def test_intersect():
import random
random.seed(577)
for i in range(100):
R = random.gauss(25.0, 0.2)
conic = random.uniform(-2.0, 1.0)
ncoefs = random.randint(0, 4)
coefs = [random.gauss(0, 1e-10) for i in range(ncoefs)]
asphere = batoid.Asphere(R, conic, coefs)
for j in range(100):
x = random.gauss(0.0, 1.0)
y = random.gauss(0.0, 1.0)
# If we shoot rays straight up, then it's easy to predict the
# intersection points.
r0 = batoid.Ray(x, y, -10, 0, 0, 1, 0)
r = asphere.intersect(r0)
np.testing.assert_allclose(r.r[0], x)
np.testing.assert_allclose(r.r[1], y)
np.testing.assert_allclose(r.r[2],
asphere.sag(x, y),
rtol=0,
atol=1e-9)
# Check normal for R=0 paraboloid (a plane)
asphere = batoid.Asphere(0.0, 0.0, [])
np.testing.assert_array_equal(asphere.normal(0.1, 0.1), [0, 0, 1])
# Check that normal parallelizes
xs = np.random.normal(size=20)
ys = np.random.normal(size=20)
np.testing.assert_array_equal(
asphere.normal(xs, ys),
np.array([asphere.normal(x, y) for x, y in zip(xs, ys)]))
# Test shape vectorization
np.testing.assert_array_equal(
asphere.normal(xs.reshape((10, 2)), ys.reshape((10, 2))),
np.array([asphere.normal(x, y)
for x, y in zip(xs, ys)]).reshape(10, 2, 3))
np.testing.assert_array_equal(
asphere.normal(xs.reshape((2, 5, 2)), ys.reshape((2, 5, 2))),
np.array([asphere.normal(x, y)
for x, y in zip(xs, ys)]).reshape(2, 5, 2, 3))
# Also test non-unit strides on last index
np.testing.assert_array_equal(
asphere.normal(xs.reshape((10, 2))[::2],
ys.reshape((10, 2))[::2]),
np.array([asphere.normal(x, y)
for x, y in zip(xs, ys)]).reshape(10, 2, 3)[::2])
def test_asphere_approximation():
rng = np.random.default_rng(5772156)
xs = np.linspace(-1, 1, 1000)
ys = np.linspace(-1, 1, 1000)
xtest = np.random.uniform(-0.9, 0.9, size=1000)
ytest = np.random.uniform(-0.9, 0.9, size=1000)
for i in range(10):
R = rng.normal(20.0, 1.0)
conic = rng.uniform(-2.0, 1.0)
ncoef = rng.choice(4)
coefs = [rng.normal(0, 1e-10) for i in range(ncoef)]
asphere = batoid.Asphere(R, conic, coefs)
zs = asphere.sag(*np.meshgrid(xs, ys))
bc = batoid.Bicubic(xs, ys, zs)
np.testing.assert_allclose(
asphere.sag(xtest, ytest),
bc.sag(xtest, ytest),
atol=1e-12, rtol=0.0
)
np.testing.assert_allclose(
asphere.normal(xtest, ytest),
bc.normal(xtest, ytest),
atol=1e-9, rtol=0
)
def test_asphere_reflection_coordtransform():
import random
random.seed(5772156)
asphere = batoid.Asphere(23.0, -0.97, [1e-5, 1e-6])
for i in range(1000):
x = random.gauss(0, 1)
y = random.gauss(0, 1)
vx = random.gauss(0, 1e-1)
vy = random.gauss(0, 1e-1)
v = np.array([vx, vy, 1])
v /= np.linalg.norm(v)
ray = batoid.Ray([x, y, -0.1], v, 0)
ray2 = ray.copy()
cs = batoid.CoordSys(
[random.uniform(-0.01, 0.01),
random.uniform(-0.01, 0.01),
random.uniform(-0.01, 0.01)],
(batoid.RotX(random.uniform(-0.01, 0.01))
.dot(batoid.RotY(random.uniform(-0.01, 0.01)))
.dot(batoid.RotZ(random.uniform(-0.01, 0.01)))
