I am very fond of painting buildings, walls, fences, windows. So my paintings have lots of lines and shapes that have to fit together. Getting the lines into their right spot on the canvas is half the battle in the quest to produce a good painting. But it’s very easy to make mistakes. Let's say I want to draw a box on a table. I could draw it like this.
Why does the composition look so awful? Because the top of the box and the far side of the table meet. I could fix the drawing to look like this where the top of the box is above the table level.
Or this is even better using two point perspective I have turned the box on an angle which makes for a far more interesting object. I have also shown it as an open box which makes the viewer wonder what might be inside.
Tangents occur where two lines touch each other. They are of course essential in mathematics. But in painting they can cause all kinds of problems and can ruin your painting. If two lines meet in a composition the viewer can become confused with the ambiguity. Let's say you want to draw or paint a tree in front of a fence. Don't place it here alongside the fence post as this will confuse your viewers.
Place it here.
I've gone back over some of my own paintings to see how I went getting the lines in the correct place. This painting, Barney Glade and His Contentments has three minor line problems which I have marked. One sock lines up with the door frame; the T-shirt lines up with the distant door architrave; and Barney's sleeve is in direct line with the drain pipe. I get away with the errors as they are not important to the basic composition. If these touching lines were more central to the painting the viewer might be bothered.
In my two Windows on a Time paintings I had all kinds of problems with the lines. If you want to show buildings through windows and doorways you are bound to run into problems. Take a look at Windows on a Time: Two and see if I have passed.
In my Night Developments I have deliberately shown the people of the night lined up like the lamp posts between the buildings. I was particularly careful not to create any confusing line intersections. I hope I was successful.
And also in my Les Toits de Paris where I had chimneys, lamp posts and windows (all contesting for attention), I was very careful to line up these objects in such a way as to avoid ambiguity.
I have never tried to paint a Still Life but I do know that this is where you really have to keep your mind on the job as you have to juggle so many objects. Let’s see how the experts do it. This first example is by Dutch artist Pieter Claesz. Notice the careful arrangement of the objects and how none of the objects touch in a way that is jarring on the eye. Also notice how the peel of the orange takes your eye off the edge of the table where the plate hangs over. Imagine what this part of the painting would look like without the peel. And the plate hanging over the right hand edge is placed with an excellent eye for composition.
This is Still Life Violin and Music by William Harnett. Study the careful arrangements of the objects so as not to cause confusion. The placement of the music, horseshoe, tin whistle and a paper note have softened the effect of the otherwise horizontal or vertical placement of the objects. Notice how the whistle just misses touching the edge of the object above it.
Even Escher who was the master of multiple perspectives within an image, was the master of intersecting lines and avoiding troublesome tangents.
And when producing his woodcut of Still Life and Street Escher obeyed the rules where no objects cause ambiguity. Even the books nearest the streetscape, lined up on the same plane, connect the still life to the street. Brilliant!
I think a safe rule would be, when in doubt overlap. Try to avoid point to point touching.
Everything I have said about tangents in paintings applies in photography. You can ruin a good photo with tangents.
If you are learning to paint and want to know more about Troublesome Tagents in paintings please go to the excellent site of Marc Dalessio which has examples of bad alignments and how to fix them.