def random_point_pair():
"""
Creates a random point pair bivector object
"""
mv_a = random_euc_mv()
mv_b = random_euc_mv()
pp = (up(mv_a) ^ up(mv_b)).normal()
return pp
def random_line():
"""
Creates a random line
"""
mv_a = random_euc_mv()
mv_b = random_euc_mv()
line_a = ((up(mv_a) ^ up(mv_b) ^ ninf)).normal()
return line_a
def random_line():
"""
Creates a random line
"""
mv_a = random_euc_mv()
mv_b = random_euc_mv()
line_a = ((up(mv_a) ^ up(mv_b) ^ ninf)).normal()
return line_a
def random_point_pair():
"""
Creates a random point pair bivector object
"""
mv_a = random_euc_mv()
mv_b = random_euc_mv()
pp = (up(mv_a) ^ up(mv_b)).normal()
return pp
def random_circle():
"""
Creates a random circle
"""
mv_a = random_euc_mv()
mv_b = random_euc_mv()
mv_c = random_euc_mv()
line_a = ((up(mv_a) ^ up(mv_b) ^ up(mv_c))).normal()
return line_a
def random_bivector():
"""
Creates a random bivector on the form described by R. Wareham in
Mesh Vertex Pose and Position Interpolation using Geometric Algebra.
$$ B = ab + c*n_{\inf}$$ where $a, b, c \in \mathcal(R)^3$
"""
a = random_euc_mv()
c = random_euc_mv()
return a * I3 + c * ninf
def random_bivector():
"""
Creates a random bivector on the form described by R. Wareham in
Mesh Vertex Pose and Position Interpolation using Geometric Algebra.
$$ B = ab + c*n_{\inf}$$ where $a, b, c \in \mathcal(R)^3$
"""
a = random_euc_mv()
c = random_euc_mv()
return a * I3 + c * ninf
def random_bivector():
"""
Creates a random bivector on the form described by R. Wareham in
TODO: Dig out the name of the interpolation paper
$$ B = ab + c*n_{\inf}$$ where $a, b, c \in \mathcal(R)^3$
"""
a = random_euc_mv()
c = random_euc_mv()
return a * I3 + c * ninf
def random_sphere():
"""
Creates a random sphere
"""
mv_a = random_euc_mv()
mv_b = random_euc_mv()
mv_c = random_euc_mv()
mv_d = random_euc_mv()
sphere = ((up(mv_a) ^ up(mv_b) ^ up(mv_c) ^ up(mv_d))).normal()
return sphere
def test_generate_translation_rotor(self):
""" Tests translation rotor generation """
for i in range(100):
rand = random_euc_mv()
starting_point = up(random_euc_mv())
r_trans = generate_translation_rotor(rand)
end_point = r_trans * starting_point * ~r_trans
translation_vec = down(end_point) - down(starting_point)
npt.assert_almost_equal(translation_vec.value, rand.value)
def random_sphere():
"""
Creates a random sphere
"""
mv_a = random_euc_mv()
mv_b = random_euc_mv()
mv_c = random_euc_mv()
mv_d = random_euc_mv()
sphere = ((up(mv_a) ^ up(mv_b) ^ up(mv_c) ^ up(mv_d))).normal()
return sphere
def test_generate_translation_rotor(self):
""" Tests translation rotor generation """
for i in range(100):
rand = random_euc_mv()
starting_point = up(random_euc_mv())
r_trans = generate_translation_rotor(rand)
end_point = r_trans * starting_point * ~r_trans
translation_vec = down(end_point) - down(starting_point)
testing.assert_almost_equal(translation_vec.value, rand.value)
def random_circle_at_origin():
"""
Creates a random circle at the origin
"""
mv_a = random_euc_mv()
mv_r = random_euc_mv()
r = generate_rotation_rotor(np.pi / 2, mv_a, mv_r)
mv_b = r * mv_a * ~r
mv_c = r * mv_b * ~r
pp = (up(mv_a) ^ up(mv_b) ^ up(mv_c)).normal()
return pp
def random_circle_at_origin():
"""
Creates a random circle at the origin
"""
mv_a = random_euc_mv()
mv_r = random_euc_mv()
r = generate_rotation_rotor(np.pi/2, mv_a, mv_r)
mv_b = r*mv_a*~r
mv_c = r * mv_b * ~r
pp = (up(mv_a) ^ up(mv_b) ^ up(mv_c) ).normal()
return pp
def run_rotor_estimation(self, object_generator, estimation_function, n_runs=5, n_objects_per_run=10):
