def test02_intersection_partials(variant_scalar_rgb):
from mitsuba.core import Frame3f, Ray3f, RayDifferential3f
from mitsuba.render import SurfaceInteraction3f
# Test the texture partial computation with some random data
o = [0.44650541, 0.16336525, 0.74225088]
d = [0.2956123, 0.67325977, 0.67774232]
time = 0.5
w = []
r = RayDifferential3f(o, d, time, w)
r.o_x = r.o + [0.1, 0, 0]
r.o_y = r.o + [0, 0.1, 0]
r.d_x = r.d
r.d_y = r.d
r.has_differentials = True
si = SurfaceInteraction3f()
si.p = r(10)
si.dp_du = [0.5514372, 0.84608955, 0.41559092]
si.dp_dv = [0.14551054, 0.54917541, 0.39286475]
si.n = ek.cross(si.dp_du, si.dp_dv)
si.n /= ek.norm(si.n)
si.t = 0
si.compute_partials(r)
# Positions reached via computed partials
px1 = si.dp_du * si.duv_dx[0] + si.dp_dv * si.duv_dx[1]
py1 = si.dp_du * si.duv_dy[0] + si.dp_dv * si.duv_dy[1]
# Manually
px2 = r.o_x + r.d_x * \
((ek.dot(si.n, si.p) - ek.dot(si.n, r.o_x)) / ek.dot(si.n, r.d_x))
py2 = r.o_y + r.d_y * \
((ek.dot(si.n, si.p) - ek.dot(si.n, r.o_y)) / ek.dot(si.n, r.d_y))
px2 -= si.p
py2 -= si.p
assert (ek.allclose(px1, px2))
assert (ek.allclose(py1, py2))
si.dp_du = [0, 0, 0]
si.compute_partials(r)
assert (ek.allclose(px1, px2))
assert (ek.allclose(py1, py2))
si.compute_partials(r)
assert (ek.allclose(si.duv_dx, [0, 0]))
assert (ek.allclose(si.duv_dy, [0, 0]))
def det(m):
if not _ek.is_matrix_v(m):
raise Exception("Unsupported target type!")
if m.Size == 1:
return m[0, 0]
elif m.Size == 2:
return _ek.fmsub(m[0, 0], m[1, 1], m[0, 1] * m[1, 0])
elif m.Size == 3:
return _ek.dot(m[0], _ek.cross(m[1], m[2]))
elif m.Size == 4:
col0, col1, col2, col3 = m
col1 = _ek.shuffle((2, 3, 0, 1), col1)
col3 = _ek.shuffle((2, 3, 0, 1), col3)
temp = _ek.shuffle((1, 0, 3, 2), col2 * col3)
row0 = col1 * temp
temp = _ek.shuffle((2, 3, 0, 1), temp)
row0 = _ek.fmsub(col1, temp, row0)
temp = _ek.shuffle((1, 0, 3, 2), col1 * col2)
row0 = _ek.fmadd(col3, temp, row0)
temp = _ek.shuffle((2, 3, 0, 1), temp)
row0 = _ek.fnmadd(col3, temp, row0)
col1 = _ek.shuffle((2, 3, 0, 1), col1)
col2 = _ek.shuffle((2, 3, 0, 1), col2)
temp = _ek.shuffle((1, 0, 3, 2), col1 * col3)
row0 = _ek.fmadd(col2, temp, row0)
temp = _ek.shuffle((2, 3, 0, 1), temp)
row0 = _ek.fnmadd(col2, temp, row0)
return _ek.dot(col0, row0)
else:
raise Exception('Unsupported array size!')
