see fig. 2).

 

fig. 2

                                  

 Details in photographs or paintings are very often found exactly on these Diagonal lines, even with a precision of millimetres. To give an example: a Diagonal line can cross an eye of a person that is seen with the whole body on a 8 x 10 inch (20,3 x 25,4 cm) photograph. Exactly this precision was the decisive factor, since my experiments could have been thrown in the dustbin if everything had been just as inaccurate as the Rule of Thirds.
A search for a solid theoretical basis did not produce very much, apart from the "force lines" in squares mentioned by Rudolf Arnheim in his classic "Art and Visual Perception". (It is by the way very awkward that he does not say a word about the perception of rectangular art, whereas most art is made within rectangles.) But recently I found a very interesting book by Brian Thomas who analysed 98 famous paintings to see what  kind of geometrical rules were used by the different masters. He found the use of the Golden Section (but not very often), the ratios of 2:4, 3:5, 5:7, triangles, rectangles, squares and lines of 30 and 60 degrees to the corners.
Interesting is that he only once found the division of thirds (Rule of Thirds) but in 15 paintings he discovered the use of  squares and the use of the diagonals in these squares (within the rectangles) for placing important details.

It is important that the Diagonal Method is discovered through experiments and is not based upon a theory. The Rule of Thirds is based on a theory, and not a very strong theory for that matter, because the original theory of the Golden Section is abandoned. After I discovered the Diagonal Method, I found that the four cross points of the Golden Rectangle are lying on the Diagonals / bisection lines, so the Golden Rectangle remains interesting.




fig. 3

 

  In fig. 3 you can see the Diagonal of the DM crossing the eye and the cross point of the Rule of Thirds on an unimportant part of the forehead. It often happens that a Diagonal crosses one of the eyes, sometimes exactly between the eyes to point out that both eyes are evenly important. To sum up a few important applications:

  1. The Diagonal Method works in all ratios (squares and rectangles)
  2. Using the Diagonals, we can see the (hidden) points of attention very fast.
  3. All points on the four Diagonals are possible locations for subjects and details which need attention.
  4. When the important subjects are not on the Diagonals, there is a good reason why this is done most of the time (the composition of the bigger parts is more important than the composition of the details).
  5. Important details are very often lying exactly on the Diagonals with an accuracy of millimetres.
  6. The DM is especially useful for (digital) cropping, designing advertisements or posters of any kind and during enlarging photographs.
  7. In (good) advertisements the (small) articles which they want to sell or point of attention, are often lying on the Diagonals.
  8. There are of course photographs which contain no details, like many landscapes. In this case the DM simply does not apply
  9. Straight lines, suggested by lines in the composition such as an arm, a table or chair leg, etc, also often coincide with Diagonals.

 In books and magazines about photographic composition authors almost always suggest that all composition rules can be applied consciously during shooting. I think this is somewhat unrealistic. Most photographers will compose their pictures by intuition, then skim over the image to see if any (minor) adjustments are necessary and only then take the photograph. Thirty years ago I did not have any theoretical knowledge of composition but the composition of my photographs in those days was just as good as it is now. In the meantime, I have learned a lot about composition and I often correct something while composing a shot but in the final moment everything goes on auto-pilot. I looked into this matter and found 33 compositional elements which can be applied consciously and 23 factors which can better be left to intuition (to prevent artificial and bad compositions).

It is therefore amazing that artists are able to place important details exactly on the Diagonals!


Edwin Westhoff

Section 2
Diagonal Method in Adobe Photoshop Lightroom (version 1.1. and higher)

In Adobe Photoshop Lightroom there is the possibility to view the Diagonal Method Grid over your photographs. It is called "Diagonal". In this way it is easy to crop a photograph according to the Diagonal Method, for instance, when important details like eys are just slightly off the Diagonals, say 2 mm. The four Diagonals are adjusted to the size and format of the photograph and when you start cropping, the Diagonal lines are automatically adjusted to the new frame.
To see this view: (first import a photograph)
1. Go to "View" (one of the pull down menu's at the top)
2. Click on "Crop R" (the crop tool is now activated - you can see this at the bottom line)
3. Go to "View" again and then in the same menu to "Crop Guide Overlay"
4. Choose in the new screen to the right for "Diagonal" (other possibilities are "Thirds", Golden Ratio, Triangle and Golden Spiral).



How Adobe found my method

One of the students of the Fotoacademie in Rotterdam (who did not know me before March 2008 and who did not know that I was the discoverer of the DM), was a tester for Adobe, when he proposed to Adobe in Feb. 2007 to build in the Diagonal Method in the beta version of Lightroom, after reading my website. He was one of a group of advisors, who wanted more compositional methods than just the Rule of Thirds in Lightroom. Adobe then built in the Diagonal Method probably in Feb. or March 2007, after reading my website, issued a test version in April 2007 and brought a new version (1.1.) on the market in June 2007. Adobe did not consult me, nor asked my permission or let me know that they were building in the DM in Lightroom. I heard about this matter in March 2008.

Section 3

CROPPING
In some cases where the Diagonal is just one or two millimetres off, it is possible and advisable to crop a photograph. This cannot be done with photographs which need extensive cropping, because the whole composition would loose its coherence and power. But often one or two millimetres can be cropped without changing the overall compostion and in those cases the attention would go exactly through the centre of the detail that is needing attention.
























Above left: original photograph                                                                   Above right: the cropped photograph

Above left we can see an other advertisement for Ebel watches. In the left photograph the Diagonal is not exactly crossing the centre of the pupil of the eye. I cut 2 mm off the right side of the photograph and the result is the photograph on the right.

Section 4

Publication in Focus Magazine
 


Publication in FOCUS Magazine, feb. 2007.


Section 5

LINKS

        Publication on Wikipedia: Wikipedia  (Dutch)
        Publication of this article in Russian
        Diagonaalmethode.nl (Dutch version)
        Wikipedia English: discussion page  
        Rembrandt and other Masters & the DM
       


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. on June, 23, 2006.

 



Section 6
Photographs and paintings 

 World Press Photo by Spencer Platt, EPA


Three of the Diagonals are crossing the (left or right) eye of the the driver and of the two girls on either side of him.
The Diagonal from the bottom left corner crosses the point between the eyes of the girl in the backseat with the sunglasses and handkerchief. The most important Diagonal (from the top left corner) is also crossing the hand (holding the cell phone) of the girl behind the driver. She seems to look at a photograph she just made with her phone. (The Diagonal line from the bottom left corner is also crossing the head of the man behind the car in the white T-shirt).

 On the left 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)

 

 

On the right we can see the cover photograph of Jane Fonda's book "My Life So Far" by Andrew Eccles.

The Diagonal from the top left corner is crossing her right eye.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                                              Photograph by Andrew Eccles

 


Below: 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.

Above right: the Rule of Thirds: there are no details on the cross points, the point on the top left is crossing an imaginary mustache and the cross point on the bottom left just misses the watch. No lines are crossing the eyes or the centre of the watch. 

 

When we compare the photograph with Nicolas Cage to the one on the left we see that the person is not very important, but the Canon Ixus camera is. To shift the attention from his face to the camera the eyes are made extra dark.
The Diagonal from the bottom right corner is crossing the centre of the lens of the camera, so attracting attention.

 

 

 

 

 

 

 

 

 

 

This is an example of an older photograph by Ogawa Kazuma from "One Hundered Beauties of Tokyo", 1902.
An other interesting aspect is that the most important Diagonal is the one from the top left corner, because people from the western world look through pictures from the top left corner to the bottom right corner as a result of reading from top to bottom and from left to right. People who write and read differently, like the Japanese, could look through photographs from right to left. But in this photograph the Diagonal comes from the left. (E. Zwaan discovered that students who grew up with Hebrew looked through pictures from the right to the left.)

