def integrator_sample(scene, sampler, rays, medium, active=True):
si = scene.ray_intersect(rays)
active = si.is_valid() & active
# Visible emitters
emitter_vis = si.emitter(scene, active)
result = ek.select(active, Emitter.eval_vec(emitter_vis, si, active), Vector3f(0.0))
ctx = BSDFContext()
bsdf = si.bsdf(rays)
# Emitter sampling
sample_emitter = active & has_flag(BSDF.flags_vec(bsdf), BSDFFlags.Smooth)
ds, emitter_val = scene.sample_emitter_direction(si, sampler.next_2d(sample_emitter), True, sample_emitter)
active_e = sample_emitter & ek.neq(ds.pdf, 0.0)
wo = si.to_local(ds.d)
bsdf_val = BSDF.eval_vec(bsdf, ctx, si, wo, active_e)
bsdf_pdf = BSDF.pdf_vec(bsdf, ctx, si, wo, active_e)
mis = ek.select(ds.delta, Float(1), mis_weight(ds.pdf, bsdf_pdf))
result += ek.select(active_e, emitter_val * bsdf_val * mis, Vector3f(0))
# BSDF sampling
active_b = active
bs, bsdf_val = BSDF.sample_vec(bsdf, ctx, si, sampler.next_1d(active), sampler.next_2d(active), active_b)
si_bsdf = scene.ray_intersect(si.spawn_ray(si.to_world(bs.wo)), active_b)
emitter = si_bsdf.emitter(scene, active_b)
active_b &= ek.neq(emitter, 0)
emitter_val = Emitter.eval_vec(emitter, si_bsdf, active_b)
delta = has_flag(bs.sampled_type, BSDFFlags.Delta)
ds = DirectionSample3f(si_bsdf, si)
ds.object = emitter
emitter_pdf = ek.select(delta, Float(0), scene.pdf_emitter_direction(si, ds, active_b))
result += ek.select(active_b, bsdf_val * emitter_val * mis_weight(bs.pdf, emitter_pdf), Vector3f(0))
return result, si.is_valid(), ek.select(si.is_valid(), si.t, Float(0.0))
def test05_scalar(t):
if not ek.is_array_v(t) or ek.array_size_v(t) == 0:
return
get_class(t.__module__)
if ek.is_mask_v(t):
assert ek.all_nested(t(True))
assert ek.any_nested(t(True))
assert ek.none_nested(t(False))
assert ek.all_nested(t(False) ^ t(True))
assert ek.all_nested(ek.eq(t(False), t(False)))
assert ek.none_nested(ek.eq(t(True), t(False)))
if ek.is_arithmetic_v(t):
assert t(1) + t(1) == t(2)
assert t(3) - t(1) == t(2)
assert t(2) * t(2) == t(4)
assert ek.min(t(2), t(3)) == t(2)
assert ek.max(t(2), t(3)) == t(3)
if ek.is_signed_v(t):
assert t(2) * t(-2) == t(-4)
assert ek.abs(t(-2)) == t(2)
if ek.is_integral_v(t):
assert t(6) // t(2) == t(3)
assert t(7) % t(2) == t(1)
assert t(7) >> 1 == t(3)
assert t(7) << 1 == t(14)
assert t(1) | t(2) == t(3)
assert t(1) ^ t(3) == t(2)
assert t(1) & t(3) == t(1)
else:
assert t(6) / t(2) == t(3)
assert ek.sqrt(t(4)) == t(2)
assert ek.fmadd(t(1), t(2), t(3)) == t(5)
assert ek.fmsub(t(1), t(2), t(3)) == t(-1)
assert ek.fnmadd(t(1), t(2), t(3)) == t(1)
assert ek.fnmsub(t(1), t(2), t(3)) == t(-5)
assert (t(1) & True) == t(1)
assert (t(1) & False) == t(0)
assert (t(1) | False) == t(1)
assert ek.all_nested(t(3) > t(2))
assert ek.all_nested(ek.eq(t(2), t(2)))
assert ek.all_nested(ek.neq(t(3), t(2)))
assert ek.all_nested(t(1) >= t(1))
assert ek.all_nested(t(2) < t(3))
assert ek.all_nested(t(1) <= t(1))
assert ek.select(ek.eq(t(2), t(2)), t(4), t(5)) == t(4)
assert ek.select(ek.eq(t(3), t(2)), t(4), t(5)) == t(5)
t2 = t(2)
assert ek.hsum(t2) == t.Value(2 * len(t2))
assert ek.dot(t2, t2) == t.Value(4 * len(t2))
assert ek.dot_async(t2, t2) == t(4 * len(t2))
value = t(1)
value[ek.eq(value, t(1))] = t(2)
value[ek.eq(value, t(3))] = t(5)
assert value == t(2)
def collatz(value: p.Int):
counter = p.Int(0)
loop = p.Loop(value, counter)
while (loop.cond(ek.neq(value, 1))):
