Rotations

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A point P=(x,y,z) is represented with the quaternion p = ix + jy + kz.
A rotation of the angle clip0067 around the x-axis is represented with the quaternion
clip0068 .
The rotated point is clip0069.

Conversion of quaternion to rotation matrix
clip0070
-->
clip0071

Conversion of rotation matrix to quaternion
clip0072
clip0064
clip0073
clip0065
clip0066