In lecture, we saw that we could represent rotations as rotation matrices, or other angles in the axis angle representation(轴角参数化). In this segment, we'll discuss a final method of representation for rotations, namely using quaternions（四数）.
A quaternion is a fourtuple. This set of numbers is often interpreted as a constant component q_zero, and a three-dimensional vector component q.
Operations with Quaternions
Application of Quaternions
The angle of rotation is a scalar, and the axis of rotation is a three-dimensional vector.
Rearrange the form, we obtained:
For its beautiful properties, we can easily compose two and more rotations:
Advantages of Quaternions
Euler angle have singularities in two poles, the quarternions can solve the problem. Rotation matrix have 9 indentical terms which is complex that using quaternions.