我可以在四元数中切换 X Y Z 吗? [英] Can i switch X Y Z in a quaternion?

问题描述

我有一个 Y 轴向上的坐标系.我需要将其转换为 Z 为 UP 的坐标系.我将旋转存储在四元数中，所以我的问题是:如果我有一个四元数 X、Y、Z，我可以将 Y 与 Z 切换并得到 Z 实际上向上的结果吗?

i have a coordinate system where the Y axis is UP. I need to convert it to a coordinate system where Z is UP. I have the rotations stored in quaternions, so my question is : if i have a quaternion X,Y,Z can i switch the Y with the Z and get the result that Z is actually UP?

推荐答案

只是在四元数中交换两个轴?不，这不起作用，因为这会翻转手性.然而，如果你翻转手性并否定四元数的实部，那么你又回到了原来的手性.在一般形式中，您可以将其写为

Just swpping two axes in a quaternions? No this doesn't work because this flips the chirality. However if you flip the chirality and negate the quaternion's real part then you're back in the original chirality. In general form you can write this as

Q'(Q, i'j'k') = ε_i'j'k' Q_w_w + Q_i_i + Q_j_j + Q_k_k

Q'(Q, i'j'k') = ε_i'j'k' Q_w_w + Q_i_i + Q_j_j + Q_k_k

哪里

是完全反对称的张量，称为 Levi-Cevita 符号.

is the totally antisymmetric tensor, known as the Levi-Cevita symbol.

这不足为奇，因为四元数的 i²、j²、k² 规则也是由同一个完全反对称的张量定义的.

This shouldn't be a surprise, as the i², j², k² rules of quaternions are defined also by the same totally antisymmetric tensor.

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