Perspective is an art technique for creating an illusion of three-dimensions (depth and space) on a two-dimensional (flat) surface. Perspective is what makes a painting seem to have form, distance, and look "real". The same rules of perspective apply to all subjects, whether it's a landscape, seascape, still life, interior scene, portrait, or figure painting.
Perspective in Western art is often called linear perspective, and was developed in the early 15th century. The system uses straight lines to plot or figure out where things must go. (Think of it as light traveling in straight lines.) The Renaissance artist Leon Battista Alberti and architect Filippo Brunelleschi are credited with the "invention" of linear perspective. Alberti set out his theory in his book "On Painting," published in 1435. We're still using Alberti's one-vanishing-point system today!
Perspective is possibly the most feared aspect of learning how to paint. The mere word "perspective" makes many a hand tremor. But it's not the basic rules of perspective that are hard, it's the consistent application of the rules to every bit of a painting that's hard. You need to have the patience to check the perspective as the painting progresses, and to take the time to fix it. The good news is that learning perspective is like learning how to mix colors. Initially you have to think about it all the time, but with practice it becomes increasingly instinctive.
There is a fair bit of terminology used in perspective, and if you try to take it in all at once, it can seem overwhelming. Take it slowly, one step or term at a time, and get comfortable with a term before moving on to the next. That's how you master perspective.
Viewpoint is the spot (point) from which you, the artist, is looking at (viewing) the scene. Linear perspective is worked out according to this viewpoint. There's no right or wrong choice of viewpoint, it's simply the first decision you make when beginning to plan your composition and figure out the perspective.
Normal viewpoint is how an adult sees the world when standing up. When painting in a realistic style, this is the viewpoint you'll probably use because it's what we're accustomed to seeing. It's what looks most real.
A low viewpoint is when you're looking at a scene from much lower than you would standing up. For instance if you were sitting on a chair, had crouched down onto your heels or, even lower down, sitting on the grass. Of course, it's also the level from which small children see the world.
A high viewpoint is when you're looking down on a scene. You might be on a ladder, up a hill, on the balcony of a tall building.
The rules of perspective don't change between a normal, low, or high viewpoint. The same rules apply in all cases. What changes is what you see in a scene. The rules of perspective help us interpret and understand what we're seeing, and enable us to "get it right" in a painting.
Perspective Assignment #1: Using a pencil or pen in your sketchbook, do at least two thumbnail sketches of two different scenes from both a standing and a low viewpoint. Start by drawing an outline of the shape of your canvas, say a rectangle that's 2x1, then put down the main lines and shapes of the scene. Label the thumbnails "viewpoint," so you'll remember why you did them at a later date.
Horizon line is a confusing perspective term because when you hear it, you tend to immediately think of "the horizon" we see in nature. That is, the horizon as in the line where the land or sea meets the sky in the distance. In a painting, the horizon line might be this if you're painting a landscape, but it's best to disconnect the two. Rather, when you hear "horizon line," you want to be thinking "eye level line."
If you draw an imaginary line across the scene at the level of your eyes, that's the horizon line. As you change position, for instance walk up a hill, the horizon line moves up with you. When you glance down or up, the horizon line doesn't move because the level of your head hasn't moved.
The horizon line is an imaginary line used to create accurate perspective in a painting. Anything above the horizon line slopes down towards it, and anything below the horizon line slopes up towards it. Depending on what it is and how it is positioned, this may be very obvious or it may be very slight. Something that straddles the horizon line will slope both up and down. The horizon line is important because the painting's perspective is constructed from this.
Perspective Assignment #2: Spend some time observing how objects are positioned in relation to your eye level, whether they're sloping up or down (or parallel to it). Sit somewhere that's got lots of strong lines, such as a large room with lots of furniture and shelves. Use one finger as the horizon line, and a finger on the other hand to judge the angles of various objects in relation to the horizon line.
Vanishing lines are imaginary lines used to create accurate perspective in a painting. They are drawn on the top and bottom horizontal edges of an object, along the object and then extended all the way to the horizon line. For instance on a building, there would be a vanishing line along the top of the roof and the bottom of the wall(s). For a window, the top and bottom of the frame.
If the object is below the horizon line, its vanishing lines angle up to the horizon line. If the object is above, they slope down. All vanishing lines end at the horizon line. And vanishing lines from parallel edges on the same object meet at a point on the horizon line.
Whether or not an object has vanishing lines depends on how it's positioned in relation to the horizon line. Edges of objects parallel to the horizon line don't have vanishing lines. (Why? Because they don't recede into the distance and never intersect the horizon line.) For example, if you're looking straight onto a house (so you're seeing one side only), the front face of the building is positioned parallel to the horizon line (and so are its edges). You can easily check if it's parallel by holding a finger along the bottom of the house and another at the horizon line (eye height).
Don't stress if it all seems complicated and confusing. Reading about perspective is harder than seeing it and doing it. "Horizon line" and "vanishing line" is all the terminology you need to implement one-point perspective and two-point perspective. You already know what one-point perspective is; while you may not know that's what it's called, you'll recognize it when you see it...
There are various methods for judging the angles of vanishing lines. The one that works best for me is to visualize it as the hour hand on a clock.
I do it like this: The minute hand serves as either the horizon line (the position it's at 9 or 3 o'clock) or a vertical (12 o'clock). Then I look at the vanishing line, and think of it as being the hour hand on a clock. I then read "the time", and remember this as I mark it on my painting.
Thus, in the photo, the vanishing line at foot level is coming up at about eight o'clock. And the vanishing line above the figure's head is coming in at about ten o'clock. (The photo is of The Art Bin.)
You're looking at one-point perspective when you're standing on a station staring down the railway track which narrows and then disappears at a spot in the distance. The same with an avenue of trees, or a long straight road.
In the photo, it's very clear how the tar road narrows and narrows as it gets further and further away. If you look carefully, you'll see how the verges on the sides of the road do the same. As do the electricity poles to the left and the white lines painted in the center of the road.
If you draw vanishing lines along the edges of the road, these meet on the horizon line, as shown in red in the photo. That's one point perspective.
That things further away from us look smaller isn't a revelation, it's something we see every day. The photos here illustrate what we mean: the height of the man on the escalator doesn't change, he's still five foot something tall when he reaches the top of the stairs. He simply appears shorter because he's further away from where I was standing when I took the photos. (It's Waverley Steps in Edinburgh, for anyone interested).
Accurate relative scale of objects is part of the illusion we're creating when we apply the rules of perspective in a composition. We can create a sense of distance by painting things in the background smaller than they are in the foreground. Yet, somehow, it's all too easy to forget and then you're left wondering why a painting isn't working!
If you're creating from imagination (rather than observation) and aren't sure how large to make an object, judge it by what else is in that part of the painting. For instance, if you have a tree and you want a person standing next to it, the tree will likely tower above the figure (unless it's a sapling, of course). If the person is standing next to a car, they'll likely be taller if they're an adult.