What are the calculations and the tools required to set up such a structure?
At first, a long ruler and a calculator! In a second, an original tool that will allow the creative to save time and to visualize immediately the proportions: the "Golden Divider for Arts".
We will draw inspiration from this "regulating lines" system, reconstruct it, and analyze how it can make it easier for us to set up the structure of a picture.
Let us divide the height and the width of the "image window" (= the painted surface of the painting) by 1.618, i.e. the Golden ratio.
This first division reveals the four red lines above. We will call them the "primary golden lines" of the structure. They intersect in four points, called "primary golden dots".
Let us do this same division in the rectangles formed by the vertical and horizontal red lines and the margins of the structure, tinted in yellow below (Click on the slide show to scroll through the images)
We get four blue lines, which we will call "secondary golden lines". They intersect in four points, called "secondary golden dots".
A third subdivision on the new rectangles appearing above gives rise to the four green lines called "tertiary golden lines" and their points of intersection called "tertiary golden dots".
The structure of our painting is ready: these surfaces and points will allow us to position the horizon of the painting, the different volumes as well as the centers of interest of the painting.
Let us superimpose those "regulating lines" on the masterpiece of Sandro Botticelli and analyze the way in which the different centers of interest are disposed.
We see below three vertical sub-sets. The dimensions of the right and left rectangles are proportional to the external dimensions of the masterpiece. Each of these rectangles forms a golden rectangle. The different human figures are arranged on the diagonal of these rectangles.
Another horizontal cut below: the upper rectangle delimits the horizon line, on which the navel of Venus aligns. The lower rectangle contains the shell. These two rectangles have a ratio of 5/8 th to the height of the painting, the proportion governed by the Golden ratio.
Venus is in a central position. The rectangle containing it is also proportioned to the outer rectangles. She is not situated in the middle of the painting: the axis of her body is situated on the red vertical line, always placed on the same principle of proportionality, to the 5/8 th of the median rectangle.
Let us superimpose this same regulating lines system on a watercolor structured according to this principle.
The horizon line is placed on the horizontal primary golden line. On this same line is located the main vanishing point, which determines the perspective of the building.
The vertical primary golden line separates the building from the tree.
The intersection of these two primary golden lines defines the center of interest of the painting: a table and two chairs out of the heat and two glasses served waiting for the occupants of the house.
You can see below is the painting without its structure:
The picture is balanced thanks to its structure based on human proportions. We do have these proportions under our eyes all day long: the shape of a face, the phalanxes of our hands, the proportions of the bodies of the persons we meet. It is therefore logical that the human eye favors a structure based on usual and reassuring proportions.
It should be noted that this "regulating line system", this structure grid, does not represent a method of use in itself. It is simply an aid to the decision, and makes the painter gain a considerable amount of time. It allows, among other things, to place the focal points efficiently and rapidly, and allows also to not "decentralize" centers of interest.
Le Corbusier, the famous Franco-Swiss architect, said: "The regulating lines system does not bring poetic or lyrical ideas, it does not inspire the theme, it is not a creator, it is a balancer."
Le Corbusier had developed in 1945 the "Modulor", a system of measures modeled on human proportions. He judged this system more suited to human morphology, and was intended to bring maximum comfort to man in his living space.
The tool used to quickly trace the structure of Botticelli's Venus Birth in the video of this site is called the "Golden Divider for Arts".
This proportional caliper based on the Golden ratio was developed by the author of this site in order to facilitate the work of the creatives of multiple fields: painters, of course, but also sculptors, photographers and graphic designers, and also architects and other designers.
It was awarded with the silver medal at the 44th Geneva International Exhibition of Inventions in 2016.
Click on the link below to visit the website dedicated to the "Golden Divider for Arts".
The "Golden Divider for Arts" avoids the use of a ruler and a calculator to implement a complex structure. It allows - among others - to easily trace a spiral of Fibonacci. It can also be used as a compass with a radius up to 75 cm.
Open at right angles, it allows to find the emblematic measures of the builders of cathedrals of the Middle Ages: palm, hand, span, foot and cubit.
These different measurements remain proportional regardless of the opening angle of the tool.
The "Golden Divider for Arts" is a measuring, plotting and sighting tool created for everyone who starts a project with a pencil and a piece of paper !