)
)
rray = asphere.reflect(ray, coordSys=cs)
rray2 = asphere.reflect(ray2.toCoordSys(cs))
assert ray_isclose(rray, rray2)
def test_asphere_reflection_reversal():
import random
random.seed(5772156)
asphere = batoid.Asphere(23.0, -0.97, [1e-5, 1e-6])
for i in range(1000):
x = random.gauss(0, 1)
y = random.gauss(0, 1)
vx = random.gauss(0, 1e-1)
vy = random.gauss(0, 1e-1)
v = np.array([vx, vy, 1])
v /= np.linalg.norm(v)
ray = batoid.Ray([x, y, -0.1], v, 0)
rray = asphere.reflect(ray.copy())
# Invert the reflected ray, and see that it ends back at the starting
# point
# Keep going a bit before turning around though
turn_around = rray.positionAtTime(rray.t+0.1)
return_ray = batoid.Ray(turn_around, -rray.v, -(rray.t+0.1))
riray = asphere.intersect(return_ray.copy())
# First check that we intersected at the same point
np.testing.assert_allclose(rray.r[0], riray.r[0], rtol=0, atol=1e-9)
np.testing.assert_allclose(rray.r[1], riray.r[1], rtol=0, atol=1e-9)
np.testing.assert_allclose(rray.r[2], riray.r[2], rtol=0, atol=1e-9)
# Reflect and propagate back to t=0.
cray = asphere.reflect(return_ray.copy())
cray = cray.positionAtTime(0)
np.testing.assert_allclose(cray[0], x, rtol=0, atol=1e-9)
np.testing.assert_allclose(cray[1], y, rtol=0, atol=1e-9)
np.testing.assert_allclose(cray[2], -0.1, rtol=0, atol=1e-9)
def test_approximate_asphere():
np.random.seed(57721)
xs = np.linspace(-1, 1, 1000)
ys = np.linspace(-1, 1, 1000)
xtest = np.random.uniform(-0.9, 0.9, size=1000)
ytest = np.random.uniform(-0.9, 0.9, size=1000)
for i in range(50):
R = np.random.normal(20.0, 1.0)
conic = np.random.uniform(-2.0, 1.0)
ncoef = np.random.randint(0, 4)
coefs = [np.random.normal(0, 1e-10) for i in range(ncoef)]
asphere = batoid.Asphere(R, conic, coefs)
zs = asphere.sag(*np.meshgrid(xs, ys))
bc = batoid.Bicubic(xs, ys, zs)
np.testing.assert_allclose(asphere.sag(xtest, ytest),
bc.sag(xtest, ytest),
atol=1e-9,
rtol=0.0)
np.testing.assert_allclose(asphere.normal(xtest, ytest),
bc.normal(xtest, ytest),
atol=1e-8,
rtol=0)
def test_rSplit():
rng = np.random.default_rng(5)
for _ in range(100):
R = rng.normal(0.7, 0.8)
conic = rng.uniform(-2.0, 1.0)
ncoef = rng.integers(0, 5)
coefs = [rng.normal(0, 1e-10) for i in range(ncoef)]
asphere = batoid.Asphere(R, conic, coefs)
theta_x = rng.normal(0.0, 1e-8)
theta_y = rng.normal(0.0, 1e-8)
rays = batoid.RayVector.asPolar(
backDist=10.0, medium=batoid.Air(),
wavelength=500e-9, outer=0.25*R,
theta_x=theta_x, theta_y=theta_y,
nrad=10, naz=10
)
coating = batoid.SimpleCoating(0.9, 0.1)
reflectedRays = asphere.reflect(rays.copy(), coating=coating)
m1 = batoid.Air()
m2 = batoid.ConstMedium(1.1)
refractedRays = asphere.refract(rays.copy(), m1, m2, coating=coating)
refractedRays2, reflectedRays2 = asphere.rSplit(rays, m1, m2, coating)
rays_allclose(reflectedRays, reflectedRays2)
rays_allclose(refractedRays, refractedRays2)