 

 

 

  


 
 



"Beauty Contest " by Frederico Patellani



Selfportrait by Vincent van Gogh


























Etchings by Rembrandt

Abraham and his sonRembrandt

In this etching by Rembrandt Abraham is on the point of sacrificing his son. An angel tries to stop him. The heads of Abraham and the angel are already important because heads of people always attract attention. The points that can use extra attention are the hand of the angel, the throat of the son and most of all, the hand with the knife. The Diagonal is "pushing" the hand upwards, so the moment stays intense. When Abraham would decide to put his knife away, he would lower his arm and hand. But this movement is "stopped" by the Diagonal. Two Diagaonals are crossing in the throat of the son, indicating that Abraham would cut his son on this spot. Points of attention:
a. the hand of the angel
b. the head of the son
c. the throat of the son (2 diagonals)
d. the hand with the knife 

 

 

In this etching 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.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

When we apply the Rule of Thirds, we see that on the four crossing points there are no important details to be seen.

One vertical line on the right is touching the moneybag in the hands of the kneeling figure, but not crossing it, one horizontal line is touching the head of the main figure, but not crossing one of the eyes, and one vertical line is crossing the moneybag on the table, which is the least important.

 

When we look at the four crossing points, we see no important details. As with most photographs, the important details are lying in the vicinity of the four crossing points, but not ON these points.


    Ginevra Benci by Leonardo da Vinci.

This portrait shows 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).


Section 7     

Wikipedia English: original text (deleted)

Diagonal Method

From Wikipedia, the free encyclopedia.

This article is about the Diagonal Method in photography. For the diagonal method proposed by Cantor, see Cantor's diagonal argument.

The Diagonal Method (DM) is a relatively new rule of thumb in photography. Dissatisfied with existing rules of thumb such as the rule of thirds, Dutch photographer and lecturer Edwin Westhoff used visual experiments in order to find a more precise and better applicable method. After having studied many photographs, paintings and sketches, he discovered that details of interest were often placed precisely on the diagonals, or bisections, of a square.

A photograph is usually cropped in a ratio of 4:3 or 3:2, which can be seen as two overlapping squares.

Theory

The DM states that details of interest are ideally found with a precision of one millimetre on one or more diagonals of 45 degrees from one of the four corners of the image. The diagonal from the upper-left corner is the strongest diagonal in Western culture. One reads text from left to right and from top to bottom, but one also does this when looking at (or "reading") a picture.


Contrary to other rules of thumb such as the rule of thirds and the golden ratio, the DM is not highly concerned with the intersections of its diagonals. Rather, a detail of interest can be located on any point on any of the four bisections, although the DM is very strict in the sense that the detail has to be exactly on the bisection with a maximum deviation of one millimetre on A4 format. This makes the DM more precise than other rules of thumb in photography.

 

Application
The DM was derived from an analysis of how artists intuitively locate details within a composition; Westhoff discovered that by drawing lines with an angle of 45 degrees from the corners of an image, one can see which details the artist intended to emphasize. This explanatory origin is also found in the practical application of the Diagonal Method: it is used as a method of analysis whilst a photograph is being edited and not as a consciously applicable theory upon making a photograph.


It is very difficult to consciously place details of attention precisely on the diagonals. Research by Westhoff has resulted in the finding that important details on photographs and on sketches of Rembrandt, such as eyes, were placed exactly on the diagonals. Skilled artists and photographers place these details there intuitively. The conscious application of many rules of thumb upon making a photograph, as is suggested by many a photography book, is regarded as unrealistic by Westhoff.


The DM can only be applied on images where certain details are supposed to be emphasized or exaggerated, such as an advertisement photo promoting a product, or a portrait in which a specific part of the body deserves extra attention by the viewer. Some photographs of landscapes also contain important details in the shape of humans, (separately placed) trees or buildings which can also be placed on the diagonals, but photographs of landscapes and buildings are usually concerned with the composition as a whole.

Evidence

Diagonals, the middle perpendiculars, the centre and the corners of a square are known to comprise the force lines in a square, and are regarded as more powerful than other parts in a square. To what extent these findings can be applied on rectangles, such as photographs in ratios of 4:3 and 3:2, has not yet been researched. Other than support for the DM derived from practical experiments, at this time there are no known scientific sources that can theoretically confirm the DM.

Wikipedia:  Edit Page

Dear Stephen, I am disappointed that I have not been notified of your deletion proposal (as suggested in WP:PROD). As a result, I would like to discuss the deletion of the Diagonal Method article in your discussion page with you.

