def test_general_logarithm_TR(self):
for i in range(5):
# R = generate_rotation_rotor(0.5, e1, e2).normal()
# T = generate_translation_rotor(e3 + 7 * e2 - e1).normal()
# V = (T*R).normal()
biv_true = random_bivector()
V = general_exp(biv_true).normal()
biv = general_logarithm(V)
V_rebuilt = (general_exp(biv)).normal()
C1 = random_point_pair()
C2 = ( V *C1 *~V).normal()
C3 = (V_rebuilt *C1 *~V_rebuilt).normal()
np.testing.assert_almost_equal(C2.value, C3.value, 2)
def test_general_logarithm_TR(self):
for i in range(5):
# R = generate_rotation_rotor(0.5, e1, e2).normal()
# T = generate_translation_rotor(e3 + 7 * e2 - e1).normal()
# V = (T*R).normal()
biv_true = random_bivector()
V = general_exp(biv_true).normal()
biv = general_logarithm(V)
V_rebuilt = (general_exp(biv)).normal()
C1 = random_point_pair()
C2 = (V * C1 * ~V).normal()
C3 = (V_rebuilt * C1 * ~V_rebuilt).normal()
npt.assert_almost_equal(C2.value, C3.value, 2)
def test_general_logarithm_scaling(self):
# Check we can reverse scaling
for i in range(50):
scale = 0.5 + np.random.rand()
biv = -np.log(scale ) *e45 /2
R = general_exp(biv).normal()
biv_2 = general_logarithm(R)
np.testing.assert_almost_equal(biv.value, biv_2.value)
def full_conformal_biv_params_to_rotor(biv_params):
"""
Converts the bivector parameters for a general conformal rotor into
the rotor
"""
biv = full_conformal_biv_params_to_biv(biv_params)
R = general_exp(biv).normal()
return R
def test_general_logarithm_conformal(self, obj_gen):
for i in range(10000):
X = obj_gen()
Y = obj_gen()
R = rotor_between_objects(X, Y)
biv = general_logarithm(R)
R_recon = general_exp(biv).normal()
npt.assert_almost_equal(R.value, R_recon.value, 4)
def test_general_logarithm_scaling(self):
# Check we can reverse scaling
for i in range(50):
scale = 0.5 + np.random.rand()
biv = -np.log(scale) * e45 / 2
R = general_exp(biv).normal()
biv_2 = general_logarithm(R)
npt.assert_almost_equal(biv.value, biv_2.value)
def TRS_biv_params_to_rotor(biv_params):
"""
Converts the bivector parameters for a general TRS rotor into
the rotor
"""
biv = TRS_biv_params_to_biv(biv_params)
R = general_exp(biv).normal()
return R
def test_general_logarithm_translation(self):
# Check we can reverse translation
for i in range(50):
t = random_euc_mv()
biv = ninf * t / 2
R = general_exp(biv).normal()
biv_2 = general_logarithm(R)
npt.assert_almost_equal(biv.value, biv_2.value)
def test_general_logarithm_translation(self):
# Check we can reverse translation
for i in range(50):
t = random_euc_mv()
biv = ninf * t /2
R = general_exp(biv).normal()
biv_2 = general_logarithm(R)
np.testing.assert_almost_equal(biv.value, biv_2.value)
def interpolate_rotors(R_n_plus_1, R_n, interpolation_fraction):
"""
Interpolates all conformal type rotors
From :cite:`wareham-interpolation` and :cite:`log-of-rotors`.
"""
if interpolation_fraction < np.finfo(float).eps:
return R_n
delta_R = R_n_plus_1 * ~R_n
delta_bivector = general_logarithm(delta_R)(2)
R_n_lambda = general_exp(interpolation_fraction * delta_bivector) * R_n
return R_n_lambda
def test_general_logarithm_TS(self):
for i in range(5):
scale = 0.5 + np.random.rand()
t = random_euc_mv()
S = generate_dilation_rotor(scale)
T = generate_translation_rotor(t)
V = (T * S).normal()
biv = general_logarithm(V)
V_rebuilt = (general_exp(biv)).normal()
C1 = random_point_pair()
C2 = (V * C1 * ~V).normal()
C3 = (V_rebuilt * C1 * ~V_rebuilt).normal()
npt.assert_almost_equal(C2.value, C3.value, 5)
def test_general_logarithm_TS(self):
for i in range(5):
scale = 0.5 +np.random.rand()
t = random_euc_mv()
S = generate_dilation_rotor(scale)
T = generate_translation_rotor(t)
V = ( T *S).normal()
biv = general_logarithm(V)
V_rebuilt = (general_exp(biv)).normal()
C1 = random_point_pair()
C2 = ( V *C1 *~V).normal()
C3 = (V_rebuilt *C1 *~V_rebuilt).normal()
np.testing.assert_almost_equal(C2.value, C3.value, 5)
def test_general_logarithm_conformal(self):
object_generators = [random_point_pair, random_line, random_circle, random_plane]
# object_generators = [random_sphere]
for obj_gen in object_generators:
print(obj_gen.__name__)
for i in range(10000):
X = obj_gen()
Y = obj_gen()
R = rotor_between_objects(X, Y)
biv = general_logarithm(R)
R_recon = general_exp(biv).normal()
np.testing.assert_almost_equal(R.value, R_recon, 3)
def test_general_logarithm_conformal(self):
object_generators = [random_point_pair, random_line, random_circle, random_plane]
# object_generators = [random_sphere]
for obj_gen in object_generators:
print(obj_gen.__name__)
for i in range(10000):
X = obj_gen()
Y = obj_gen()
R = rotor_between_objects(X, Y)
biv = general_logarithm(R)
R_recon = general_exp(biv).normal()
np.testing.assert_almost_equal(R.value, R_recon, 3)
def test_general_logarithm_TRS(self):
for i in range(5):
scale = 0.5 + np.random.rand()
S = generate_dilation_rotor(scale)
R = generate_rotation_rotor(0.5, e1, e2)
T = generate_translation_rotor(e3 + 7 * e2 - e1)
V = (T * R * S).normal()
biv = general_logarithm(V)
V_rebuilt = general_exp(biv).normal()
biv2 = general_logarithm(V)
C1 = random_point_pair()
C2 = (V * C1 * ~V).normal()
C3 = (V_rebuilt * C1 * ~V_rebuilt).normal()
npt.assert_almost_equal(C2.value, C3.value)
def interpolate_rotors(R_n_plus_1, R_n, interpolation_fraction):
"""
Interpolates all conformal type rotors
Mesh Vertex Pose and Position Interpolation using Geometric Algebra
Rich Wareham and Joan Lasenby
and
Square Root and Logarithm of Rotors
Leo Dorst and Robert Valkenburg
"""
if interpolation_fraction < np.finfo(float).eps:
return R_n
delta_R = R_n_plus_1 * ~R_n
delta_bivector = general_logarithm(delta_R)(2)
R_n_lambda = general_exp(interpolation_fraction * delta_bivector) * R_n
return R_n_lambda
def test_general_logarithm_TRS(self):
for i in range(5):
scale = 0.5 + np.random.rand()
S = generate_dilation_rotor(scale)
R = generate_rotation_rotor(0.5, e1, e2)
T = generate_translation_rotor(e3 + 7* e2 - e1)
V = (T * R * S).normal()
biv = general_logarithm(V)
V_rebuilt = general_exp(biv).normal()
biv2 = general_logarithm(V)
C1 = random_point_pair()
C2 = (V * C1 * ~V).normal()
C3 = (V_rebuilt * C1 * ~V_rebuilt).normal()
np.testing.assert_almost_equal(C2.value, C3.value)
