Everything in the world is subject to the laws of perspective. Even if that sounds both tedious and slightly scary, we have to go with it if we are going to try to draw objects. But we will also discover how perspective can help us understand how objects look. And that we can actually cheat with perspective, too—so we’re not getting superfrustrated instead of having fun. And let’s start with some good news: It’s the same technique for both rectangles and for circles… .
First, let’s think about this mathematical rule:
Perspective = location within a space + viewpoint + vanishing point + horizon line.
The vanishing point is an imaginary point representing the infinite distance, which we place on the horizon line of the drawing. The horizon line marks the separation between the ground and the sky. And we need a vanishing point because all the parallel lines in a drawing will converge toward this exact point.
To start a drawing, we first need to decide where to place the horizon line and the vanishing point. Just by doing this, we are already making some big decisions about the drawing. There are an infinite number of vanishing points along the horizon line, and by taking just one step to one side or the other will already change the viewpoint, which will in turn change the vanishing point, and the perspective. The key is to figure out how to choose a good vanishing point, and a good horizon line.
With the horizon line midway down the sheet of paper, and the vanishing point midway along the horizon line, you get a head-on viewpoint. This is one to avoid. The perspective won’t be any easier to construct, and the drawing will risk looking a bit dull.
Putting the horizon line higher up on the paper can give the impression that we, the viewer, are either nearer to the ground, or small in relation to the overall scene, or even that the background is quite close to our viewpoint (like the wall of a room).
On the other hand, if the horizon line is lower down, it could show that we are very high up, or relatively tall, or that the backdrop is a long way off.
Here is the horizon line with a red dot showing the vanishing point (chosen at random), and a rectangle.
To draw a rectangular solid shape, start by tracing lines from each corner and back to the vanishing point. These lines are called vanishing lines, or construction lines.
The vanishing lines create a sort of “corridor” in which you could draw an infinite number of rectangles. So next, just select one point on one of the vanishing lines, and then simply draw in the horizontals and verticals. We now have a rectangle that has changed dimensions (becoming smaller) while keeping the exact proportions of the original rectangle. This allows our brain to pick up an effect of depth in the drawing: the illusion of three dimensions.
No need to draw any more lines. I can use the vanishing lines as the edges of my shape—and so here is the finished rectangle in perspective.
One thing to watch: in the previous example, we placed our rectangle completely below the horizon line. But we can just as easily place it across this line, or completely above it—and still be able to draw in the construction lines to the vanishing point.
In the first example, we were looking down onto the object from above, and could see the top of it. This time, we are slightly below it, with the object placed on the ground and extending up into the sky section of the drawing. So we can no longer see the top of it.
Yes but … what happens if the first rectangle that we draw is not seen head-on? In this case, things are a little more complicated because we now need TWO vanishing points.
The basic principle is the same, and the aim is still to draw vanishing lines from the corners of the shape and back to the vanishing points.
Once again, you can decide how deep you want to make your object, but this time you will locate the four corners of the second rectangle by crossing the two “corridors” created by the two sets of lines heading to the two vanishing points.
The result is an object that is not directly facing the viewer, and which perspective has “deformed” into an interesting shape!
So how about a circle? It has no straight edges or corners, so how do we put it in perspective? Well, to start with, remember that a circle can also be drawn inside a square… .
Once you do that, the circle simply follows the same transformations that the square shape goes through when drawn in perspective—so it basically becomes more of an elliptical shape.
If you put the circle into a square, you can always figure out how circles are going to look in perspective—even with two vanishing points. And these circles-in-boxes combinations look pretty good, too.
If you try to put a circular profile in perspective with a vanishing point …
… you end up with a cylinder!
Without any corners to connect up to the vanishing lines, you can see how tricky this can be. You may find it easier to do this by drawing the circle in a square, and then creating a cube. If you try to draw a circle in perspective with two vanishing points, you end up with a sphere. Seriously. Try it!
Right through the center there is an axis that also runs through the center of all the circles that make up the cylinder.
All the curves that run around the cylinder are parallel with each other.