def test02_sample_pol_local(variant_scalar_mono_polarized):
from mitsuba.core import Frame3f, Transform4f, Spectrum, UnpolarizedSpectrum, Vector3f
from mitsuba.core.xml import load_string
from mitsuba.render import BSDFContext, TransportMode, SurfaceInteraction3f, fresnel_conductor
from mitsuba.render.mueller import stokes_basis, rotate_mueller_basis
def spectrum_from_stokes(v):
res = Spectrum(0.0)
for i in range(4):
res[i, 0] = v[i]
return res
# Create a Silver conductor BSDF and reflect different polarization states
# at a 45˚ angle.
# All tests take place directly in local BSDF coordinates. Here we only
# want to make sure that the output of this looks like what you would
# expect from a Mueller matrix describing specular reflection on a mirror.
eta = 0.136125 + 4.010625j # IoR values of Ag at 635.816284nm
bsdf = load_string("""<bsdf version='2.0.0' type='conductor'>
<spectrum name="eta" value="{}"/>
<spectrum name="k" value="{}"/>
</bsdf>""".format(eta.real, eta.imag))
theta_i = 45 * ek.pi / 180
wi = Vector3f([-ek.sin(theta_i), 0, ek.cos(theta_i)])
ctx = BSDFContext()
ctx.mode = TransportMode.Importance
si = SurfaceInteraction3f()
si.p = [0, 0, 0]
si.wi = wi
n = [0, 0, 1]
si.sh_frame = Frame3f(n)
bs, M_local = bsdf.sample(ctx, si, 0.0, [0.0, 0.0])
wo = bs.wo
# Rotate into standard coordinates for specular reflection
bi_s = ek.normalize(ek.cross(n, -wi))
bi_p = ek.normalize(ek.cross(-wi, bi_s))
bo_s = ek.normalize(ek.cross(n, wo))
bo_p = ek.normalize(ek.cross(wo, bi_s))
M_local = rotate_mueller_basis(M_local, -wi, stokes_basis(-wi), bi_p, wo,
stokes_basis(wo), bo_p)
# Apply to unpolarized light and verify that it is equivalent to normal Fresnel
a0 = M_local @ spectrum_from_stokes([1, 0, 0, 0])
F = fresnel_conductor(ek.cos(theta_i),
ek.scalar.Complex2f(eta.real, eta.imag))
a0 = a0[0, 0]
assert ek.allclose(a0[0], F, atol=1e-3)
# Apply to horizontally polarized light (linear at 0˚)
# Test that it is..
# 1) still fully polarized (though with reduced intensity)
# 2) still horizontally polarized
a1 = M_local @ spectrum_from_stokes([1, +1, 0, 0])
assert ek.allclose(a1[0, 0], ek.abs(a1[1, 0]), atol=1e-3) # 1)
a1 /= a1[0, 0]
assert ek.allclose(a1, spectrum_from_stokes([1, 1, 0, 0]), atol=1e-3) # 2)
# Apply to vertically polarized light (linear at 90˚)
# Test that it is..
# 1) still fully polarized (though with reduced intensity)
# 2) still vertically polarized
a2 = M_local @ spectrum_from_stokes([1, -1, 0, 0])
assert ek.allclose(a2[0, 0], ek.abs(a2[1, 0]), atol=1e-3) # 1)
a2 /= a2[0, 0]
assert ek.allclose(a2, spectrum_from_stokes([1, -1, 0, 0]),
atol=1e-3) # 2)
# Apply to (positive) diagonally polarized light (linear at +45˚)
# Test that..
# 1) The polarization is flipped to -45˚
# 2) There is now also some (left) circular polarization
a3 = M_local @ spectrum_from_stokes([1, 0, +1, 0])
assert ek.all(a3[2, 0] < UnpolarizedSpectrum(0.0))
assert ek.all(a3[3, 0] < UnpolarizedSpectrum(0.0))
# Apply to (negative) diagonally polarized light (linear at -45˚)
# Test that..
# 1) The polarization is flipped to +45˚
# 2) There is now also some (right) circular polarization
a4 = M_local @ spectrum_from_stokes([1, 0, -1, 0])
assert ek.all(a4[2, 0] > UnpolarizedSpectrum(0.0))
assert ek.all(a4[3, 0] > UnpolarizedSpectrum(0.0))
# Apply to right circularly polarized light
# Test that the polarization is flipped to left circular
a5 = M_local @ spectrum_from_stokes([1, 0, 0, +1])
assert ek.all(a5[3, 0] < UnpolarizedSpectrum(0.0))
# Apply to left circularly polarized light
# Test that the polarization is flipped to right circular
a6 = M_local @ spectrum_from_stokes([1, 0, 0, -1])
assert ek.all(a6[3, 0] > UnpolarizedSpectrum(0.0))
def inverse_transpose(m):
if not _ek.is_matrix_v(m):
raise Exception("Unsupported target type!")
