Quaternion to matrix rotation only one axis

问题

I have a quaternion that contains the rotation of the three axes (x, y, z) at the same time.

I want to convert this quaternion to a rotation matrix but only the rotation on the Y axis of the quaternion or of any of the other axes, without all three at the same time.

回答1:

A possible route:

• Transform unit vectors X=(1,0,0) and Z=(0,0,1) by the quaternion
• Call these rotated vectors (x0,x1,x2) and (z0,z1,z2)
• If the rotation would have been purely around Y, we would have:
  • (x0,x1,x2) = (cos(theta), 0, sin(theta))
  • (z0,z1,z2) = (-sin(theta), 0, cos(theta))
  • not used is (y0,y1,y2) = (0, 1, 0)
• so, calculate
  • c = (x0+z2) / 2
  • and s = (x2-z0) / 2
• then normalize to get c² + s² equal to 1
  • norm = sqrt(c * c + s * s)
  • if norm != 0:
    • c = c / norm
    • s = s / norm
    • (if the norm would be zero, there is not much we can do)
• the angle would be atan2(c, s)
• the rotation matrix would be [[c,0,-s],[0,1,0],[s,0,c]]

来源：https://stackoverflow.com/questions/58946202/quaternion-to-matrix-rotation-only-one-axis