The reason for deletion you have given is that this method is not verifiable from a reliable source. Note that the Diagonal Method concerns a theory in aesthetics, an area in cognitive sciences we know too little about to actually be certain about anything (i.e. Studying aesthetics in photographic images using a computational approach by Datta, Joshi, Li, & Wang, 2006; full reference by request).

That same source (Datta et al., 2006) nicely puts that the rule of thirds is “a sloppy approximation of the Golden Ratio” (para 2.3). The rule of thirds is often used in photography but any more experienced photographer knows the rule of thirds is ambiguous. Thus, basing myself on the reason you provided, the article on the rule of thirds (which I did translate to Dutch; nl:Regel van derden) should be removed also. Note that the article on the rule of thirds lacks any reference and only mentions a few Web sites that blindly follow the rule of thirds.

On the basis of Wikipedia:No original research it can be said that the article provided sufficient information to not lure the reader into blindly believing it has all been confirmed (as the rule of thirds suggests), that it was not the place where the Diagonal Method is first proposed, and that the article does not draw its own inferences. Outside from Wikipedia, the Diagonal Method has been published in the Dutch photography magazine Focus (February 2007) and is starting to be analysed at the universities of Twente and Utrecht, and at Saxion Hogeschool Enschede (all in the Netherlands).

In conclusion, the Diagonal Method has shown to be useful in the analysis of two-dimensional art and photography, similar to the rule of thirds which is widely used but has no proper basis and is ambiguous (the reason it is so popular is because it does serve as a proper method to prevent beginning photographers from making basic mistakes). Though at this time there has been no additional published research on the Diagonal Method, I deem it sufficiently justified to be mentioned on Wikipedia, with research-founded updates expected to be added in the relatively nearby future.

Eddyspeeder 19 May 2007 (UTC)


Section 8

"Westhoff's Diagonal Method: Unraveling Photography"  by  Fleur Jongepier

I first came in contact with the Diagonal Method in September 2006, when I took up a photography course offered by Edwin Westhoff. When we got into discussing The Rule of Thirds and composition in general, Edwin introduced us to his recent discovery: the Diagonal Method (hereafter DM).

            First things first: I do not believe, and nor does Edwin, that there are set rules in composition. This has particular consequences for the DM, for it raises all kinds of questions. Like: if there are no such rules, what is the DM good for? How can a theory of composition be discovered when there aren’t even set rules for it in the first place? For now, I will not go into the discussion of whether there are rules in composition or not. Because either way, the DM remains a powerful theory, as will hopefully follow from this article, so for now it suffices to leave that discussion aside.

 

The technical side of the Diagonal Method is rather simple. You can apply the DM in any work of art or photograph that has a square or rectangular format. Each or any of the 90 degree corners can be divided in two 45 degree angles. This dividing line is called the bissectrice or bisection line. In a square the bisection lines are also the diagonals that are crossing the square from corner to corner. In rectangular works the bisection lines are the diagonals of the two overlapping squares (see fig. 1). Edwin Westhoff discovered that details like eyes were often lying on these bisection lines, called by him "Diagonals", with a capital D.


fig. 1


My first thoughts concerning the DM were rather sceptical. I shall specify these worries or "objections" of mine, because I can imagine others having the same worries as I had. Afterwards, I will show there’s an appropriate answer to all of them.

            First of all, I was worried its proposed success might just prove to be leaning on "wishful thinking". The central question being: to which degree is it likely for one to want the photograph to pass the test? For instance, photograph X passes the test because a diagonal crosses exactly between both eyebrows. Wouldn’t we have let the photograph pass the test if the diagonal crossed the eye (or both)?

            A second difficulty I stumbled upon, was the amount of credibility that is necessary for the DM to be credible. Over 30%, 50% or even a 100% of the tested photographs? When is the DM credible? I found, in testing the photographs, some surprising examples of how the DM cut right through the central elements. Yet, there were also numerous photographs where I wasn’t quite sure to let the picture "pass" or "fail" the DM-test. Obviously, the problem of credibility is thus closely related to "wishful thinking". In fact, both problems circle around the acknowledgement of what counts as an important or vital element in a photograph. Is this acknowledgement suggestive, and should it perhaps be universal?