t = type(m)
if m.Size == 1:
return t(_ek.rcp(m[0, 0]))
elif m.Size == 2:
inv_det = _ek.rcp(_ek.fmsub(m[0, 0], m[1, 1], m[0, 1] * m[1, 0]))
return t(m[1, 1] * inv_det, -m[1, 0] * inv_det, -m[0, 1] * inv_det,
m[0, 0] * inv_det)
elif m.Size == 3:
col0, col1, col2 = m
row0 = _ek.cross(col1, col2)
row1 = _ek.cross(col2, col0)
row2 = _ek.cross(col0, col1)
inv_det = _ek.rcp(_ek.dot(col0, row0))
return t(row0 * inv_det, row1 * inv_det, row2 * inv_det)
elif m.Size == 4:
col0, col1, col2, col3 = m
col1 = _ek.shuffle((2, 3, 0, 1), col1)
col3 = _ek.shuffle((2, 3, 0, 1), col3)
temp = _ek.shuffle((1, 0, 3, 2), col2 * col3)
row0 = col1 * temp
row1 = col0 * temp
temp = _ek.shuffle((2, 3, 0, 1), temp)
row0 = _ek.fmsub(col1, temp, row0)
row1 = _ek.shuffle((2, 3, 0, 1), _ek.fmsub(col0, temp, row1))
temp = _ek.shuffle((1, 0, 3, 2), col1 * col2)
row0 = _ek.fmadd(col3, temp, row0)
row3 = col0 * temp
temp = _ek.shuffle((2, 3, 0, 1), temp)
row0 = _ek.fnmadd(col3, temp, row0)
row3 = _ek.shuffle((2, 3, 0, 1), _ek.fmsub(col0, temp, row3))
temp = _ek.shuffle((1, 0, 3, 2),
_ek.shuffle((2, 3, 0, 1), col1) * col3)
col2 = _ek.shuffle((2, 3, 0, 1), col2)
row0 = _ek.fmadd(col2, temp, row0)
row2 = col0 * temp
temp = _ek.shuffle((2, 3, 0, 1), temp)
row0 = _ek.fnmadd(col2, temp, row0)
row2 = _ek.shuffle((2, 3, 0, 1), _ek.fmsub(col0, temp, row2))
temp = _ek.shuffle((1, 0, 3, 2), col0 * col1)
row2 = _ek.fmadd(col3, temp, row2)
row3 = _ek.fmsub(col2, temp, row3)
temp = _ek.shuffle((2, 3, 0, 1), temp)
row2 = _ek.fmsub(col3, temp, row2)
row3 = _ek.fnmadd(col2, temp, row3)
temp = _ek.shuffle((1, 0, 3, 2), col0 * col3)
row1 = _ek.fnmadd(col2, temp, row1)
row2 = _ek.fmadd(col1, temp, row2)
temp = _ek.shuffle((2, 3, 0, 1), temp)
row1 = _ek.fmadd(col2, temp, row1)
row2 = _ek.fnmadd(col1, temp, row2)
temp = _ek.shuffle((1, 0, 3, 2), col0 * col2)
row1 = _ek.fmadd(col3, temp, row1)
row3 = _ek.fnmadd(col1, temp, row3)
temp = _ek.shuffle((2, 3, 0, 1), temp)
row1 = _ek.fnmadd(col3, temp, row1)
row3 = _ek.fmadd(col1, temp, row3)
inv_det = _ek.rcp(_ek.dot(col0, row0))
return t(row0 * inv_det, row1 * inv_det, row2 * inv_det,
row3 * inv_det)
else:
raise Exception('Unsupported array size!')