def test_sag():
rng = np.random.default_rng(57)
for i in range(100):
zmax = np.inf
while zmax > 3.0:
R = 0.0
while abs(R) < 15.0: # Don't allow too small radius of curvature
R = 1. / rng.normal(0.0, 0.3) # negative allowed
conic = rng.uniform(-2.0, 1.0)
ncoef = rng.choice(5)
coefs = [rng.normal(0, 1e-8) for i in range(ncoef)]
asphere = batoid.Asphere(R, conic, coefs)
lim = min(0.7 * abs(R) / np.sqrt(1 + conic) if conic > -1 else 5,
5)
zmax = abs(asphere.sag(lim, lim))
for j in range(100):
lim = 0.7 * abs(R) / np.sqrt(1 + conic) if conic > -1 else 1
x = rng.uniform(-lim, lim)
y = rng.uniform(-lim, lim)
result = asphere.sag(x, y)
np.testing.assert_allclose(result,
asphere_sag(R, conic, coefs)(x, y))
# Check that it returned a scalar float and not an array
assert isinstance(result, float)
# Check vectorization
x = rng.uniform(-lim, lim, size=(10, 10))
y = rng.uniform(-lim, lim, size=(10, 10))
np.testing.assert_allclose(asphere.sag(x, y),
asphere_sag(R, conic, coefs)(x, y))
# Make sure non-unit stride arrays also work
np.testing.assert_allclose(
asphere.sag(x[::5, ::2], y[::5, ::2]),
asphere_sag(R, conic, coefs)(x, y)[::5, ::2])
def test_asphere_refraction_plane():
import random
random.seed(57721)
wavelength = 500e-9 # arbitrary
asphere = batoid.Asphere(25.0, -0.97, [1e-3, 1e-5])
m1 = batoid.ConstMedium(1.7)
m2 = batoid.ConstMedium(1.2)
for i in range(1000):
x = random.gauss(0, 1)
y = random.gauss(0, 1)
vx = random.gauss(0, 1e-1)
vy = random.gauss(0, 1e-1)
v = normalized(np.array([vx, vy, 1]))/m1.getN(wavelength)
ray = batoid.Ray((x, y, -0.1), (v[0], v[1], v[2]), 0)
rray = asphere.refract(ray.copy(), m1, m2)
np.testing.assert_allclose(np.linalg.norm(rray.v), 1./m2.getN(wavelength), rtol=1e-14)
# ray.v, surfaceNormal, and rray.v should all be in the same plane, and
# hence (ray.v x surfaceNormal) . rray.v should have zero magnitude.
# magnitude zero.
normal = asphere.normal(rray.r[0], rray.r[1])
np.testing.assert_allclose(
np.dot(np.cross(ray.v, normal), rray.v),
0.0, rtol=0, atol=1e-14)
# Test Snell's law
np.testing.assert_allclose(
m1.getN(wavelength)*np.linalg.norm(np.cross(normalized(ray.v), normal)),
m2.getN(wavelength)*np.linalg.norm(np.cross(normalized(rray.v), normal)),
rtol=0, atol=1e-15)
def test_table_medium_refraction():
import random
random.seed(57721566)
filename = os.path.join(batoid.datadir, "media", "silica_dispersion.txt")
wave, n = np.genfromtxt(filename).T
table = batoid.Table(wave, n, batoid.Table.Interpolant.linear)
silica = batoid.TableMedium(table)
air = batoid.ConstMedium(1.000277)
asphere = batoid.Asphere(25.0, -0.97, [1e-3, 1e-5])
for i in range(10000):
x = random.gauss(0, 1)
y = random.gauss(0, 1)
vx = random.gauss(0, 1e-1)
vy = random.gauss(0, 1e-1)
wavelength = random.uniform(0.3, 1.2)
ray = batoid.Ray(x, y, -0.1, vx, vy, 1, 0, wavelength)
cm1 = batoid.ConstMedium(silica.getN(wavelength))