            I shall be very clear on the last question: central elements in photographs that are on the diagonal bisectrix are not there for some underlying universal reason or (mathematical) rule. I will not hesitate to say that they are on the diagonal bisectrix for suggestive and subjective reasons. This is an important point to make, because it implies that diagonals on either eyes or eyebrows are both legitimate, because we are not to justify this legitimacy. This might sound rather odd, but in fact it’s rather simple. When holding a sheet with the proposed diagonals over a particular photograph, and you find that, for instance, the left eye is crossed by such a diagonal, it means that the photographer, on purpose or unconsciously, had his or her focus on precisely this eye (or whichever element in question).

            Of course, it is hereby not meant that every element in a picture passes the DM-test. It does not necessarily follow from a diagonal crossing a cheek for example, that precisely this part of the cheek is essential (or, better said, that the photographer found this part essential).The reason for this reduction of legitimacy of central elements lies in the exact precision of the DM, which is precise on one millimetre. A cheek, to continue on the same example, covers a relatively large area and cannot be qualified as "an element". The statement of such precision is a heavy one. The Rule of Thirds works approximately, but in most cases this approximacy is insufficient and hardly ever consistent. The DM is restricted to particular elements of interest in a photograph that are not to be "close to" a diagonal but rather precisely on the diagonal. This 1 mm-accuracy is important because this increases the method’s credibility. Whereas the Rule of Thirds applies to large areas, the DM applies to small elements only which makes the cases in which the diagonal is indeed on the element more significant. Also, the problem of wishful thinking is diminished since all elements that are not on the diagonal with a distance of 1mm will not past the test, whether we want them to or not.

            A third problem I’d like to mention is the question of dominance: what is more important, the crop of a photograph or the diagonal on the elements? What I’m aiming at here is that different crops or compositional layouts in one photograph change location of the bisectrix. Theoretically we could crop every picture in such a way that the bisectrix is in fact always on an element or another. This however, is obviously not the intention. When taking a photograph, the photographer takes a certain angle and afterwards he is able to adjust the proportions and make a different crop. Cropping the photograph until a diagonal cuts through an important element can lead to awkward results. Of course the overall layout is more important than the presence of diagonals cutting certain elements. In some cases however, it could be the case that a slight crop on one side in order to place the element on the diagonal could’ve improved the photograph. 

            Due to the problems named before, I tested 100 famous photographs to see whether the 1mm accuracy is correct (when photographs are approximately 16 cm. on the longest side). I picked 100 photographs out of hundreds, because a fair amount of photographs is unsuitable since there are for instance no central elements (e.g. landscape photography) or the layout of the photograph made it impossible for diagonals to be meaningful. For the remaining 100 there were 68 photographs where a diagonal cut through an important element. In several cases there was more than one working diagonal. I believe it is unnecessary that all photographs that are suitable for the DM should pass the test. This is because, once again, the DM is no rule for composition.

            Then, you might ask, what is it’s function? Well, DM’s value lies mainly in the fact that we can, for a part, get to know the photographer’s focus or centre of attention. Furthermore, we can improve photographs. In some cases we can crop the photograph (when speaking of millimetres and 1-2 centimetres maximum) in such a way that the diagonal cuts right through the element. Sacrilege for the photographer? Maybe, but photographers don’t always get it right the first time. They do the cropping afterwards, too.

The DM works on intuition, and this is why it’s so effective. Even amateur photographers have the habit of making a picture with correct "use" of diagonals. For some still unknown reason, photographers themselves (and artists, but this is another story) seem to have an integrated structure of these diagonals. It might be the case that, when intuitively choosing a composition, they make use of this structure.

As being very analytical myself, I saw no future for DM since it rests on terms such as "subjective", "suggestive" and "intuition". When testing many pictures and works of art, however, I couldn’t convince myself of this being coincidence or wishful thinking anymore. My best advice for the ones that have become curious or critical on DM is to test photographs themselves, as I have done. Do keep in mind that not al photographs qualify to be tested at all. It still is photography, which is a form of art that is defined by dozens of factors that make a photograph a good photograph. The DM is ‘just’ another, but a strong one, that allows us to unravel the secrets behind the photograph just a little more.

