“距离"是指四元数之间的距离(或角度大小)? [英] "Distance" (or angular magnitude) between two quaternions?

问题描述

我想找到两个四元数之间的距离".距离"是指单个浮点数或整数，而不是另一个四元数(这就是区别，即 inverse(q1)* q2 ).我猜你可以称呼我想要的角度大小".

I want to find the "distance" between two quaternions. By "distance" I mean a single float or int, not another quaternion (that would be the difference, i.e. inverse(q1)*q2). I guess you could call what I want "angular magnitude".

我需要从物理角度进一步旋转物理对象，然后再施加更大的扭矩.

I need to apply more torque to a physics object the further it's rotated from its original angle.

我不了解四元数中涉及的数学，因此基于代码的示例将非常有帮助.我已经看过其他几个问题，但我不相信有任何答案，或者至少不会以我理解的方式回答.

I don't understand the maths involved in quaternions, so a code-based example would be most helpful. I've looked at several other questions but I don't believe any answer my question, or at least not in a way I understand it.

推荐答案

找出差分四元数qd = inverse(q1)* q2).

Find the difference quaternion qd = inverse(q1)*q2).

通过角度= 2 *找到q1和q2之间的角度* atan2(qd.vec().length()，qd.w())//注意:带符号

Than find the angle between q1 and q2 by angle = 2 * atan2(qd.vec().length(), qd.w()) // NOTE: signed

这里的角度"是从q1到q2的最短弧线旋转角度.

The "angle" here, is the angle of rotation from q1 to q2 by shortest arc.

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