The word tangent comes from a Latin word tangens. It means "to touch." Although tangent has precise mathematical meanings in both geometry and calculus, we'll stick with the original definition and apply it to the visual geometry of images.
Mathematically, a "tangent point" is the location where a line intersects with an arc. Although the mathematical definition applies to a single line and a single arc, PJs must herd cats into a single frame and might have several arcs and lines within the same frame. Any of these intersections may create unwanted or avoidable tangents.
How PJs define tangent
Most tangents occur with a line and an arc. For practical PJ applications, any part of a defined geometric shape (or entire image element) intersecting another geometric shape is considered a tangent.
There are two significant ways we apply the word tangent when we shoot and critique images. The first is held within the image. The second applies to frame edges. Generally, the word tangent isn't good to hear during a critique. It means the PJ was probably sloppy while shooting or cropping an image.
Sometimes tangents can't be avoided. More often, they can (and should be).
When are tangents good?
Many PJs say, "never." However, a tangent is also a powerful tool if used with skill.
As with everything involved in both art and composition, the use or avoidance of tangents is subjective. The rules can be broken, but do so deliberately rather than through ignorance or inattention.
Viewers follow lines with their eyes. When the line encounters a tangent point, the viewer momentarily stops. The viewer scans around the tangent point for signals before proceeding.
In this way, a tangent acts like a four-way traffic intersection. If PJs place important information near one of these tangential locations, viewers are more likely to notice it.
Often the word "leading line" is encountered while explaining this idea. However, most new PJs obsess about the leading line while missing the point. PJs must understand the leading line can't go tangent with the main subject.
A tangent line is a visual spear. When it's placed through someone's skull, it's not a leading line. It's the death of an image.
The line's purpose is to lead the eye toward the focal point without intersecting. The leading line is made more powerful when a tangent is placed near the focal point. Thus, the eye is directed to the appropriate area and stops momentarily to get to the purpose of the image. This is subtle and requires finesse.
Tangents within images
Unless an image is made against seamless paper or a clean backdrop, the likelihood of a tangent line is high. This is due to both the common shape of our primary subjects (people) and environment (shelters). Bluntly, people are arcs and structures are lines.
Even in nature, fauna are combinations of arcs while flora tend to be lines. Consider a bear walking through the woods. The bear is a series of arcs while the trees are at least two lines (one on each side of the trunk and two more for each branch).
If the bear walks in front of three small trees, there are 12 tangent points (two per tree both above and below the bear).
Although we could obsess, the point is to understand the problem exists. Then, we can further understand when to ignore or spaz about these tangents.
2D geometric design
Photography is a two dimensional art. We detailed this in the Address basic composition post. Every visual element within the frame ultimately becomes a series of geometric shapes once captured in these two dimensions.
We learned it's important to keep visual elements separated through the use of tone, contrast and color.
Once we are looking at 3-D scenes as a series of adjustable 2-D geometric shapes, then life becomes easier. Often, all it takes is closing one eye to understand the difference, but it still takes some training beyond this simple exercise.
We must "see" in 2-D to understand how it translates to the finished image. This is only accomplished after many, many images and failures.
Tangents along frame edges
I'll probably do an entire post on frame edges one day because they're so important. However, since we're talking tangents today, let's at least address the problem.
The entire length of each of the frame's four edges is a line. Any element that intersects the lines makes a tangent. Each tangent along the frame's edge is a potential leaping point for a viewer. Thus, it's critical to keep frame edges clean and tangent-free.
Whenever possible, use curved lines (arcs) to redirect the viewer away from the edges and back to the focal point of the image. It's much better to incorporate a dark area or completely out-of-focus foreground element along the edges than to allow a tangent to occur and lose a viewer. PJs only get a few seconds with each viewer; we must keep the viewer as long as we can on each image.
How to avoid tangents
Often, it's a matter of looking at the scene and seeing the 2-D elements within the scene. Then, select the appropriate lens based on depth of field and background options.
Experienced PJs already position themselves to avoid tangents. Sometimes it's impossible. Then, try to minimize the tangents' impact or use it to your advantage. However, newer PJs need to learn to move around the scene to get the right separation of elements with the proper lens to avoid tangent lines. This is best done with the PJ's eye up to the viewfinder.
All of this must be kept within the four edges of the frame without causing additional tangents.
Once this is accomplished, we can add layers of information for a stong skeletal structure and make sure we have dark corners and, hopefully, we started with interesting subject matter and quality light.
Like I said, it's like herding cats into a single frame. Quality images are everywhere, it's up to PJs to find them. Knowing to recognize avoidable tangents is a significant step in the right direction.
Test your knowledge
Take a look at today's images. As you look through them, ask yourself which image presents the most obstacles to telling the story and keeping a viewer's attention. I'd say it's frame No. 2 of the Jefferson County Courthouse.
Now, ask yourself, "why?" and answer the question. Hint: it involves tangents.
Enough for now,