Fleur Jongepier


section 9

Composition in general and the The Golden Ratio

In this section:
1. The problem with using "rules of composition".
2. The Golden Ratio.
3. Leonardo da Vinci's "Vitruvian Man" and the Golden Ratio.
4. Bottom-up and Top-down perception and the Diagonal Method.
5. The problem with "Beauty".

1. The problem with using "rules of composition"
As you can see in the article by Fleur Jongepier, I do not "believe in set rules of composition". Actually, I do not use the word "rules" in my classes, except when I have to explain something in relation to a certain known rule, such as the Rule of Thirds. The reason is rather simple. As a photographer, sooner or later you will encounter a situation in which you have to break a rule of composition, because the purpose of the photograph demands this. This could be the case with all the rules. There are simply too many exceptions in actual photography. So forget rules. In stead we could use the term "points of attention". Many times there are certain factors that are needing attention. Let's take the horizon as an example. Normally you will have to check whether the horizon is exactly straight, level. But it is no rule. It is perfectly legitimate to place it under an angle, when the purpose of the photograph demands this. You see this sometimes in a movie, and in movies these kinds of things are most of the time planned very much in advance. 
Other factors often also need attention: the location of a rather small object in the frame, the direction in which a person looks in relation to the placement in the frame, what to do with vertical lines, how to compose clouds, etc. You can follow a certain rule, or go against it when necessary.
The important thing is that the results (of either following or breaking them) have a meaning.
We "read" photographs and we use general, unconscious ways of reading them. So, using the example with the horizon, when a person sees a photograph with a level horizon, he reads this in a certain manner, and when the horizon is under an angle, the person reads it in another manner, it has another meaning. But both meanings are legitimate or good, depending on what the photographer wants to communicate. In criticizing photographs this matter gets specially important.
One cannot simply dismiss a photograph because a certain rule is not applied. If you do not understand a photograph, you have to know the meaning of it. In classes, you can simply ask the photographer what the purpose of a photograph is. Most of the time all the elements and the way the photograph is made, fall into place. If not, certain things have to be altered in relation to the purpose of the photographer, but not to our own believes (in rules of composition).

2. The Golden Ratio
In order to be able to understand the meaning and use of the Golden Ratio (in history) it is necessary to distinguish the different area's where the Golden Ratio is used:
1. Mathematics (e.g. the ratio 1:1,6180339)
2. Geometry (e.g. the Golden Triangle)
3. Architecture (e.g. the pyramid of Cheops)
4. Nature (e.g. the human body)
5. Filosophy (e.g. the "Divine proportion" mentioned by Plato)
6. Esthetics (e.g. the Golden Ratio in photographs and paintings)
In this article (and on this website) were are mainly concerned with esthetics (in photographs).

Historical background of the Golden Ratio.
Albert van der Schoot writes  in his book (Agora, Baarn, 1999) "De ontstelling van Pythagoras" (which could be translated as "The Disproposition of Pythagoras"), that the "Golden Section" as an expression and idea was used for the first time in 1864 in English literature and the expression "Divine Proportion" was used for the first time by a Italian monk called Luca Pacioli (1445-1517), in 1509.

Pacioli wrote about mathematics, not about geometry, let alone esthetics. Pythagoras (c580-c500 B.C.) had an exoteric and an esoteric school were he taught mathematics and the symbolic and esoteric meaning of numbers and ratios. Not about geometry. Plato (c427-c347 B.C.) and Leonardo da Vinci (1452-1519) both wrote about the "Divine Proportion", but nothing in their work points to the ratio of 1:1,618, according to van der Schoot. What Plato and da Vinci meant was probably the general proportion in the cosmos, and not a very precise mathematical ratio.

Since the expression "Golden Section" was used, first in 1864 in England and also in 1835 by Martin Ohm (1792-1872) in Germany, this term was more and more used in general and was also used in connection with paintings and drawings. To this day artists, critics, reporters and even scientists write about the Golden Section as if this is a proven ratio of beauty in art works. Van der Schoot discovered that the Golden Section as an ideal of beauty in two dimensional art, is actually..... a myth.

