def test_dual_quaternions_from_pqs_0dims():
random_state = np.random.RandomState(844)
pq = random_state.randn(7)
pq[3:] /= np.linalg.norm(pq[3:], axis=-1)[..., np.newaxis]
dq = dual_quaternions_from_pqs(pq)
pq2 = pqs_from_dual_quaternions(dq)
assert_array_almost_equal(pq[:3], pq2[:3])
assert_quaternion_equal(pq[3:], pq2[3:])
def test_batch_dual_quaternion_vector_product_0dims():
random_state = np.random.RandomState(849)
pq = random_state.randn(7)
pq[3:] /= np.linalg.norm(pq[3:], axis=-1)[..., np.newaxis]
dq = dual_quaternions_from_pqs(pq)
v = random_state.randn(3)
assert_array_almost_equal(batch_dq_prod_vector(dq, v),
dq_prod_vector(dq, v))
def test_dual_quaternions_from_pqs_2dims():
random_state = np.random.RandomState(846)
pqs = random_state.randn(5, 5, 7)
pqs[..., 3:] /= np.linalg.norm(pqs[..., 3:], axis=-1)[..., np.newaxis]
dqs = dual_quaternions_from_pqs(pqs)
pqs2 = pqs_from_dual_quaternions(dqs)
for pq, pq2 in zip(pqs.reshape(-1, 7), pqs2.reshape(-1, 7)):
assert_array_almost_equal(pq[:3], pq2[:3])
assert_quaternion_equal(pq[3:], pq2[3:])
def test_dual_quaternions_from_pqs_1dim():
random_state = np.random.RandomState(845)
pqs = random_state.randn(20, 7)
pqs[..., 3:] /= np.linalg.norm(pqs[..., 3:], axis=-1)[..., np.newaxis]
dqs = dual_quaternions_from_pqs(pqs)
pqs2 = pqs_from_dual_quaternions(dqs)
for pq, pq2 in zip(pqs, pqs2):
assert_array_almost_equal(pq[:3], pq2[:3])
assert_quaternion_equal(pq[3:], pq2[3:])
def test_batch_concatenate_dual_quaternions_0dims():
random_state = np.random.RandomState(847)
pqs = random_state.randn(2, 7)
pqs[..., 3:] /= np.linalg.norm(pqs[..., 3:], axis=-1)[..., np.newaxis]
dqs = dual_quaternions_from_pqs(pqs)
dq1 = dqs[0]
dq2 = dqs[1]
assert_array_almost_equal(batch_concatenate_dual_quaternions(dq1, dq2),
concatenate_dual_quaternions(dq1, dq2))
def test_batch_conversions_dual_quaternions_transforms_0dims():
random_state = np.random.RandomState(851)
pq = random_state.randn(7)
pq[3:] /= np.linalg.norm(pq[3:], axis=-1)[..., np.newaxis]
dq = dual_quaternions_from_pqs(pq)
A2B = transforms_from_dual_quaternions(dq)
dq2 = dual_quaternions_from_transforms(A2B)
assert_unit_dual_quaternion_equal(dq, dq2)
A2B2 = transforms_from_dual_quaternions(dq2)
assert_array_almost_equal(A2B, A2B2)
def test_batch_dual_quaternion_vector_product_2dims():
random_state = np.random.RandomState(850)
pqs = random_state.randn(3, 4, 7)
pqs[..., 3:] /= np.linalg.norm(pqs[..., 3:], axis=-1)[..., np.newaxis]
dqs = dual_quaternions_from_pqs(pqs)
V = random_state.randn(3, 4, 3)
V_transformed = batch_dq_prod_vector(dqs, V)
for v_t, dq, v in zip(V_transformed.reshape(-1, 3), dqs.reshape(-1, 8),
V.reshape(-1, 3)):
assert_array_almost_equal(v_t, dq_prod_vector(dq, v))
def test_batch_conversions_dual_quaternions_transforms_3dims():
random_state = np.random.RandomState(852)
pqs = random_state.randn(3, 4, 5, 7)
pqs[..., 3:] /= np.linalg.norm(pqs[..., 3:], axis=-1)[..., np.newaxis]
dqs = dual_quaternions_from_pqs(pqs)
A2Bs = transforms_from_dual_quaternions(dqs)
dqs2 = dual_quaternions_from_transforms(A2Bs)
for dq1, dq2 in zip(dqs.reshape(-1, 8), dqs2.reshape(-1, 8)):
assert_unit_dual_quaternion_equal(dq1, dq2)
A2Bs2 = transforms_from_dual_quaternions(dqs2)
assert_array_almost_equal(A2Bs, A2Bs2)
def test_batch_concatenate_dual_quaternions_2dims():
random_state = np.random.RandomState(848)
pqs = random_state.randn(2, 2, 2, 7)
pqs[..., 3:] /= np.linalg.norm(pqs[..., 3:], axis=-1)[..., np.newaxis]
dqs = dual_quaternions_from_pqs(pqs)
dqs1 = dqs[0]
dqs2 = dqs[1]
dqs_result = batch_concatenate_dual_quaternions(dqs1, dqs2)
for dq_result, dq1, dq2 in zip(dqs_result.reshape(-1, 8),
dqs1.reshape(-1, 8), dqs2.reshape(-1, 8)):
assert_array_almost_equal(concatenate_dual_quaternions(dq1, dq2),
dq_result)