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请问单位四元数点乘等于其夹角的余弦值, 可以添加证明吗? #34

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young40 opened this issue Jul 1, 2022 · 1 comment

young40 commented Jul 1, 2022

“因为 𝑞0 与 𝑞1 都是单位四元数，𝑞0 · 𝑞1 正好是这两个四元数在 4D 空间中夹角的余弦值”, 这句在三维的情况下成立, 四维的情况, 是不是需要添加个证明?

谢谢!

cam1681 commented Apr 7, 2024

这个很简单，是把四元数当成一个4D的向量来看的， q0\cdot q1 = |q0| * |q_1| * cos<q0, q_1> 因为是单位四元数，所以 |q0|=|q1|=1

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