diff --git a/lib/mpl_toolkits/mplot3d/axes3d.py b/lib/mpl_toolkits/mplot3d/axes3d.py
index 5d522cd0988a..10f693ace0cf 100644
--- a/lib/mpl_toolkits/mplot3d/axes3d.py
+++ b/lib/mpl_toolkits/mplot3d/axes3d.py
@@ -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()
@@ -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
diff --git a/lib/mpl_toolkits/mplot3d/tests/test_axes3d.py b/lib/mpl_toolkits/mplot3d/tests/test_axes3d.py
index 0afcae99c980..07ecb0086030 100644
--- a/lib/mpl_toolkits/mplot3d/tests/test_axes3d.py
+++ b/lib/mpl_toolkits/mplot3d/tests/test_axes3d.py
@@ -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)
@@ -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():
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