is_even = ek.eq(value & 1, 0)
value.assign(ek.select(is_even, value // 2, 3 * value + 1))
counter += 1
return counter
def sample_direction(self, ref, sample, active):
# as the shape init happens after the emitter init
if (not (hasattr(self, "m_shape"))):
self.set_shape_area()
ds = self.m_shape.sample_direction(ref, sample, active)
active &= (ek.dot(ds.d, ds.n) < 0) & (ek.neq(ds.pdf, 0))
si = SurfaceInteraction3f(ds, ref.wavelengths)
# spatially varying
cosTheta = -ek.dot(ds.d, ds.n)
fall = self.fallof(cosTheta)
spec = self.m_radiance.eval(si, active) * fall / ds.pdf
ds.object = 0 # HACK
return (ds, ek.select(active, spec, ek.zero(type(spec))))
def neq_(a0, a1):
ar, sr = _check2_mask(a0, a1)
for i in range(sr):
ar[i] = _ek.neq(a0[i], a1[i])
return ar
def render_sample(scene, sampler, rays, bdata, heightmap_pybind, bssrdf=None):
"""
Sample RTE
TODO: Support multi channel sampling
Args:
scene: Target scene object
sampler: Sampler object for random number
rays: Given rays for sampling
bdata: BSSRDF Data object
heightmap_pybind: Object for getting height map around incident position.
Refer src/librender/python/heightmap.cpp
Returns:
result: Sampling RTE result
valid_rays: Mask data whether rays are valid or not
scatter: Scatter components of Sampling RTE result
non_scatter: Non scatter components of Sampling RTE result
invalid_sample: Sampling RTE result with invalid sampled data by VAEBSSRDF
"""
eta = Float(1.0)
emission_weight = Float(1.0)
throughput = Spectrum(1.0)
result = Spectrum(0.0)
scatter = Spectrum(0.0)
non_scatter = Spectrum(0.0)
invalid_sample = Spectrum(0.0)
active = True
is_bssrdf = False
##### First interaction #####
si = scene.ray_intersect(rays, active)
active = si.is_valid() & active
valid_rays = si.is_valid()
emitter = si.emitter(scene, active)
depth = 0
# Set channel
# At and after evaluating BSSRDF, a ray consider only this one channel
n_channels = 3
channel = UInt32(
ek.min(sampler.next_1d(active) * n_channels, n_channels - 1))
d_out_local = Vector3f().zero()
d_out_pdf = Float(0)
sss = Mask(False)
while (True):
depth += 1
if config.aovs and depth == 2:
sss = is_bssrdf
##### Interaction with emitters #####
emission_val = emission_weight * throughput * Emitter.eval_vec(
emitter, si, active)
result += ek.select(active, emission_val, Spectrum(0.0))
invalid_sample += ek.select(active, emission_val, Spectrum(0.0))
scatter += ek.select(active & sss, emission_val, Spectrum(0.0))
non_scatter += ek.select(active & ~sss, emission_val, Spectrum(0.0))
active = active & si.is_valid()
# Process russian roulette
if depth > config.rr_depth:
q = ek.min(ek.hmax(throughput) * ek.sqr(eta), 0.95)
active = active & (sampler.next_1d(active) < q)
throughput *= ek.rcp(q)
# Stop if the number of bouces exceeds the given limit bounce, or
# all rays are invalid. latter check is done only when the limit
# bounce is infinite
if depth >= config.max_depth:
break
##### Emitter sampling #####
bsdf = si.bsdf(rays)
ctx = BSDFContext()
active_e = active & has_flag(BSDF.flags_vec(bsdf), BSDFFlags.Smooth)
ds, emitter_val = scene.sample_emitter_direction(
si, sampler.next_2d(active_e), True, active_e)
active_e &= ek.neq(ds.pdf, 0.0)
# Query the BSDF for that emitter-sampled direction
wo = si.to_local(ds.d)
bsdf_val = BSDF.eval_vec(bsdf, ctx, si, wo, active_e)