error_count = 0
for i in range(n_runs):
query_model = [object_generator().normal() for i in range(n_objects_per_run)]
r = (generate_translation_rotor(random_euc_mv(l_max=0.01)) * generate_rotation_rotor(np.random.randn() / 10,
random_euc_mv().normal(),
random_euc_mv().normal())).normal()
reference_model = [(r * l * ~r).normal() for l in query_model]
r_est = estimation_function(reference_model, query_model)
error_flag = False
for a, b in zip([(r_est * l * ~r_est).normal() for l in query_model], reference_model):
if abs(a + b) < 0.0001:
c = -b
print('SIGN FLIP')
else:
c = b
if np.any(np.abs(a.value - c.value) > 0.01):
error_flag = True
if error_flag:
error_count += 1
print(i, error_count)
print('\n\nESTIMATION SUMMARY')
print('OBJECTS ', n_objects_per_run)
print('RUNS ', n_runs)
print('ERRORS ', error_count)
print('ERROR percentage ', 100 * error_count / float(n_runs), '%')
def run_rotor_estimation(self, object_generator, estimation_function, n_runs=5, n_objects_per_run=10):
error_count = 0
for i in range(n_runs):
query_model = [object_generator().normal() for i in range(n_objects_per_run)]
r = (generate_translation_rotor(random_euc_mv(l_max=0.01)) * generate_rotation_rotor(np.random.randn() / 10,
random_euc_mv().normal(),
random_euc_mv().normal())).normal()
reference_model = [(r * l * ~r).normal() for l in query_model]
r_est = estimation_function(reference_model, query_model)
error_flag = False
for a, b in zip([(r_est * l * ~r_est).normal() for l in query_model], reference_model):
if abs(a + b) < 0.0001:
c = -b
print('SIGN FLIP')
else:
c = b
if np.any(np.abs(a.value - c.value) > 0.01):
error_flag = True
if error_flag:
error_count += 1
print(i, error_count)
print('\n\nESTIMATION SUMMARY')
print('OBJECTS ', n_objects_per_run)
print('RUNS ', n_runs)
print('ERRORS ', error_count)
print('ERROR percentage ', 100 * error_count / float(n_runs), '%')
def test_draw_points(self):
from clifford.tools.g3 import random_euc_mv
from clifford.g3 import layout
gs = GanjaScene()
gs.add_objects([random_euc_mv().value[0:8] for i in range(10)], static=False)
with open('test_file.html', 'w') as test_file:
print(generate_full_html(str(gs), sig=layout.sig, grid=True, scale=1.0, gl=False), file=test_file)
render_cef_script(str(gs), sig=layout.sig, grid=True, scale=1.0, gl=False)
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 test_from_value_array(self):
mv = []
for i in range(100):
p = random_euc_mv()
mv.append(p)
test_array = ConformalMVArray(mv)
up_array = test_array.up()
new_mv_array = ConformalMVArray.from_value_array(up_array.value)
npt.assert_almost_equal(new_mv_array.value, up_array.value)
def test_from_value_array(self):
mv = []
for i in range(100):
p = random_euc_mv()
mv.append(p)
test_array = ConformalMVArray(mv)
up_array = test_array.up()
new_mv_array = ConformalMVArray.from_value_array(up_array.value)
np.testing.assert_almost_equal(new_mv_array.value, up_array.value)
def random_point_pair_at_origin():
"""
Creates a random point pair bivector object at the origin
"""
mv_a = random_euc_mv()
plane_a = (mv_a*I3).normal()
mv_b = plane_a*mv_a*plane_a
pp = (up(mv_a) ^ up(mv_b)).normal()
return pp
def random_point_pair_at_origin():
"""
Creates a random point pair bivector object at the origin
"""
mv_a = random_euc_mv()
plane_a = (mv_a * I3).normal()
mv_b = plane_a * mv_a * plane_a
pp = (up(mv_a) ^ up(mv_b)).normal()
return pp
def test_dual(self):
mv = []
for i in range(100):
p = random_euc_mv()
mv.append(p)