A different matter is the use of the ratio of 1:1,618 in architecture. It could well be that this was used in the construction of the Great Pyramid. I did not research this, so I do not know.

Anyway, if this was used, it was not called the "Golden Section", because this term originated in the 19th century. Also because of this, Pythagoras could not have known about he Golden Ratio or Golden Section, since the term did not exist in those days. Of course I don't mean by this that the proportion of 1:1,618 did not exist then, but that the meaning which was given very much later (concerning the ideal of beauty in two dimensional art), was simply nonexistent. It was just a matter of mathematics during the time of Pythagoras. In architecture the same mathematical aspects could have been made three dimensional. But esthetics  is something entirely different.

When we look at certain objects which allegedly contain the Golden Ratio, such as a particular shell, a bull, or a painting, the Golden Ratio is almost in every case not really present when we take a precise measurement. Of course it is possible that a few painters deliberately constructed their paintings according to the Golden Ratio. But in that case the composition is an artificial one.
As stated earlier in section 1, it is widely known that the Rule of Thirds is based on the Golden Section (rather the Golden Rectangle). This statement becomes rather interesting when one knows that the Golden Ratio as an ideal for beauty in two-dimensional art appeared to be a myth.
When you base a theory on a myth, you cannot expect that the new theory becomes more realistic than the original myth. Especially when you know that the core of the myth, the ratio of 1:1,6180339, is completely removed from the new theory. By removing this ratio, the Rule of Thirds becomes an empty shell.

3. The "Vitruvian Man" by Leonardo da Vinci (1452-1519) and the Golden Ratio.

It is said that in the drawing of the Vitruvian man by da Vinci, the Golden Ratio or Golden Section can be seen. It concerns the distance from the fingertip to the wrist and the distance of the wrist to the elbow. (Da Vinci drew vertical lines at the position of two of these points: at the wrist and at the elbow.)
These two distances would have a proportion of 1:1,618 to each other. This is called "The Golden Section". In this subsection we are going to investigate this statement.

 

fig. 1


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Leonardo da Vinci added a line with proportions under the drawing, in which we can see what proportions he used (within the red rectangle).

 

fig. 2

We can copy this line with the little vertical markings as seen below:
(I did not draw all the lines on the left side, but they are equal to the lines on the right side.)

 fig. 3


Let us see whether there are ratios of 1:1,6180339 in da Vinci's line.

Below ( fig. 4) is a line with the "real" Golden Section of 1:1,6180339: the line b-c has the same ratio to the line a-b, as the line a-b has to the line a-c (or the shorter line has the same ratio to the longer line as the longer line has to the whole line):




   fig. 4

 

At first sight, without calculating, we can see that this is not the case with the line made by da Vinci (see fig. 3). In his line the line a-b has the ratio to the line b-d (the ratio of the shorter line tot the longer line) of 1: 2,97.

If we look at the ratio of the longer line to the whole line (b-d to a-d) we get a ratio of 1:1,36, a completely different ratio than 1: 2,97.

Of course we can now look at the ratio of the distance between the lines with the smallest distance (blue lines in fig. 3) and the distance between the lines with a little more distance (red lines in fig. 3), as mentioned in the website in which the ratio between the distance from the fingertip and the wrist to the wrist and the elbow was allegedly 1:1,618. (We have to take the average of the distances between these lines, because da Vinci drew this lines apparently by hand, so the distances differ a little.) This ratio is 1: 2,66. Again here is no ratio of 1:1,618.

