def test_transform_many_matrices_one_vector():
for dim in [2, 3, 4]:
# no translation:
v = np.random.random((dim))
xforms = np.random.random(((1000, dim, dim)))
reference = np.array([M.dot(v) for M in xforms])
result = V.transform(v, xforms)
assert result.shape == (1000, dim)
npt.assert_allclose(reference, result)
# with translation, no perspective (e.g. the common 3x4 matrices)
v = np.random.random((dim))
xforms = np.random.random(((1000, dim, dim + 1)))
reference = np.array([M.dot(V.hom(v)) for M in xforms])
result = V.transform(v, xforms)
assert result.shape == (1000, dim)
npt.assert_allclose(reference, result)
# with translation, no perspective
v = np.random.random((dim))
xforms = np.random.random(((1000, dim + 1, dim + 1)))
reference = np.array([V.dehom(M.dot(V.hom(v))) for M in xforms])
result = V.transform(v, xforms)
assert result.shape == (1000, dim)
npt.assert_allclose(reference, result)
def test_transform_one_matrices_one_vector():
for dim in [2, 3, 4]:
# no translation:
v = np.random.random((dim))
M = np.random.random(((dim, dim)))
reference = M.dot(v)
result = V.transform(v, M)
assert result.shape == v.shape
npt.assert_allclose(reference, result)
# with translation, no perspective (e.g. the common 3x4 matrices)
v = np.random.random((dim))
M = np.random.random(((dim, dim + 1)))
reference = M.dot(V.hom(v))
result = V.transform(v, M)
assert result.shape == v.shape
npt.assert_allclose(reference, result)
# with translation, no perspective
v = np.random.random((dim))
M = np.random.random(((dim + 1, dim + 1)))
reference = V.dehom(M.dot(V.hom(v)))
result = V.transform(v, M)
assert result.shape == v.shape
npt.assert_allclose(reference, result)
def test_transform_one_matrix_many_vectors():
for dim in [2, 3, 4]:
# no translation:
vectors = np.random.random((1000, dim))
M = np.random.random(((dim, dim)))
reference = np.array([M.dot(v) for v in vectors])
result = V.transform(vectors, M)
assert result.shape == vectors.shape
npt.assert_allclose(reference, result)
# with translation, no perspective (e.g. the common 3x4 matrices)
vectors = np.random.random((1000, dim))
M = np.random.random(((dim, dim + 1)))
reference = np.array([M.dot(V.hom(v)) for v in vectors])
result = V.transform(vectors, M)
assert result.shape == vectors.shape
npt.assert_allclose(reference, result)
# with translation, no perspective
vectors = np.random.random((1000, dim))
M = np.random.random(((dim + 1, dim + 1)))
reference = np.array([V.dehom(M.dot(V.hom(v))) for v in vectors])
result = V.transform(vectors, M)
assert result.shape == vectors.shape
npt.assert_allclose(reference, result)
def test_procrustes3d_reflection():
for axis in [0, 1, 2]:
N = 100
pts1 = np.random.random((N, 3))
S = np.eye(3)
S[axis, axis] = -1
pts2 = V.transform(pts1, S)
M = procrustes3d(pts1, pts2)
R = M[:3, :3]
np.testing.assert_allclose(np.linalg.det(R), 1)
assert not np.allclose(R, S)
assert V.veclen(V.transform(pts1, M) - pts2).sum() > 0
M2 = procrustes3d(pts1, pts2, allow_reflection=True)
np.testing.assert_allclose(M2[:3, :3], S, atol=1.e-9)
np.testing.assert_allclose(V.transform(pts1, M2), pts2)
def test_procrustes3d():
# test with 100 random rotations/translations
trials = 0
while trials < 100:
R = np.linalg.qr(np.random.uniform(-1, 1, size=(3, 3)))[0]
print((np.linalg.det(R)))
if np.linalg.det(R) < 0:
continue
t = np.random.uniform(-2, 2, size=3)
M = np.eye(4)
M[:3, :3] = R
M[:3, 3] = t
N = np.random.randint(3, 1000)
frompts = np.random.random((N, 3))
topts = V.transform(frompts, M)
M_est = procrustes3d(frompts, topts)
np.testing.assert_allclose(M, M_est)
np.testing.assert_allclose(V.transform(frompts, M_est), topts)
R = M_est[:3, :3]
trials += 1