test_array = ConformalMVArray(mv)
up_array = test_array.up()
I5 = self.layout.blades['e12345']
np.testing.assert_almost_equal((up_array * ConformalMVArray([I5])).value,
ConformalMVArray([i * I5 for i in up_array]).value)
def test_dual(self):
mv = []
for i in range(100):
p = random_euc_mv()
mv.append(p)
test_array = ConformalMVArray(mv)
up_array = test_array.up()
I5 = self.layout.blades['e12345']
np.testing.assert_almost_equal((up_array * ConformalMVArray([I5])).value,
ConformalMVArray([i * I5 for i in up_array]).value)
def test_fit_plane(self):
noise = 0.1
trueP = random_plane()
point_list = project_points_to_plane(
[random_conformal_point() for i in range(100)], trueP)
point_list = [
up(down(P) + noise * random_euc_mv()) for P in point_list
]
print(trueP)
plane = fit_plane(point_list)
print(plane)
def test_fit_sphere(self):
try:
noise = 0.1
trueP = random_sphere()
point_list = project_points_to_sphere([random_conformal_point() for i in range(100)], trueP)
point_list = [up(down(P) + noise * random_euc_mv()) for P in point_list]
print(trueP)
sphere = fit_sphere(point_list)
print(sphere)
#draw([sphere] + point_list, static=False, scale=0.1)
except:
print('FAILED TO FIND SPHERE')
def test_fit_plane(self):
try:
noise = 0.1
trueP = random_plane()
point_list = project_points_to_plane([random_conformal_point() for i in range(100)], trueP)
point_list = [up(down(P) + noise * random_euc_mv()) for P in point_list]
print(trueP)
plane = fit_plane(point_list)
print(plane)
#draw(point_list + [plane], static=False, scale=0.1)
except:
print('FAILED TO FIND PLANE')
def test_fit_sphere(self):
try:
noise = 0.1
trueP = random_sphere()
point_list = project_points_to_sphere([random_conformal_point() for i in range(100)], trueP)
point_list = [up(down(P) + noise * random_euc_mv()) for P in point_list]
print(trueP)
sphere = fit_sphere(point_list)
print(sphere)
#draw([sphere] + point_list, static=False, scale=0.1)
except:
print('FAILED TO FIND SPHERE')
def test_fit_plane(self):
try:
noise = 0.1
trueP = random_plane()
point_list = project_points_to_plane([random_conformal_point() for i in range(100)], trueP)
point_list = [up(down(P) + noise * random_euc_mv()) for P in point_list]
print(trueP)
plane = fit_plane(point_list)
print(plane)
#draw(point_list + [plane], static=False, scale=0.1)
except:
print('FAILED TO FIND PLANE')
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_apply_rotor(self):
mv = []
for i in range(100):
p = random_euc_mv()
mv.append(p)
test_array = ConformalMVArray(mv)
up_array = test_array.up()
# Test apply rotor
for i in range(100):
R = ConformalMVArray([self.layout.randomRotor()])
rotated_array = up_array.apply_rotor(R)
for i, v in enumerate(rotated_array):
np.testing.assert_almost_equal(v.value, apply_rotor(up_array[i], R[0]).value)
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_apply_rotor(self):
mv = []
for i in range(100):
p = random_euc_mv()
mv.append(p)
test_array = ConformalMVArray(mv)
up_array = test_array.up()
# Test apply rotor
for i in range(100):
R = ConformalMVArray([self.layout.randomRotor()])
rotated_array = up_array.apply_rotor(R)
for i, v in enumerate(rotated_array):
np.testing.assert_almost_equal(v.value, apply_rotor(up_array[i], R[0]).value)
def test_up_down(self):
mv = []
up_mv = []
for i in range(100):
p = random_euc_mv()
mv.append(p)
up_mv.append(up(p))
test_array = ConformalMVArray(mv)
up_array = test_array.up()
down_array = up_array.down()
for a, b in zip(up_array, up_mv):
np.testing.assert_almost_equal(a.value, b.value)
