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Photoshop plug-ins for retouching

Golden sections

Quick introduction

This Photoshop plug-in draws all the golden divisions, the golden spiral and the harmonious divisions on your image. Apply it to an empty layer and use it as an aid in composing and cropping. This is the Golden Section plugin’s control panel. Click on the image for a larger view. It works with the following image modes: 8 & 16 bit/channel: RGB, CMYK, Grayscale, Duotone, Lab.
The best way to use the plugin is to create a transparent layer on the image you want to edit or crop. In Photoshop you do this with Shift-Ctl-N. Its color should be None, which is transparent. To get a resizable transparent golden section in Photoshop: 1. First create a new empty layer in Photoshop. 2. In the plugin draw the sections or divisions you want onto this transparent layer filling the entire image. 3. apply. 4. In Photoshop, with the golden section layer still active, select 'Free Transform' from the menu 'Edit' to resize the golden section and move it around the image.

Golden sections and divine proportions

The divine proportions  and   the golden sections  are two expressions for the same thing. Basically it is the division of a line in two sections, where the ratio between the smallest section and the largest section is identical to the ratio between the largest section and the entire length of the line. In other words A/B = B/(A+B). The ratio is about 1:1.618.
One interesting consequence of this ratio is that if you have a rectangle where the sides have the golden ratio, then you can divide the rectangle into a square and a rectangle, where the new rectangle also has the golden ratio between its sides. This can go on ad infinitum and is known as golden spiral sections .
You can use this to construct an equiangular spiral, known as   the golden spiral,  where the size of the revolutions grow with the golden ratio.
If you want a more dynamic composition than the simple golden sections, then you can draw the golden triangles . Below you will see an example of the harmonious triangles. If your image has the divine proportion, then the golden triangles and the harmonious triangles will be identical.

Harmonius divisions

Harmonious divisions  rely on the principle of similarity. The most common is the   rule of thirds  where you simply divide a line into three equal part. This is often misnamed as the golden section.
Another harmonious division is the division of a rectangle into equiangular harmonious triangles  based on the diagonal. When the proportions of the rectangle are identical to the golden proportions, then the harmonious triangles will of course be identical to the golden triangles.

Midpoints

Midpoints offer a nice rule of composition. Diagonals are an all time classic.
So are the diagonals from the corners to the midponts of the oposing sides

Leonard Fibonnaci

Leonard Fibonacci discovered that if you have a sequence of numbers beginning with 0,1, where the next number in line is the sum of the previous two, then the sequence will progress towards a more and more exact representation of the golden ratio. The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc. Oddly enough nature tends to organize growth and limbs according to this sequence. F.ex. the ratio between the length of limbs of your fingers is the golden ratio. The ratio between the length of your nose and the distance from the bottom of the chin to the bottom of the nose is the golden ratio. The spiral growth of crustaceans follows the golden spiral. The divine proportions are an in-built (or in-grained) aesthetic parameter we judge beauty by.

Classical example

Vermeer van Delft

Vermeer was a master of composition and he was obsessed with the golden sections.
Vermeer used the basic golden sections to arrange the masses.
He used the golden triangles to create a pyramid containing the two persons, thus bringing them into relationship
By constructing the focalpoint of a golden spiral, he located the main dynamic focus of the composition: the girls hands and the glass of wine.
In fact Vermeer subdivided minutely and found the exact space occupied by the glass and the edges of the hands holding it.
Vermeer also used the symmetrical focalpoint of the rotated spiral.
It exactly locates the placement of the open window with the faint reflection of a woman outside.
Vermeer also divided the picture into two halves along the vertical center. He then divided each half into the golden sections.
He did the same with the horizontal halves. The horizontal middle is the mans eye-hight. It is a well known compositional principle that the horizontal middle is to be avoided since it creates a too rigid and obvious division of the picture.
Of course there are other compositional principles, that have been in use for centuries. Diagonals and diagonals to midpoints are classics.