def test03_sample_eval_pdf(variant_scalar_rgb, interaction):
from mitsuba.core.math import InvPi
from mitsuba.core.warp import square_to_uniform_sphere
from mitsuba.render import BSDFContext
from mitsuba.core.xml import load_string
bsdf = load_string("""<bsdf version="2.0.0" type="twosided">
<bsdf type="diffuse">
<rgb name="reflectance" value="0.1, 0.1, 0.1"/>
</bsdf>
<bsdf type="diffuse">
<rgb name="reflectance" value="0.9, 0.9, 0.9"/>
</bsdf>
</bsdf>""")
n = 5
ctx = BSDFContext()
for u in ek.arange(UInt32, n):
for v in ek.arange(UInt32, n):
interaction.wi = square_to_uniform_sphere([u / float(n-1),
v / float(n-1)])
up = ek.dot(interaction.wi, [0, 0, 1]) > 0
for x in ek.arange(UInt32, n):
for y in ek.arange(UInt32, n):
sample = [x / float(n-1), y / float(n-1)]
(bs, s_value) = bsdf.sample(ctx, interaction, 0.5, sample)
if ek.any(s_value > 0):
# Multiply by square_to_cosine_hemisphere_theta
s_value *= bs.wo[2] * InvPi
if not up:
s_value *= -1
e_value = bsdf.eval(ctx, interaction, bs.wo)
p_pdf = bsdf.pdf(ctx, interaction, bs.wo)
assert ek.allclose(s_value, e_value, atol=1e-2)
assert ek.allclose(bs.pdf, p_pdf)
assert not ek.any(ek.isnan(e_value) | ek.isnan(s_value))
def test06_rgb2spec_fetch_eval_mean(variant_scalar_spectral):
from mitsuba.render import srgb_model_fetch, srgb_model_eval, srgb_model_mean
from mitsuba.core import MTS_WAVELENGTH_MIN, MTS_WAVELENGTH_MAX, MTS_WAVELENGTH_SAMPLES
import numpy as np
rgb_values = np.array([
[0, 0, 0],
[0.0129831, 0.0129831, 0.0129831],
[0.0241576, 0.0241576, 0.0241576],
[0.0423114, 0.0423114, 0.0423114],
[0.0561285, 0.0561285, 0.0561285],
[0.0703601, 0.0703601, 0.0703601],
[0.104617, 0.104617, 0.104617],
[0.171441, 0.171441, 0.171441],
[0.242281, 0.242281, 0.242281],
[0.814846, 0.814846, 0.814846],
[0.913098, 0.913098, 0.913098],
[0.930111, 0.930111, 0.930111],
[0.955973, 0.955973, 0.955973],
[0.973445, 0.973445, 0.973445],
[0.982251, 0.982251, 0.982251],
[0.991102, 0.991102, 0.991102],
[1, 1, 1],
])
wavelengths = np.linspace(MTS_WAVELENGTH_MIN, MTS_WAVELENGTH_MAX,
MTS_WAVELENGTH_SAMPLES)
for i in range(rgb_values.shape[0]):
rgb = rgb_values[i, :]
assert np.all((rgb >= 0.0) & (rgb <= 1.0)), "Invalid RGB attempted"
coeff = srgb_model_fetch(rgb)
mean = srgb_model_mean(coeff)
value = srgb_model_eval(coeff, wavelengths)
assert not ek.any(ek.isnan(coeff)), "{} => coeff = {}".format(
rgb, coeff)
assert not ek.any(ek.isnan(mean)), "{} => mean = {}".format(rgb, mean)
assert not ek.any(ek.isnan(value)), "{} => value = {}".format(
rgb, value)
def test09_eval_parameterization(variant_scalar_rgb, variant_packet_rgb):
from mitsuba.core.xml import load_string
shape = load_string('''
<shape type="obj" version="2.0.0">
<string name="filename" value="resources/data/common/meshes/rectangle.obj"/>
</shape>
''')
print(shape)
si = shape.eval_parameterization([-0.01, 0.5])
assert not ek.any(si.is_valid())
si = shape.eval_parameterization([1.0 - 1e-7, 1.0 - 1e-7])
assert ek.all(si.is_valid())
assert ek.allclose(si.p, [1, 1, 0])
si = shape.eval_parameterization([1e-7, 1e-7])
assert ek.all(si.is_valid())
assert ek.allclose(si.p, [-1, -1, 0])
si = shape.eval_parameterization([.2, .3])
assert ek.all(si.is_valid())
assert ek.allclose(si.p, [-.6, -.4, 0])
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 compare_results(res_a, res_b, atol=0.0):
assert ek.all(res_a.is_valid() == res_b.is_valid())
if ek.any(res_a.is_valid()):
assert ek.allclose(res_a.t, res_b.t,
atol=atol), "\n%s\n\n%s" % (res_a.t, res_b.t)
diff_vertex_ref = []
diff_vertex_init = []
for j in range(10):
opt = Adam(params_opt, lr = 0.001)
# opt = SGD(params_opt, lr = 0.001, momentum = 0.9)
for i in range(10):
unravel(vertex_positions + Vector3f(0,0,1) * params_opt['displacements'], params[vertex_pos_key])
params.set_dirty(vertex_pos_key)
params.update()
image = render(scene)
if j == 0 and i == 0:
image_init = image
if ek.any(ek.any(ek.isnan(params[vertex_pos_key]))):
print("[WARNING] NaNs in the vertex positions.")
if ek.any(ek.isnan(image)):
print("[WARNING] NaNs in the image.")
# Write a gamma encoded PNG
image_np = image.numpy().reshape(height, width, 3)
output_file = output_path + 'out_%03i_%03i.png' % (j, i)
print("Writing image %s" % (output_file))
Bitmap(image_np).convert(pixel_format=Bitmap.PixelFormat.RGB, component_format=Struct.Type.UInt8, srgb_gamma=True).write(output_file)
# Objective function
if task == 'plain2bumpy' or task == 'bumpy2bumpy':
loss = ek.hsum(ek.hsum(ek.sqr(image - image_ref))) / (height*width*3)
if task == 'bumpy2plain':