np.testing.assert_almost_equal(a.value, b.value)
for a, b in zip(down_array, mv):
np.testing.assert_almost_equal(a.value, b.value)
def test_up_down(self):
mv = []
up_mv = []
for i in range(100):
p = random_euc_mv()
mv.append(p)
up_mv.append(up(p))
test_array = ConformalMVArray(mv)
up_array = test_array.up()
down_array = up_array.down()
for a, b in zip(up_array, up_mv):
npt.assert_almost_equal(a.value, b.value)
npt.assert_almost_equal(a.value, b.value)
for a, b in zip(down_array, mv):
npt.assert_almost_equal(a.value, b.value)
def test_find_rotor_aligning_vectors(self, rng): # noqa: F811
"""
Currently fails, needs to be dug into
"""
from clifford.g3c import layout
e1 = layout.blades['e1']
e2 = layout.blades['e2']
from clifford.tools.g3 import random_euc_mv, random_rotation_rotor, rotor_align_vecs
u_list = [random_euc_mv(rng=rng) for i in range(50)]
for i in range(100):
r = random_rotation_rotor(rng=rng)
v_list = [r * u * ~r for u in u_list]
r_2 = rotor_align_vecs(u_list, v_list)
print(r_2)
print(r)
testing.assert_almost_equal(r.value, r_2.value)
def test_find_rotor_aligning_vectors(self):
"""
Currently fails, needs to be dug into
"""
from clifford.g3c import layout
e1 = layout.blades['e1']
e2 = layout.blades['e2']
from clifford.tools.g3 import random_euc_mv, random_rotation_rotor, rotor_align_vecs
u_list = [random_euc_mv() for i in range(50)]
for i in range(100):
r = random_rotation_rotor()
v_list = [r*u*~r for u in u_list]
r_2 = rotor_align_vecs(u_list, v_list)
print(r_2)
print(r)
testing.assert_almost_equal(r.value, r_2.value)
def test_get_properties_of_sphere(self):
for i in range(100):
# Make a sphere
scale_factor = np.random.rand()
sphere = (up(scale_factor * e1) ^ up(-scale_factor * e1)
^ up(scale_factor * e3)
^ up(scale_factor * e2)).normal()
# Translate it
rand_trans = random_euc_mv()
trans_rot = generate_translation_rotor(rand_trans)
sphere = (trans_rot * sphere * ~trans_rot).normal()
center = get_center_from_sphere(sphere)
radius = get_radius_from_sphere(sphere)
npt.assert_almost_equal(down(center).value, rand_trans.value)
npt.assert_almost_equal(radius, scale_factor)
def test_get_properties_of_sphere(self):
for i in range(100):
# Make a sphere
scale_factor = np.random.rand()
sphere = (up(scale_factor * e1) ^ up(-scale_factor * e1) ^ up(scale_factor * e3) ^ up(
scale_factor * e2)).normal()
# Translate it
rand_trans = random_euc_mv()
trans_rot = generate_translation_rotor(rand_trans)
sphere = (trans_rot * sphere * ~trans_rot).normal()
center = get_center_from_sphere(sphere)
radius = get_radius_from_sphere(sphere)
testing.assert_almost_equal(down(center).value, rand_trans.value)
testing.assert_almost_equal(radius, scale_factor)
def random_translation_rotor(maximum_translation=10.0):
""" generate a random translation rotor """
return generate_translation_rotor(random_euc_mv(maximum_translation))
def test_generate_translation_rotor(self):
for i in range(10000):
euc_vector_a = random_euc_mv()
res = generate_translation_rotor(euc_vector_a)
res2 = (1 + ninf * euc_vector_a / 2)
npt.assert_almost_equal(res.value, res2.value)
def random_conformal_point(l_max=10):
"""
Creates a random conformal point
"""
return up(random_euc_mv(l_max=l_max))
def random_translation_rotor(maximum_translation=10.0):
""" generate a random translation rotor """
return generate_translation_rotor(random_euc_mv(maximum_translation))
def random_conformal_point(l_max=10):
"""
Creates a random conformal point
"""
return up(random_euc_mv(l_max=l_max))