Question

我有一个四元数，来自具有以下内容的系统：

Right handed.
Forward direction: Y axis
Right direction: X axis
Up direction: Z axis

我需要将其转换为以下坐标系：

left-handed.
Forward direction: X axis
Right direction: Y axis
Up direction: Z axis

我试过否定轴和角度，我试过切换值，我不能让它工作。所有帮助非常感谢！我在C＃工作，

Microsoft.Xna.Quaternion.

Answer 1

A quaternion is a structure of four values (w, x, y, z). If it represents a rotation, then w = cos(phi/2) (phi being the rotation angle) and (x, y, z) = sin(phi/2) * (ax, ay, az) ((ax, ay, az) being the rotation axis).

In order to convert the quaternion to another system, it is sufficient to transform the rotation axis. For your example, the transform is:

    / 0  1  0 \
T = | 1  0  0 |
    \ 0  0  1 /

Finally, since you are changing handedness, you must invert the quaternion or it will rotate in the wrong direction. Summarizing, the transformed quaternion is:

(w*, x*, y*, z*) = (w, -y, -x, -z)

In general:

(x*, y*, z*) = det(T) T (x, y, z) //Assuming column vectors

切换四元数的轴和手性？

1 个答案: