def test_sample_texture_range():
world = CylinderWorld(rng=np.random.RandomState(SEED))
alpha0, alpha1 = 0.5, 0.75
alphas = np.linspace(alpha0, alpha1, 100000)
smpls = world.sample_texture(alphas)
smpl_range = world.sample_texture_range(alpha0, alpha1)
assert np.abs(np.mean(smpls) - smpl_range) < 1e-5
def test_sample_texture_derivative():
world = CylinderWorld(rng=np.random.RandomState(SEED))
eta = 1e-6
alpha = 0.5
smpl0 = world.sample_texture(alpha - 0.5 * eta)
smpl1 = world.sample_texture(alpha + 0.5 * eta)
dsmpl_num = (smpl1 - smpl0) / eta
dsmpl_direct = world.sample_texture_derivative(alpha)
assert np.abs(dsmpl_direct - dsmpl_num) < 1e-5
def test_inner_angle():
assert CylinderWorld._inner_angle(1.0, 2.0) == 1.0
assert CylinderWorld._inner_angle(2.0, 1.0) == -1.0
assert CylinderWorld._inner_angle(-0.25, 0.25) == 0.5
assert CylinderWorld._inner_angle(0.25, -0.25) == -0.5
assert CylinderWorld._inner_angle(3.0 * np.pi, 2.0 * np.pi) == np.pi
assert CylinderWorld._inner_angle(2.0 * np.pi, 3.0 * np.pi) == -np.pi
assert CylinderWorld._inner_angle(3.0 * np.pi, 1.0 * np.pi) == 0.0
assert CylinderWorld._inner_angle(1.0 * np.pi, 3.0 * np.pi) == 0.0
assert CylinderWorld._inner_angle(-1.0 * np.pi, 4.0 * np.pi) == np.pi
assert CylinderWorld._inner_angle(4.0 * np.pi, -1.0 * np.pi) == -np.pi
def test_render_with_gradient():
world = CylinderWorld(resolution=1000,
n_coeffs=4,
rng=np.random.RandomState(SEED))
for anti_alias in [False, True]:
for x in np.linspace(-0.9, 0.9, 11):
for y in np.linspace(-0.9, 0.9, 11):
if x**2 + y**2 >= 0.9:
continue
for theta in np.linspace(-np.pi, np.pi, 11):
I, dI_direct = world.render_with_gradient(
x, y, theta, anti_alias=anti_alias)
dI_num = (0.5 * (np.roll(I, -1) - np.roll(I, 1)) *
world.resolution / (2.0 * np.pi))
np.testing.assert_allclose(dI_direct, dI_num, atol=1e-2)
def test_render_at_angles_with_gradient():
world = CylinderWorld(resolution=1000,
n_coeffs=4,
rng=np.random.RandomState(SEED))
eta = 1e-6
for anti_alias in [False, True]:
for β in np.linspace(-np.pi, np.pi, 11):
for x in np.linspace(-0.9, 0.9, 11):
for y in np.linspace(-0.9, 0.9, 11):
if x**2 + y**2 >= 0.9:
continue
for theta in np.linspace(-np.pi, np.pi, 11):
I, dI_direct = world.render_at_angles_with_gradient(
β, x, y, theta, anti_alias=anti_alias)
I0 = world.render_at_angles(β - 0.5 * eta, x, y, theta,
anti_alias)
I1 = world.render_at_angles(β + 0.5 * eta, x, y, theta,
anti_alias)
dI_num = (I1 - I0) / eta
np.testing.assert_allclose(dI_direct,
dI_num,
atol=1e-5)
def test_radius():
world_r1 = CylinderWorld(resolution=128,
n_coeffs=4,
rng=np.random.RandomState(SEED),
radius=1.0)
for radius in np.linspace(0.5, 2, 11):
world = CylinderWorld(resolution=128,
n_coeffs=4,
rng=np.random.RandomState(SEED),
radius=radius)
for x in np.linspace(-0.9 * radius, 0.9 * radius, 11):
for y in np.linspace(-0.9 * radius, 0.9 * radius, 11):
if np.sqrt(x**2 + y**2) >= world.radius:
continue
for theta in np.linspace(-np.pi, np.pi, 11):
I = world.render(x, y, theta)
I2 = world_r1.render(x / radius, y / radius, theta)
np.testing.assert_allclose(I, I2, atol=1e-6)
def test_depth():
for radius in np.linspace(0.5, 2, 11):
world = CylinderWorld(resolution=128,
n_coeffs=4,
rng=np.random.RandomState(SEED),
radius=radius)
# At the origin, the distance to the cylinder must be equal to the
# radius of the cylinder.
ds = world.depth(0.0, 0.0, 0.0)
np.testing.assert_allclose(np.ones_like(ds) * radius, ds)
# Move in the x- direction and compute the depth
d = world.depth_at_angles(0.0, 0.5 * radius, 0.0, 0.0)
np.testing.assert_allclose(0.5 * radius, d)
d = world.depth_at_angles(-np.pi, 0.5 * radius, 0.0, 0.0)
np.testing.assert_allclose(1.5 * radius, d)
# Move in the y- direction and compute the depth
d = world.depth_at_angles(np.pi / 2, 0.0, 0.5 * radius, 0.0)
np.testing.assert_allclose(0.5 * radius, d)
d = world.depth_at_angles(-np.pi / 2, 0.0, 0.5 * radius, 0.0)
np.testing.assert_allclose(1.5 * radius, d)
def test_cylinder_world_image_space_angles():
world = CylinderWorld(rng=np.random.RandomState(SEED))
np.testing.assert_allclose(0.5 * (world._βs[:-1] + world._βs[1:]),
world._βs_centre)