# Determine density of sampling that same direction using BSDF sampling
bsdf_pdf = BSDF.pdf_vec(bsdf, ctx, si, wo, active_e)
mis = ek.select(ds.delta, Float(1), mis_weight(ds.pdf, bsdf_pdf))
emission_val = mis * throughput * bsdf_val * emitter_val
result += ek.select(active, emission_val, Spectrum(0.0))
invalid_sample += ek.select(active, emission_val, Spectrum(0.0))
scatter += ek.select(active & sss, emission_val, Spectrum(0.0))
non_scatter += ek.select(active & ~sss, emission_val, Spectrum(0.0))
##### BSDF sampling #####
bs, bsdf_val = BSDF.sample_vec(bsdf, ctx, si, sampler.next_1d(active),
sampler.next_2d(active), active)
##### BSSRDF replacing #####
if (config.enable_bssrdf):
# Replace bsdf samples by ones of BSSRDF
bs.wo = ek.select(is_bssrdf, d_out_local, bs.wo)
bs.pdf = ek.select(is_bssrdf, d_out_pdf, bs.pdf)
bs.sampled_component = ek.select(is_bssrdf, UInt32(1),
bs.sampled_component)
bs.sampled_type = ek.select(is_bssrdf,
UInt32(+BSDFFlags.DeltaTransmission),
bs.sampled_type)
############################
throughput *= ek.select(is_bssrdf, Float(1.0), bsdf_val)
active &= ek.any(ek.neq(throughput, 0))
eta *= bs.eta
# Intersect the BSDF ray against the scene geometry
rays = RayDifferential3f(si.spawn_ray(si.to_world(bs.wo)))
si_bsdf = scene.ray_intersect(rays, active)
##### Checking BSSRDF #####
if (config.enable_bssrdf):
# Whether the BSDF is BSS RDF or not?
is_bssrdf = (active
& has_flag(BSDF.flags_vec(bsdf), BSDFFlags.BSSRDF)
& (Frame3f.cos_theta(bs.wo) < Float(0.0))
& (Frame3f.cos_theta(si.wi) > Float(0.0)))
# Decide whether we should use 0-scattering or multiple scattering
is_zero_scatter = utils_render.check_zero_scatter(
sampler, si_bsdf, bs, channel, is_bssrdf)
is_bssrdf = is_bssrdf & ~is_zero_scatter
throughput *= ek.select(is_bssrdf, ek.sqr(bs.eta), Float(1.0))
###########################
###### Process for BSSRDF ######
if (config.enable_bssrdf and not ek.none(is_bssrdf)):
# Get projected samples from BSSRDF
projected_si, project_suc, abs_prob = bssrdf.sample_bssrdf(
scene, bsdf, bs, si, bdata, heightmap_pybind, channel,
is_bssrdf)
if config.visualize_invalid_sample and (depth <= 1):
active = active & (~is_bssrdf | project_suc)
invalid_sample += ek.select((is_bssrdf & (~project_suc)),
Spectrum([100, 0, 0]),
Spectrum(0.0))
# Sample outgoing direction from projected position
d_out_local, d_out_pdf = utils_render.resample_wo(
sampler, is_bssrdf)
# Apply absorption probability
throughput *= ek.select(is_bssrdf,
Spectrum(1) - abs_prob, Spectrum(1))
# Replace interactions by sampled ones from BSSRDF
si_bsdf = SurfaceInteraction3f().masked_si(si_bsdf, projected_si,
is_bssrdf)
################################
# Determine probability of having sampled that same
# direction using emitter sampling
emitter = si_bsdf.emitter(scene, active)
ds = DirectionSample3f(si_bsdf, si)
ds.object = emitter
delta = has_flag(bs.sampled_type, BSDFFlags.Delta)
emitter_pdf = ek.select(delta, Float(0.0),
scene.pdf_emitter_direction(si, ds))
emission_weight = mis_weight(bs.pdf, emitter_pdf)
si = si_bsdf
return result, valid_rays, scatter, non_scatter, invalid_sample
def run(self, significance_level=0.01, test_count=1, quiet=False):
"""
Run the Chi^2 test
Parameter ``significance_level`` (float):
Denotes the desired significance level (e.g. 0.01 for a test at the
1% significance level)
Parameter ``test_count`` (int):
Specifies the total number of statistical tests run by the user.
