Learn how you can understand and implement quaternion rotations in your game projects


Quaternions are like vegetables. You know they are good for you but you aren’t sure why and if only you knew how to make them taste good. Okay so you aren’t going to be eating quaternions, but you get the idea.  They are this really advanced topic in geometry and mathematics that anyone who designs or programs games has heard about, might have even used, but have no real understanding about what they are achieving and why they are better than other methods.

This short course will demystify the concept for you.  No, it won’t give you the level of understanding of a postgraduate university mathematics major but it will provide you with the theory that will help you put quaternions and rotations in 3D space in context and give you the skills to use them with confidence in your game projects to overcome the limitations of other rotational methods.

Learn how to program and work with:

  • 4×4 Matrices to represent Euler angles.
  • Quaternion operations included in the Unity API.
  • Rotational controls for Slerp, RotateTowards, and LookAt.

Contents and Overview

In this short course, you will gain an understanding of the history of rotational mathematics and how quaternions came into existence.  It begins by examining Euler angles and how they are used to orient objects in 3D while then proceeding to explain how Euler angle multiplication breaks down into the issue known as ‘gimbal lock’.

Following this, a conceptual examination of basic rotational geometry is extrapolated from 2D space into the quaternion 4D.  It is then explained how 4 dimensions can be applied to 3D by implementing axis-angle rotations.

The second half of the course provides some hands-on tutorials for applying quaternions to move and rotate 3D objects in the Unity Game Engine using C#.

What students are saying about Penny’s courses:

  • Turns out, the hardest part of this course for me is finding the words to describe how glad I am to have enrolled in it.
  • I honestly love Hollistic’s teaching approach and I’ve never learned so much within a few hours about coding effectively with such detailed explanations!
  • Penny is an excellent instructor and she does a great job of breaking down complex concepts into smaller, easy-to-understand topics.






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Euler Angles

Euler Rotation Matrices

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Euler Angles with Matrices

Gimbal Lock


What are Quaternions?

Rotating Around World Axes with Quaternions

Yawing, Pitching and Rolling an Aircraft



Slerping Again

Challenge Project

Final Words

Some Final Words from Penny

Where to now?