cm2 = batoid.ConstMedium(air.getN(wavelength))
rray1 = asphere.refract(ray, silica, air)
rray2 = asphere.refract(ray, cm1, cm2)
assert rray1 == rray2
def test_intersect_vectorized():
import random
random.seed(5772)
r0s = [
batoid.Ray([
random.gauss(0.0, 0.1),
random.gauss(0.0, 0.1),
random.gauss(10.0, 0.1)
], [
random.gauss(0.0, 0.1),
random.gauss(0.0, 0.1),
random.gauss(-1.0, 0.1)
], random.gauss(0.0, 0.1)) for i in range(1000)
]
r0s = batoid.RayVector(r0s)
for i in range(100):
R = random.gauss(25.0, 0.2)
conic = random.uniform(-2.0, 1.0)
ncoefs = random.randint(0, 4)
coefs = [random.gauss(0, 1e-10) for i in range(ncoefs)]
asphere = batoid.Asphere(R, conic, coefs)
r1s = asphere.intersect(r0s)
r2s = batoid.RayVector([asphere.intersect(r0) for r0 in r0s])
np.testing.assert_allclose(asphere.sag(r1s.x, r1s.y),
r1s.z,
rtol=0,
atol=1e-12)
assert r1s == r2s
def test_fail():
asphere = batoid.Asphere(1.0, 1.0, [1.0, 1.0])
ray = batoid.Ray([0,0,-1], [0,0,-1])
ray = asphere.intersect(ray)
assert ray.failed
ray = batoid.Ray([0,0,-1], [0,0,-1])
asphere.intersect(ray)
assert ray.failed
def test_fail():
asphere = batoid.Asphere(1.0, 0.0, [])
rv = batoid.RayVector(0, 10, 0, 0, 0, -1) # Too far to the side
rv2 = batoid.intersect(asphere, rv.copy())
np.testing.assert_equal(rv2.failed, np.array([True]))
# This one passes
rv = batoid.RayVector(0, 0, -1, 0, 0, 1)
rv2 = batoid.intersect(asphere, rv.copy())
np.testing.assert_equal(rv2.failed, np.array([False]))
def test_properties():
import random
random.seed(5)
for i in range(100):
R = random.gauss(0.7, 0.8)
conic = random.uniform(-2.0, 1.0)
ncoef = random.randint(0, 4)
coefs = [random.gauss(0, 1e-10) for i in range(ncoef)]
asphere = batoid.Asphere(R, conic, coefs)
assert asphere.R == R
assert asphere.conic == conic
assert asphere.coefs == coefs
do_pickle(asphere)
def test_quad_plus_poly():
import random
random.seed(5772)
for i in range(100):
R = random.gauss(25.0, 0.2)
conic = random.uniform(-2.0, 1.0)
ncoefs = random.randint(0, 4)
coefs = [random.gauss(0, 1e-10) for i in range(ncoefs)]
asphere = batoid.Asphere(R, conic, coefs)
quad = batoid.Quadric(R, conic)
poly = py_poly(coefs)
for j in range(100):
x = random.gauss(0.0, 1.0)
y = random.gauss(0.0, 1.0)
np.testing.assert_allclose(asphere.sag(x, y), quad.sag(x, y)+poly(x, y))
def test_ne():
objs = [
batoid.Asphere(10.0, 1.0, []),
batoid.Asphere(10.0, 1.0, [0]),
batoid.Asphere(10.0, 1.0, [0,1]),
batoid.Asphere(10.0, 1.0, [1,0]),
batoid.Asphere(10.0, 1.1, []),
batoid.Asphere(10.1, 1.0, []),
batoid.Quadric(10.0, 1.0)
]
all_obj_diff(objs)
def test_asphere_reflection_plane():
import random
random.seed(577215)
asphere = batoid.Asphere(25.0, -0.97, [1e-3, 1e-5])
for i in range(1000):
x = random.gauss(0, 1)
y = random.gauss(0, 1)
vx = random.gauss(0, 1e-1)
vy = random.gauss(0, 1e-1)
ray = batoid.Ray((x, y, -0.1), (vx, vy, 1), 0)
rray = asphere.reflect(ray.copy())
