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Fix 3D rotation precession #28823

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Fix 3D rotation precession #28823

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12 changes: 8 additions & 4 deletions lib/mpl_toolkits/mplot3d/axes3d.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1568,10 +1568,11 @@ def _on_move(self, event):
q = _Quaternion.from_cardan_angles(elev, azim, roll)

# Update quaternion - a variation on Ken Shoemake's ARCBALL
current_vec = self._arcball(self._sx/w, self._sy/h)
new_vec = self._arcball(x/w, y/h)
scale = np.sqrt(2)/2 # slow down the rate of rotation
current_vec = self._arcball(self._sx*scale/w, self._sy*scale/h)
new_vec = self._arcball(x*scale/w, y*scale/h)
dq = _Quaternion.rotate_from_to(current_vec, new_vec)
q = dq * q
q = dq * dq * q

# Convert to elev, azim, roll
elev, azim, roll = q.as_cardan_angles()
Expand Down Expand Up @@ -4020,11 +4021,14 @@ def from_cardan_angles(cls, elev, azim, roll):
def as_cardan_angles(self):
"""
The inverse of `from_cardan_angles()`.
This function acts on the quaternion as if it were unit normed.
Note that the angles returned are in radians, not degrees.
"""
qw = self.scalar
qx, qy, qz = self.vector[..., :]
azim = np.arctan2(2*(-qw*qz+qx*qy), qw*qw+qx*qx-qy*qy-qz*qz)
elev = np.arcsin( 2*( qw*qy+qz*qx)/(qw*qw+qx*qx+qy*qy+qz*qz)) # noqa E201
# Clip below is to avoid floating point round-off errors
elev = np.arcsin(np.clip(2*(qw*qy+qz*qx)
/ (qw*qw+qx*qx+qy*qy+qz*qz), -1, 1))
roll = np.arctan2(2*( qw*qx-qy*qz), qw*qw-qx*qx-qy*qy+qz*qz) # noqa E201
return elev, azim, roll
11 changes: 5 additions & 6 deletions lib/mpl_toolkits/mplot3d/tests/test_axes3d.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1950,10 +1950,10 @@ def test_rotate():
for roll, dx, dy, new_elev, new_azim, new_roll in [
[0, 0.5, 0, 0, -90, 0],
[30, 0.5, 0, 30, -90, 0],
[0, 0, 0.5, -90, 0, 0],
[0, 0, 0.5, -90, -180, 180],
[30, 0, 0.5, -60, -90, 90],
[0, 0.5, 0.5, -45, -90, 45],
[30, 0.5, 0.5, -15, -90, 45]]:
[0, np.sqrt(2)/4, np.sqrt(2)/4, -45, -90, 45],
[30, np.sqrt(2)/4, np.sqrt(2)/4, -15, -90, 45]]:
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1, projection='3d')
ax.view_init(0, 0, roll)
Expand All @@ -1967,9 +1967,8 @@ def test_rotate():
xdata=dx*ax._pseudo_w, ydata=dy*ax._pseudo_h))
fig.canvas.draw()

assert np.isclose(ax.elev, new_elev)
assert np.isclose(ax.azim, new_azim)
assert np.isclose(ax.roll, new_roll)
np.testing.assert_allclose((ax.elev, ax.azim, ax.roll),
(new_elev, new_azim, new_roll), atol=1e-6)


def test_pan():
Expand Down
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