Ellipses

If you look straight down at the top of a cylinder, it’s a circle. But if you look at it at an angle, it becomes an ellipse, which is essentially a squashed circle.

You can draw a basic ellipse using string and push pins, as shown in the photo. (By the way, notice how smoothly the ends are rounded – it’s not a football shape.) You’ll often see a basic, symmetrical ellipse like that used to represent a circle seen in perspective. And sometimes that’s accurate enough. But circles are not immune to the laws of perspective, so let’s look a bit deeper.

A circle can be inscribed in a square. Let’s start there. Notice that the square and the circle have the same centre point, and that the circle touches the square at the midpoint of each side:

Now here it is viewed in perspective:

The perspective centre of the square is still the perspective centre of the circle also. And the circle still only touches the square at the (perspective) middle of each side – but that’s no longer the (measured) halfway point. One other thing to notice: the top and bottom halves of the circle are not mirror images. Although the circle only touches the side of the square at the midpoint, it actually continues widening slightly on the near side of the tangent point (past the green vertical line).

Similarly, the easiest way to draw a cylinder in correct perspective is to draw it inside a box, as shown in the video below. Also, the roundness of the ellipses in a cylinder increases as they move farther from eye level. So the top of the cylinder on the left in the video  is a flatter ellipse than the bottom.