Drawabox.com | Part One: The Basics | Lesson 1: Lines, Ellipses and Boxes | Ellipses | The degree
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Lesson 1: Lines, Ellipses and Boxes

Ellipses

What is an ellipse?

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.

The anatomy of an ellipse

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.

The degree

This is going to become quite important as we get into the next lesson, but I think it's important to introduce this concept now. If you take a circular coin, or some other similar object like a CD and hold it up so its face points towards you, you're going to see a circle. It's still an ellipse (a circle is an ellipse after all), but the degree of this ellipse (literally measured in degrees) is going to be 90°. That is the angle between your vision (like an arrow coming straight out of your face) and the surface of the circle.

As this disc or coin turns however, the degree of the ellipse gets smaller, and therefore the ellipse gets narrower and narrower, until finally you're looking at the edge of the object, or an ellipse with a degree of 0°, as shown with the image above. Far left is 90°, far right is 0°.

The minor axis

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.

Homework and exercises

Every Drawabox lesson consists of lecture content and exercises that are assigned as homework. It's best to complete this homework before moving onto the next section. As this lesson consists of three sections (lines, ellipses, boxes), it is best that you only submit your work for review when you've completed all three.

The homework assignment for this section is as follows:

All the assigned work for this section should be done in ink, using fineliners/felt tip pens as described here. In a pinch, I will accept work done in ballpoint, but only if the situation is dire. This is an exception only for this lesson as students get started.

All of these ellipses are making me dizzy! I need to go take a nap. I'll be back later, but for now...

You can listen to my reading of this lesson material!

<<< Lines: Homework
Boxes >>>
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Getting Your Work Critiqued

Critiques on reddit.com Critiques on our discord chat server

Having your work reviewed by others is critical, as those who are just starting out aren't in a position to properly judge their own work, and won't be for quite some time. Don't be afraid to show your struggles - it's by analyzing your mistakes that we can help you grow. Perfect homework is not what we're looking for; we just need it to be complete.

There are currently two places you can get your work critiqued by the community - Reddit and our Discord Chat Server.

Both of these are completely free.

Private Patreon Critiques

Critiques on reddit.com

If you are interested in receiving extra help, I critique the work of those who support Drawabox on Patreon.

All of these private critiques are done through reddit, in specific threads where students post their work as a comment, including a link to their work (often hosted on Imgur, though most image hosts are okay).

My requirements are more strict than the free community critiques:

  • You must complete the lessons in order, in their entirety, starting from lesson 1
  • All work for the lesson must be completed - that means all exercises in the lesson, not just those in a given section
  • You may only move onto the next lesson once the previous has been marked complete
  • The work must be done in the tools recommended in the lesson

The minimum pledge for this lesson is $5.00/month. The orange button above will take you to the reddit thread for this lesson, you can post a link to your work there and I'll be notified. Once I catch the submission, I'll add it to this backlog spreadsheet.

Pledges are collected at the beginning of the following month, but you may start submitting your work immediately. If you're a new patron, I'll be reaching out to your shortly to collect your reddit username.

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