def test_integration(self):
rotation_rate = [0, 0, 2*pi] # one rev per sec around z
v = [1, 0, 0] # test vector
for dt in [0, 0.25, 0.5, 0.75, 1, 2, 10, 1e-10, random()*10]: # time step in seconds
qt = Quaternion() # no rotation
qt.integrate(rotation_rate, dt)
q_truth = Quaternion(axis=[0,0,1], angle=dt*2*pi)
a = qt.rotate(v)
b = q_truth.rotate(v)
np.testing.assert_almost_equal(a, b, decimal=ALMOST_EQUAL_TOLERANCE)
self.assertTrue(qt.is_unit())
# Check integrate() is norm-preserving over many calls
q = Quaternion()
for i in range(1000):
q.integrate([pi, 0, 0], 0.001)
self.assertTrue(q.is_unit())
def test_is_unit(self):
q1 = Quaternion()
q2 = Quaternion(1.0, 0, 0, 0.0001)
self.assertTrue(q1.is_unit())
self.assertFalse(q2.is_unit())
self.assertTrue(q2.is_unit(0.001))