Lesson 1: Lines, Ellipses and Boxes

So, what is an ellipse? Is it just a fancy word for an oval?

Ellipses are extremely important and notoriously annoying to draw. You'll find them all over the place in mechanical drawings. Cars, space ships, tanks, machines - anything man made will probably make extensive use of ellipses.

They're so prevalent because they allow us to, with relative accuracy, represent a circle as it sits in 3D space. If you take any circular object - a coin for instance - and turn it this way and that, you'll notice that the 2D shape your eyes actually see isn't always going to be a circle. It will however, generally be ellipsoid.

An ellipse has several specific properties:

• Its scale, the overall size of the ellipse

• Its orientation, the angle at which it is positioned

• Its degree, effectively the width of the narrower dimension of the ellipse

You'll also see here that there are two axes:

• The major axis, which defines the widest span of the ellipse

• The minor axis, which defines the narrowest span of the ellipse (which is also its degree)

These two axes run perpendicular to one another. The major axis does not, and will never, matter. The minor axis is extremely important however. That can be a little difficult to grasp at first, due to their infuriatingly unintuitive naming scheme.

Now, while the major axis is largely irrelevant, the minor axis is critical when we start thinking about 3D space. The reason it's so important is that while the minor axis represents something in 2D space (the narrowest span across the ellipse), it also represents something important in 3D space as well.

In 3D, the minor axis represents a line, or in math terms a vector that points straight off the surface of the circle. It runs perfectly perpendicular to that surface.

This is incredibly useful when drawing cylinders and other ellipse-based 3D forms. In a cylinder, you can imagine that there is a straight spine that connects the circles on either end. This spine is the minor axis, which runs perpendicular to both circles and helps us to align them correctly.

If their minor axes don't match up, then you'd end up with a tube with one end sheared off at an angle, rather than straight across.