# ray.v, surfaceNormal, and rray.v should all be in the same plane, and
# hence (ray.v x surfaceNormal) . rray.v should have zero magnitude.
# magnitude zero.
np.testing.assert_allclose(
np.dot(np.cross(ray.v, asphere.normal(rray.r[0], rray.r[1])), rray.v),
0.0, rtol=0, atol=1e-15)
def test_rSplit():
for i in range(100):
R = np.random.normal(0.7, 0.8)
conic = np.random.uniform(-2.0, 1.0)
ncoef = np.random.randint(0, 4)
coefs = [np.random.normal(0, 1e-10) for i in range(ncoef)]
asphere = batoid.Asphere(R, conic, coefs)
rays = batoid.rayGrid(10, 2*R, 0.0, 0.0, -1.0, 16, 500e-9, 1.0, batoid.Air())
coating = batoid.SimpleCoating(0.9, 0.1)
reflectedRays = asphere.reflect(rays, coating)
m1 = batoid.Air()
m2 = batoid.ConstMedium(1.1)
refractedRays = asphere.refract(rays, m1, m2, coating)
reflectedRays2, refractedRays2 = asphere.rSplit(rays, m1, m2, coating)
assert reflectedRays == reflectedRays2
assert refractedRays == refractedRays2
def test_refract():
rng = np.random.default_rng(577215)
size = 10_000
for i in range(100):
zmax = np.inf
while zmax > 3.0:
R = 0.0
while abs(R) < 15.0: # Don't allow too small radius of curvature
R = 1. / rng.normal(0.0, 0.3) # negative allowed
conic = rng.uniform(-2.0, 1.0)
ncoef = rng.choice(5)
coefs = [rng.normal(0, 1e-8) for i in range(ncoef)]
asphere = batoid.Asphere(R, conic, coefs)
lim = min(0.7 * abs(R) / np.sqrt(1 + conic) if conic > -1 else 5,
5)
zmax = abs(asphere.sag(lim, lim))
m0 = batoid.ConstMedium(rng.normal(1.2, 0.01))
m1 = batoid.ConstMedium(rng.normal(1.3, 0.01))
x = rng.uniform(-lim, lim, size=size)
y = rng.uniform(-lim, lim, size=size)
z = np.full_like(x, -10.0)
vx = rng.uniform(-1e-5, 1e-5, size=size)
vy = rng.uniform(-1e-5, 1e-5, size=size)
vz = np.sqrt(1 - vx * vx - vy * vy) / m0.n
rv = batoid.RayVector(x, y, z, vx, vy, vz, t=0)
rvr = batoid.refract(asphere, rv.copy(), m0, m1)
rvr2 = asphere.refract(rv.copy(), m0, m1)
rays_allclose(rvr, rvr2)
# print(f"{np.sum(rvr.failed)/len(rvr)*100:.2f}% failed")
normal = asphere.normal(rvr.x, rvr.y)
# Test Snell's law
s0 = np.sum(np.cross(normal, rv.v * m0.n)[~rvr.failed], axis=-1)
s1 = np.sum(np.cross(normal, rvr.v * m1.n)[~rvr.failed], axis=-1)
np.testing.assert_allclose(m0.n * s0, m1.n * s1, rtol=0, atol=1e-9)
# Test that rv.v, rvr.v and normal are all in the same plane
np.testing.assert_allclose(np.einsum("ad,ad->a",
np.cross(normal, rv.v),
rv.v)[~rvr.failed],
0.0,
rtol=0,
atol=1e-12)
def test_properties():
rng = np.random.default_rng(5)
for i in range(100):
zmax = np.inf
while zmax > 3.0:
R = 0.0
while abs(R) < 15.0: # Don't allow too small radius of curvature
R = 1. / rng.normal(0.0, 0.3) # negative allowed
conic = rng.uniform(-2.0, 1.0)
ncoef = rng.choice(5)
