Study vectors (arrows) to make better compositions:

Dear friend,

An interesting idea:

A lot of compositional concepts in photography come from mathematics– specifically, geometry.

I stumbled upon this idea purely by chance– by looking at geometry and mathematic textbooks at the house of my friend Alexander Amy, and my other buddy Kevin.

One of the concepts I want to explore with you is this notion of a ‘vector’ (AB−→), also known as a ‘Euclidean vector‘ (discovered by our friend, the geometrician Euclid– from his book, ‘Elements‘).

What is a vector?

The word ‘vector’ comes from Latin, which means “carrier, transporter.” It comes from the word, ‘veho’– which means “I carry, I transport, I bear.”

So essentially, a vector is an arrow that (in the terms of photography or composition) transports or directs your eye a certain direction.

Why vector?

I like the idea of ‘cross-pollination‘ — the basic concept that we can mix different fields of knowledge to discover new ideas.

For example, one big interest I have at the moment is this:

Math/Geometry x Photography

The terminology ‘vector’ is useful because it concertizes something we already know in photography:

When we look at a picture, our eyes are directed by vectors (arrows).

Let us examine deeper.

Eye Contact

You can draw a vector (an arrow) that follows the movement of the direction that your subjects look at.

Vectors get very interesting when you have a scene with multiple subjects looking in different directions, like this scene in Citizen Kane:

Vectors with visual elements

Another scene from Citizen Kane: Note the low angle composition, and the elements in the background which point in different directions– outlined with vectors (screenshot tool with MacOS Mojave):

What direction is the thing going?

If you imagine your subjects as vectors (arrows)– ask yourself:

What direction is it heading?

A tip:

Add some negative space in front of the direction the vector is heading:

Vectors which come out towards you

Vectors which come towards you, or go into a picture. The vector on the left (X) means the vector is going straight into a picture. The vector on the right (·) symbolized the vector is coming straight towards you.

One of the great things about studying vectors is this:

You can have vectors (arrows) which go INTO a picture (symbolized by (X)), or vectors which come OUT TOWARDS YOU (symbolized by the mathematical notation: (·)).

For example, let us look at this picture:

Outlining the eye which is coming towards you as a three-dimensional vector:

Imagine the poster in the background as this three dimensional head (seen from the side):

Apologies– not doing a good job explaining this. Let us move on.

Vectors in three-dimensions:

An easy way to imagine vectors (arrows) in three dimensions:

Stick out your three fingers like this– and have them point in opposite directions (x, y, z) axis.

How objects are rotated in three dimensions:

Applied to the real world — let us see this scene from Citizen Kane:

Think to yourself– who is closest to you in the frame, and who is furthest away?

With edge detection added:

Now see the vectors added with the eye contact, and also the hand pointing:

Layers and vectors

One of my favorite Citizen Kane scenes– note all the epic layers, and the different vectors in which the subjects are looking:

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