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Let's get started

Before we begin, let's establish some assumptions I'll be making. I hate the way many articles leave this important section out, causing a great deal of confusion when it comes to the mathematics.

Coordinate System - This article assumes a right hand coordinate system, like OpenGL. If you are using a left handed coordinate system like Direct3D, you may need to transpose the matrices. Note that the Direct3D samples have a quaternion library already, though I recommend you check through their implementation before using it.

Rotation Order - The sequence of rotations in the Euler representation is X, then Y, and then Z. In matrix form:

RotX * RotY * RotZ      <-- Very Important

Matrix - Matrices are in column major format, like they are in OpenGL.

Example [ 0  4  8  12
          1  5  9  13
          2  6  10 14
          3  7  11 15 ]

Vectors and Points - Implemented as a 4x1 matrix so applying a transformation is of the order

Rotation Matrix*  [ vx
                    vy
                    vz
                    1  ]  <-- 4x1 vector

This does not imply that I prefer OpenGL over Direct3D. It just happened that I learned OpenGL first, and so my quaternion knowledge was gained in OpenGL.

Note: If you specify rotations in another order, certain quaternion functions will be implemented differently, especially those that deal with Euler representation.

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