Euler angles and Quaterean

• what is Euler angles ?（欧拉角是什么东西？）

• The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system (被欧拉引入用三个角度来描述刚体相对于固定参考系的旋转)

• Euler angles are typically denoted as α, β, γ, or ψ, θ, φ. Different authors may use different sets of rotation axes to define Euler angles, or different names for the same angles. Therefore, any discussion employing Euler angles should always be preceded by their definition.
  （欧拉角的旋转次序并不是固定的，可以有不同的旋转顺序。常见的欧拉角旋转顺序包括：ZYX、ZYZ、XYZ、XZY、YXZ、YZX等等。这些不同的旋转次序会影响到最终的旋转结果，因此在使用欧拉角时需要明确所采用的旋转次序）

使用欧拉角推导旋转的过程 要注意两个对应点向量在旋转平面内始终垂直。

why is quaternion ?

First introduce the complex numbers and 2-D rotation
z = a + bi , there, the real part is the a and the imaginary part is b.
一个复数 z = a + bi 和任意一个复数c 相乘 等价于将c 逆时针旋转 thata = atan2 (b,a), 并将其缩放 ||z|| = square ( pow(a,2), pow(b,2)).