What is a Tangent? And How To Solve Them
By Neil Blevins
Created On: Aug 29th 2020

When I joined Pixar in 2002 to work on The Incredibles, all people working on a film were free to attend dailies, a series of reviews where various departments showed their work to the director and got comments. I learned many important lessons at those dailies, but perhaps the most important was about tangents. People were constantly calling out tangents that people needed to fix. So what is a tangent? And how do you fix them?

You have two choices with this lesson, watch me discuss the issue in the video below, or read the full text.

A tangent simply is an area where two things in an image are nearly touching or actually touching, and in doing so create a visual mistake that the human eye doesn't like. Sometimes this is also referred to as objects "kissing". It can lead to confusion in the viewer, like it can draw the eye to a part of the painting that's unimportant, it can just feel wrong or strange, or it can confuse the viewer as to the relative depth of the two objects. And that's why tangent are best to be avoided.

Most tangent can be easily fixed, you just need to identify them first, and then move one of more of the objects, or make an object less contrasty compared to the other object to avoid the tangent.

For all the examples below, I'm going to be using this painting I did for my "The Story Of Inc" book. All the painted or 3d elements in this painting were done on separate layers, so I'll be adjusting elements in the painting to create tangents so you can see what I mean, and then show various solutions to the problems.

If you do a search for tangents on google, you'll find many lists of different types of tangents, but here are the ones that I tend to find the most often.
1. The Object Is Touching Another Object
2. The Object Is Touching The Edge Of The Frame
3. An Object In The Foreground Is Touching An Object In The Background
4. A Foreground Object Is Touching A Background Object In A Straight Line
5. Two Unrelated Objects Share The Same Horizontal Or Vertical Line
6. Cut Down The Middle
7. Animated Tangent
The Object Is Touching Another Object

This is the most simple form of a tangent. Take a look at this example.

Something feels not quite right. And its because Landis' cape (the human) is touching the hand of Inc The Robot.

So let's fix this by separating the 2 characters, giving them enough space.

Or another way to solve it is to overlap the two characters like this...

But wait! By overlapping, we've created a new tangent, Landis' head with Inc's arm.

So lets pull Landis a little to the left...

That works better, they still overlap, but no part of Landis is causing a tangent with Inc.

The Object Is Touching The Edge Of The Frame

As well as an object touching another object, and object can also cause a tangent by touching the edge of the piece. For example, this feels wrong...

Because the building is touching the top of the image...

Giving the building some headroom feels much better...

An Object In The Foreground Is Touching An Object In The Background

Similar to the first type of tangent, but in this case, unlike Inc and Landis who are standing at approximately the same depth in the painting, these two objects are at a radically different depth.

So not only are two objects touching which create a tangent, but one object is in the background and the other in the foreground, which confuses the eye even further. It causes you to ask "Is the building and the person at the same visual depth?"

This can be fixed by the same technique as before, moving the objects...

Or in the case of my final painting, I used mist / fog to eliminate the tangent.

A Foreground Object Is Touching A Background Object In A Straight Line

If a foreground object line continues a background object line, it can feel odd.

Fix this by moving one of the objects

Two Unrelated Objects Share The Same Horizontal Or Vertical Line

This is similar to the last one, but the two objects don't have to touch or be a line.

Let's decide that I wanted to add a bird to this painting.

This would be the worst spot for the bird, because it is directly above the head of Landis. In fact, if it were any lower, someone may think it was a hat instead of being a bird in the background.

So move the bird so it doesn't line up directly with any other objects in the scene.

Cut Down The Middle

Avoid cutting any reasonably symmetrical object down the middle, especially people, faces and hands. And avoid cutting people exactly half way down the center with the edge of the frame.

Oh no, Landis' face has been cut in half!

That's better. Oh wait, his left hand is too close to the edge of the frame, causing a new tangent!

Let's fix that. Ahhhhh!

Oh no! Looks like a tangent made it's way into my final painting!

Ah well, no one's perfect :)

Animated Tangent

Sp this is any of the tangent's above, but as part of an animation. The thing to remember is, if you still pause a single from of an animation, there may be a tangent, but the very next frame, the tangent might gone. So instead of looking at any specific frame of the animation, you instead only need to worry about tangents that hold on frame long enough to be noticed. So don't knit pick each individual frame, watch stuff at the same speed the audience will and fix any tangent you see in that context.

Using Tangents On Purpose

So one of the reasons tangents are best avoided is because the draw the eye, they become a focal point. And you don't want to draw the eye to a mistake. But there are instances where you can use tangents in order to draw the eye.

The most famous example would be the Sistine Chapel, painted by Michelangelo. The painting of God reaching out to touch Adam into life, those fingers create a major tangent. But it draws the eye to the most important part of the painting, where God gives Adam life. And so in this case, it would be using a tangent for good, not evil.

A less serious example, one of my favorite films is the Blues Brothers. There's a scene in the film where Murphy Dunne is talking outside Bob's country bunker, and directly behind him is a neon hat that's moving from side to side.

This obviously violates the Two Unrelated Objects Share The Same Horizontal Or Vertical Line rule, but it's done intentionally because the film is a comedy, and this tangent is funny, it looks like he's wearing a neon hat.

And here's artist John Baldessari using tangents as part of a conceptual art piece. The tree coming out of the man's head is obviously wrong, but that's the point of the art piece.

Conclusion

In conclusion, tangents are generally something best to be avoided, do your best, give a check to any piece of work you've made to make sure you don't have any, and don't be too hard on yourself if one or two slip in.

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