任意一个角位移都有两个四元数的表示法，即 q 和 -q。
w 的绝对值越接近 1 表示没有旋转
public x: number = 0,
public y: number = 0,
public z: number = 0,
public w: number = 1
应该永远返回1，因为我们使用单位四元数
应该永远返回1，因为我们使用单位四元数
点乘与Vector类似，结果是一个标量，单位四元数点乘的结果范围为 −1 ≤ a · b ≤ 1
the quaternion dot product gives the cosine of half of the angle needed to rotate one quaternion into the other
If q1 • q2 is close to 1 (assuming that they're normalized), then they apply very similar rotations. Also, since we know that the negation of a quaternion performs the same rotation as the original, if the dot product is close to −1, the two still apply very similar rotations.
conjugate() 为反转向量部分
q∗ = [w v]* = [w −v]
由于是单位四元数 invert() 与 conjugate() 返回值相同
/**
* rotation quaternions are all unit quaternions
* so the conjugate and inverse are equivalent
*/
四元数乘法又叫 Hamilton product , 与矩阵乘法类似，乘法顺序不可交换， 单位四元数与单位四元数相乘后结果仍然是单位四元数。
p′ = qpq^−1
fromAxisAngle / toAxisAngle
//-----------------
cos(θ/2) sin(θ/2)nˆ,
// https://www.3dgep.com/understanding-quaternions/
http://allenchou.net/2018/05/game-math-deriving-the-slerp-formula/
https://github.com/mrdoob/three.js/blob/dev/src/math/Quaternion.js