This value will be used to adjust the provided significance level
so that the combination of the entire set of tests has the provided
significance level.
Returns → bool:
``True`` upon success, ``False`` if the null hypothesis was
rejected.
"""
from mitsuba.core import UInt32, Float64
from mitsuba.core.math import chi2
from mitsuba.python.math import rlgamma
if self.histogram is None:
self.tabulate_histogram()
if self.pdf is None:
self.tabulate_pdf()
index = UInt32(
[i[0] for i in sorted(enumerate(self.pdf), key=lambda x: x[1])])
# Sort entries by expected frequency (increasing)
pdf = Float64(ek.gather(self.pdf, index))
histogram = Float64(ek.gather(self.histogram, index))
# Compute chi^2 statistic and pool low-valued cells
chi2val, dof, pooled_in, pooled_out = \
chi2(histogram, pdf, 5)
if dof < 1:
self._log('Failure: The number of degrees of freedom is too low!')
self.fail = True
if ek.any(ek.eq(pdf, 0) & ek.neq(histogram, 0)):
self._log('Failure: Found samples in a cell with expected '
'frequency 0. Rejecting the null hypothesis!')
self.fail = True
if pooled_in > 0:
self._log('Pooled %i low-valued cells into %i cells to '
'ensure sufficiently high expected cell frequencies' %
(pooled_in, pooled_out))
pdf_time = (self.pdf_end - self.pdf_start) * 1000
histogram_time = (self.histogram_end - self.histogram_start) * 1000
self._log('Histogram sum = %f (%.2f ms), PDF sum = %f (%.2f ms)' %
(self.histogram_sum, histogram_time, self.pdf_sum, pdf_time))
self._log('Chi^2 statistic = %f (d.o.f = %i)' % (chi2val, dof))
# Probability of observing a test statistic at least as
# extreme as the one here assuming that the distributions match
self.p_value = 1 - rlgamma(dof / 2, chi2val / 2)
# Apply the Šidák correction term, since we'll be conducting multiple
# independent hypothesis tests. This accounts for the fact that the
# probability of a failure increases quickly when several hypothesis
# tests are run in sequence.
significance_level = 1.0 - \
(1.0 - significance_level) ** (1.0 / test_count)
if self.fail:
self._log('Not running the test for reasons listed above. Target '
'density and histogram were written to "chi2_data.py')
result = False
elif self.p_value < significance_level \
or not ek.isfinite(self.p_value):
self._log('***** Rejected ***** the null hypothesis (p-value = %f,'
' significance level = %f). Target density and histogram'
' were written to "chi2_data.py".' %
(self.p_value, significance_level))
result = False
else:
self._log('Accepted the null hypothesis (p-value = %f, '
'significance level = %f)' %
(self.p_value, significance_level))
result = True
if not quiet:
print(self.messages)
if not result:
self._dump_tables()
return result
def sample(self, scene, sampler, ray, medium=None, active=True):
result = Vector3f(0.0)
si = scene.ray_intersect(ray, active)
active = si.is_valid() & active