coefs = [rng.normal(0, 1e-8) for i in range(ncoef)]
asphere = batoid.Asphere(R, conic, coefs)
lim = min(0.7 * abs(R) / np.sqrt(1 + conic) if conic > -1 else 5,
5)
zmax = abs(asphere.sag(lim, lim))
assert asphere.R == R
assert asphere.conic == conic
assert np.array_equal(asphere.coefs, coefs)
do_pickle(asphere)
def test_reflect():
rng = np.random.default_rng(57721)
size = 10_000
for i in range(100):
zmax = np.inf
while zmax > 3.0:
R = 0.0
while abs(R) < 15.0: # Don't allow too small radius of curvature
R = 1. / rng.normal(0.0, 0.3) # negative allowed
conic = rng.uniform(-2.0, 1.0)
ncoef = rng.choice(5)
coefs = [rng.normal(0, 1e-8) for i in range(ncoef)]
asphere = batoid.Asphere(R, conic, coefs)
lim = min(0.7 * abs(R) / np.sqrt(1 + conic) if conic > -1 else 5,
5)
zmax = abs(asphere.sag(lim, lim))
x = rng.uniform(-lim, lim, size=size)
y = rng.uniform(-lim, lim, size=size)
z = np.full_like(x, -10.0)
vx = rng.uniform(-1e-5, 1e-5, size=size)
vy = rng.uniform(-1e-5, 1e-5, size=size)
vz = np.full_like(x, 1)
rv = batoid.RayVector(x, y, z, vx, vy, vz)
rvr = batoid.reflect(asphere, rv.copy())
rvr2 = asphere.reflect(rv.copy())
rays_allclose(rvr, rvr2)
# print(f"{np.sum(rvr.failed)/len(rvr)*100:.2f}% failed")
normal = asphere.normal(rvr.x, rvr.y)
# Test law of reflection
a0 = np.einsum("ad,ad->a", normal, rv.v)[~rvr.failed]
a1 = np.einsum("ad,ad->a", normal, -rvr.v)[~rvr.failed]
np.testing.assert_allclose(a0, a1, rtol=0, atol=1e-12)
# Test that rv.v, rvr.v and normal are all in the same plane
np.testing.assert_allclose(np.einsum("ad,ad->a",
np.cross(normal, rv.v),
rv.v)[~rvr.failed],
0.0,
rtol=0,
atol=1e-12)
def test_asphere_refraction_reversal():
import random
random.seed(577215)
wavelength = 500e-9 # arbitrary
asphere = batoid.Asphere(23.0, -0.97, [1e-5, 1e-6])
m1 = batoid.ConstMedium(1.7)
m2 = batoid.ConstMedium(1.9)
for i in range(1000):
x = random.gauss(0, 1)
y = random.gauss(0, 1)
vx = random.gauss(0, 1e-1)
vy = random.gauss(0, 1e-1)
ray = batoid.Ray([x, y, -0.1],
normalized(np.array([vx, vy, 1])) /
m1.getN(wavelength), 0)
rray = asphere.refract(ray, m1, m2)
np.testing.assert_allclose(np.linalg.norm(rray.v),
1. / m2.getN(wavelength),
rtol=1e-15)
# Invert the refracted ray, and see that it ends back at the starting
# point
# Keep going a bit before turning around though
turn_around = rray.positionAtTime(rray.t + 0.1)
return_ray = batoid.Ray(turn_around, -rray.v, -(rray.t + 0.1))
riray = asphere.intersect(return_ray)
# First check that we intersected at the same point
np.testing.assert_allclose(rray.r[0], riray.r[0], rtol=0, atol=1e-10)
np.testing.assert_allclose(rray.r[1], riray.r[1], rtol=0, atol=1e-10)
np.testing.assert_allclose(rray.r[2], riray.r[2], rtol=0, atol=1e-10)
