Quaternions

• Manual: https://docs.unity3d.com/Manual/class-Quaternion.html

• Scripting: https://docs.unity3d.com/ScriptReference/Quaternion.html

• Unity uses the Quaternion class to store the 3 dimensional rotation of gameobjects

  • The Euler angles - the XYZ values you see in the inspector
  • The Quaternion values - the underlying value which Unity stores the actual rotation of GameObjects

• When handling rotations, you should use the Quaternion class and its functions to create and modify rotational values

  • You should use the Quaternion Class functions that deal with Euler angles - Retrieving, modifying, and re-applying Euler values from a rotation can cause unintentional side-effects

• Orientation

  • Where the object is pointing at

• Rotation

  • Changing the orientation

Eulers

• Rotation order matters (XYZ, YZX Eulers results differently with the same values!)
• Gimbal locks
  • It overlaps! The blue and green rotation represents the same axis
  • Quaternions remove this issue!

Quaternions

• used to represent rotations

• four-tuple of real numbers {x,y,z,w}

  • x,y,z aren’t an axis!!

• After normalization we have a “Unit” Quaternion

  • Divide each components by its length
  • $U_q=q/||q||$
  • It’s recommended to mormalize your quaternions

https://youtu.be/1yoFjjJRnLY?si=042uY6ao__8gbbRt