# emitter = si.emitter(scene)
# result = ek.select(active, Emitter.eval_vec(emitter, si, active), Vector3f(0.0))
# z_axis = np.array([0, 0, 1])
# vertex = si.p.numpy()
# v_count = vertex.shape[0]
# vertex = np.expand_dims(vertex, axis=1)
# vertex = np.repeat(vertex, self.light.vertex_count(), axis=1)
# light_vertices = self.light.vertex_positions_buffer().numpy().reshape(self.light.vertex_count(), 3)
# light_vertices = np.expand_dims(light_vertices, axis=0)
# light_vertices = np.repeat(light_vertices, v_count, axis=0)
# sph_polygons = light_vertices - vertex
# sph_polygons = sph_polygons / np.linalg.norm(sph_polygons, axis=2, keepdims=True)
# z_axis = np.repeat( np.expand_dims(z_axis, axis=0), v_count, axis=0 )
# result_np = np.zeros(v_count, dtype=np.double)
# for idx in range( self.light.vertex_count() ):
# idx1 = (idx+1) % self.light.vertex_count()
# idx2 = (idx) % self.light.vertex_count()
# dp = np.sum( sph_polygons[:, idx1, :] * sph_polygons[:, idx2, :], axis=1 )
# acos = np.arccos(dp)
# cp = np.cross( sph_polygons[:, idx1, :], sph_polygons[:, idx2, :] )
# cp = cp / np.linalg.norm(cp, axis=1, keepdims=True)
# dp = np.sum( cp * z_axis, axis=1 )
# result_np += acos * dp
# result_np *= 0.5 * 1.0/math.pi
# result_np = np.repeat( result_np.reshape((v_count, 1)), 3, axis=1 )
# fin = self.light_radiance * Vector3f(result_np)
# fin[fin < 0] = 0
# result += ek.select(active, fin, Vector3f(0.0))
ctx = BSDFContext()
bsdf = si.bsdf(ray)
# bs, bsdf_val = BSDF.sample_vec(bsdf, ctx, si, sampler.next_1d(active), sampler.next_2d(active), active)
# pdf = bs.pdf
# wo = si.to_world(bs.wo)
ds, emitter_val = scene.sample_emitter_direction(
si, sampler.next_2d(active), True, active)
pdf = ds.pdf
active_e = active & ek.neq(ds.pdf, 0.0)
wo = ds.d
bsdf_val = BSDF.eval_vec(bsdf, ctx, si, wo, active_e)
emitter_val[emitter_val > 1.0] = 1.0
bsdf_val *= emitter_val
# _, wi_theta, wi_phi = sph_convert(si.to_world(si.wi))
_, wo_theta, wo_phi = sph_convert(wo)
y_0_0_ = y_0_0(bsdf_val, wo_theta, wo_phi) / ek.select(
pdf > 0, pdf, Float(0.01))
y_1_n1_ = y_1_n1(bsdf_val, wo_theta, wo_phi) / ek.select(
pdf > 0, pdf, Float(0.01))
y_1_0_ = y_1_0(bsdf_val, wo_theta, wo_phi) / ek.select(
pdf > 0, pdf, Float(0.01))
y_1_p1_ = y_1_p1(bsdf_val, wo_theta, wo_phi) / ek.select(
pdf > 0, pdf, Float(0.01))
y_2_n2_ = y_2_n2(bsdf_val, wo_theta, wo_phi) / ek.select(
pdf > 0, pdf, Float(0.01))
y_2_n1_ = y_2_n1(bsdf_val, wo_theta, wo_phi) / ek.select(
pdf > 0, pdf, Float(0.01))
y_2_0_ = y_2_0(bsdf_val, wo_theta, wo_phi) / ek.select(
pdf > 0, pdf, Float(0.01))
y_2_p1_ = y_2_p1(bsdf_val, wo_theta, wo_phi) / ek.select(
pdf > 0, pdf, Float(0.01))
y_2_p2_ = y_2_p2(bsdf_val, wo_theta, wo_phi) / ek.select(
pdf > 0, pdf, Float(0.01))
return result, si.is_valid(), [ Float(y_0_0_[0]), Float(y_0_0_[1]), Float(y_0_0_[2]),\
Float(y_1_n1_[0]), Float(y_1_n1_[1]), Float(y_1_n1_[2]),\
Float(y_1_0_[0]), Float(y_1_0_[1]), Float(y_1_0_[2]),\
Float(y_1_p1_[0]), Float(y_1_p1_[1]), Float(y_1_p1_[2]),\
Float(y_2_n2_[0]), Float(y_2_n2_[1]), Float(y_2_n2_[2]),\
Float(y_2_n1_[0]), Float(y_2_n1_[1]), Float(y_2_n1_[2]),\
Float(y_2_0_[0]), Float(y_2_0_[1]), Float(y_2_0_[2]),\
Float(y_2_p1_[0]), Float(y_2_p1_[1]), Float(y_2_p1_[2]),\
Float(y_2_p2_[0]), Float(y_2_p2_[1]), Float(y_2_p2_[2]) ]