# Refract and propagate back to t=0.
cray = asphere.refract(return_ray, m2, m1)
np.testing.assert_allclose(np.linalg.norm(cray.v),
1. / m1.getN(wavelength),
rtol=1e-15)
cpoint = cray.positionAtTime(0)
np.testing.assert_allclose(cpoint[0], x, rtol=0, atol=1e-10)
np.testing.assert_allclose(cpoint[1], y, rtol=0, atol=1e-10)
np.testing.assert_allclose(cpoint[2], -0.1, rtol=0, atol=1e-10)
def test_sag():
import random
random.seed(57)
for i in range(100):
R = random.gauss(25.0, 0.2)
conic = random.uniform(-2.0, 1.0)
ncoefs = random.randint(0, 4)
coefs = [random.gauss(0, 1e-10) for i in range(ncoefs)]
asphere = batoid.Asphere(R, conic, coefs)
for j in range(100):
x = random.gauss(0.0, 1.0)
y = random.gauss(0.0, 1.0)
result = asphere.sag(x, y)
np.testing.assert_allclose(result,
py_asphere(R, conic, coefs)(x, y))
# Check that it returned a scalar float and not an array
assert isinstance(result, float)
# Check vectorization
x = np.random.normal(0.0, 1.0, size=(10, 10))
y = np.random.normal(0.0, 1.0, size=(10, 10))
# Make sure non-unit stride arrays also work
np.testing.assert_allclose(asphere.sag(x[::5, ::2], y[::5, ::2]),
py_asphere(R, conic, coefs)(x, y)[::5, ::2])
def test_intersect():
rng = np.random.default_rng(5772)
size = 10_000
for i in range(100):
zmax = np.inf
while zmax > 3.0:
R = 0.0
while abs(R) < 15.0: # Don't allow too small radius of curvature
R = 1. / rng.normal(0.0, 0.3) # negative allowed
conic = rng.uniform(-2.0, 1.0)
ncoef = rng.choice(5)
coefs = [rng.normal(0, 1e-8) for i in range(ncoef)]
asphere = batoid.Asphere(R, conic, coefs)
lim = min(0.7 * abs(R) / np.sqrt(1 + conic) if conic > -1 else 5,
5)
zmax = abs(asphere.sag(lim, lim))
asphereCoordSys = batoid.CoordSys(origin=[0, 0, -1])
x = rng.uniform(-lim, lim, size=size)
y = rng.uniform(-lim, lim, size=size)
z = np.full_like(x, -10.0)
# If we shoot rays straight up, then it's easy to predict the
# intersection
vx = np.zeros_like(x)
vy = np.zeros_like(x)
vz = np.ones_like(x)
rv = batoid.RayVector(x, y, z, vx, vy, vz)
np.testing.assert_allclose(rv.z, -10.0)
rv2 = batoid.intersect(asphere, rv.copy(), asphereCoordSys)
assert rv2.coordSys == asphereCoordSys
rv2 = rv2.toCoordSys(batoid.CoordSys())
np.testing.assert_allclose(rv2.x, x)
np.testing.assert_allclose(rv2.y, y)
np.testing.assert_allclose(rv2.z,
asphere.sag(x, y) - 1,
rtol=0,
atol=1e-12)
# Straight down works too.
rv2 = rv.copy()
rv2.vz[:] *= -1
rv2 = batoid.intersect(asphere, rv.copy(), asphereCoordSys)
assert rv2.coordSys == asphereCoordSys
rv2 = rv2.toCoordSys(batoid.CoordSys())
np.testing.assert_allclose(rv2.x, x)
np.testing.assert_allclose(rv2.y, y)
np.testing.assert_allclose(rv2.z,
asphere.sag(x, y) - 1,
rtol=0,
atol=1e-12)
# Check default intersect coordTransform
rv2 = rv.copy().toCoordSys(asphereCoordSys)
batoid.intersect(asphere, rv2)
assert rv2.coordSys == asphereCoordSys
rv2 = rv2.toCoordSys(batoid.CoordSys())
np.testing.assert_allclose(rv2.x, x)
np.testing.assert_allclose(rv2.y, y)
np.testing.assert_allclose(rv2.z,
asphere.sag(x, y) - 1,
rtol=0,
atol=1e-12)