将四元数拆分为轴旋转 [英] Split quaternion into axis rotations

问题描述

我有一个表示对象(黄色框和球体)方向的四元数.我想知道是否有可能将该四元数分解为其他四元数，从而使每个局部轴(X，Y和Z)旋转.

I have a quaternion representing the orientantion of an object (yellow box and sphere). I would like to know if it is possible to split that quaternion into other quaternions that give us the rotation of each local axis (X, Y and Z).

到目前为止，我一直在做Euler表示并使用它，但这并不是针对我的特定情况的正确解决方案:

What I have been doing until now is getting the Euler representation and work with it, but it is not the correct solution for my particular case:

给出两个点(蓝色框)，我想限制对象的方向，以便即使四元数从该平面之外也不能指向灰色平面.
我想分割(分解)四元数，因为当我的对象达到平面的极限(例如，右侧)时，我想使其保持在该位置(在该组件中)，然后在垂直组件中旋转我的对象，使用新的分裂四元数之一.

Given two points (blue boxes), I want to limit the orientation of my object so that it can't point out of the grey plane, even if my quaternion looks out of that plane.
I want to split (decompose) the quaternion, because when my object reachs the limit of the plane (for instance, the right), I want to make it stay there (in that component), and then rotate my object in the vertical component, using one of the new splitted quaternion.

我正在与Unity合作.

I am working with Unity.

我希望这是可以理解的问题:)

I hope it is understandable my problem :)

推荐答案

这里是一种仅获取y轴局部旋转的方法.可以修改此功能以获取x轴或z轴.

Here's a way to get the local rotation of just the y-axis. This function can be modified to get the x or z-axis.

/// <summary> isolate the y-Component of a rotation </summary>
private Quaternion yRotation(Quaternion q)
{
    float theta = Mathf.Atan2(q.y, q.w);

    // quaternion representing rotation about the y axis
    return new Quaternion(0, Mathf.Sin(theta), 0, Mathf.Cos(theta));
}

您可以通过转换为Euler在Unity检查器中验证结果:

You can verify the result in the Unity inspector by converting to Euler:

public float yLocal;
void Update()
{
    yLocal = yRotation(this.transform.rotation).eulerAngles.y;
}

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