 

Luckily, da Vinci made notes above and beneath the drawing, so we can see whether these will give more information concerning the used proportions.
 

    fig. 5
 

In fig. 5 we can see what da Vinci wrote beneath the drawing. For those who cannot read his notes or cannot read Dutch it says: (sentence with large letters directly under the line with markings): "The length of the spread arms of a man equals his height."
And beneath the notes: "From the roots of the hair till the bottom of the chin is one tenth of the total length; from the bottom of the chin till the crown it is one eighth of the total; from the top of the chest till the roots of the hair it is one seventh of the total man. From the nipples till the crown it is one fourth of a man. From the elbow till the top of the middle finger it is one fifth; and from the elbow till the armpit it is one eighth of the height of a man. The whole hand is one tenth of the man, the beginning of the penis marks the center of the man. The foot is one seventh part. From the sole of the foot till just under the knee it is one fourth. From just under the knee till where the penis begins is one fourth of a man."


    fig. 6

The notes (which are above the drawing of the Vitruvian man) in fig. 6: "The architect Vitruvius says in his work about architecture that the measures of the human body are divided by nature as follows: 4 fingers constitute one hand width, 4 widths of a hand constitute one foot, 6 widths of a hand constitute one fore arm or yard, 4 yards constitute the height of a man. And 4 yards constitute a pace en 24 widths of a hand a man's height; and these measures he used for constructing buildings. One have to know that when spreading one's legs the height of the body decreases by 1/4 and when lifting and spreading the arms, the middle fingers are at the level of the crown, the centre of the spreaded arms are at the navel and the space between the legs is a equilateral triangle."

(to be continued)

(Article 4 and 5: under construction)


section 10
Quotes from the internet

  • Avoid centered compositions like the plague, unless a photograph is asking for a very symmetrical composition. Generally many photographers would refer to the "rule of thirds" and I can say out of experience that this rule is off by far. I'd recommend the diagonal method, normally a pleasing photograph has some key elements falling along those lines. reference: http://www.diagonalmethod.info/. Markus Hartel.

    The complete Mike Hartel interview   http://www.markushartel.com/blog/about/another-interview.html
    is published in Digital Photographer, issue 74 (Sept. 2008)

  •  The The golden number, the rule of thirds, that's old school! In this new millinium, we're talking "Diagonal"! Go here (http://www.diagonalmethod.info/) and discover the new trend in composition/design. Mozbee.

  • These are fine examples of the Rule of Thirds with bigger subjects. With small details in the
    photograph like eyes, the Diagonal Method works better. Anonymous from "Photospot".
  • My photography teacher taught me another 'rule' a few months ago. He created this method and wrote an article about it. It might be interesting to read it, because he did some good
    research. Youri.
  • It is not the rules that make good pictures, it is good pictures that make the rules. The
    Traveler.

  • This man is a brilliant photographer who has  a very interesting and frequently overlooked theory on composition. Dolcemente.
  • This man claims he found a new method which does - and it sure sounds very plausible.
    Dolcemente. 

  • I was not really aware of this...but it is very interesting..I like how they explain what is going on and if you think about the compsition make not only sense but maybe very appealing ...At least to my eye. Great article thank you...Jerry.
  • Ich hab grad einen Hirnkrampf. Für eine Broschur möchte ich den Satzspiegel im goldenen
    Schnitt anlegen. Hat auch uber die Diagonal Methode gut funktioniert. Amba.

  • Very interesting reading.  ALL information is valuable.  You can choose to implement it or not, but it is still valuable -Tom.

  • Edwin Westhoff  descubrió un método interesante (que denominó el "método diagonal")
    mientras realizaba estudios e invstigaciones en relacion a la "regla de los tercios.
    Marcelo Espinoza.

  • I agree. The Diagonal Method is perhaps my favorite. Kaaredyret.

  • Alors, là, chapeau...tu m'époustoufles...quitte à me répéter, toutes tes dernières compo suivent la règle des diagonales, et cela fonctionne nickel. En plus, je sens une meilleure maîtrise dans le post-traitement...comme le bon vin, tu bonifies... Super Manu.

  • Dan beveel jij dus de onbewuste diagonaalmethode aan, als ik het goed begrijp. En dus toch niet ver gezocht......Karel. Ik kan mij er iets bij voorstellen: een archetype van de fotografie.

  • Glad it worked out, and I agree about the 'diagonal method': the guy that noticed and documented that should win some sort of prize. Dan.



     

    There are no rules for good photographs, there are only good photographs -  Ansel Adams

    It is not the rules that make good pictures, it is good pictures that make the rules - The Traveler



    Section 11
    Test sheet
    This sheet was used to test all photographs. It is just a 90 degree corner divided in half.

 

Section 12

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