def test30_acos(m):
x = ek.linspace(m.Float, -.8, .8, 10)
ek.enable_grad(x)
y = ek.acos(x * x)
ek.backward(y)
acos_x = ek.acos(ek.sqr(ek.detach(x)))
assert ek.allclose(y, acos_x)
assert ek.allclose(
ek.grad(x),
m.Float(2.08232, 1.3497, 0.906755, 0.534687, 0.177783, -0.177783,
-0.534687, -0.906755, -1.3497, -2.08232))
def test04_normal_weighting_scheme(variant_scalar_rgb):
from mitsuba.core import Vector3f
from mitsuba.render import Mesh
import numpy as np
"""Tests the weighting scheme that is used to compute surface normals."""
m = Mesh("MyMesh", 5, 2, has_vertex_normals=True)
vertices = m.vertex_positions_buffer()
normals = m.vertex_normals_buffer()
a, b = 1.0, 0.5
vertices[:] = [0, 0, 0, -a, 1, 0, a, 1, 0, -b, 0, 1, b, 0, 1]
n0 = Vector3f(0.0, 0.0, -1.0)
n1 = Vector3f(0.0, 1.0, 0.0)
angle_0 = ek.pi / 2.0
angle_1 = ek.acos(3.0 / 5.0)
n2 = n0 * angle_0 + n1 * angle_1
n2 /= ek.norm(n2)
n = np.vstack([n2, n0, n0, n1, n1]).transpose()
m.faces_buffer()[:] = [0, 1, 2, 0, 3, 4]
m.recompute_vertex_normals()
for i in range(5):
assert ek.allclose(normals[i * 3:(i + 1) * 3], n[:, i], 5e-4)
def test09_trig():
for i in range(-5, 5):
for j in range(-5, 5):
a = ek.sin(C(i, j))
b = C(cmath.sin(complex(i, j)))
assert ek.allclose(a, b)
a = ek.cos(C(i, j))
b = C(cmath.cos(complex(i, j)))
assert ek.allclose(a, b)
sa, ca = ek.sincos(C(i, j))
sb = C(cmath.sin(complex(i, j)))
cb = C(cmath.cos(complex(i, j)))
assert ek.allclose(sa, sb)
assert ek.allclose(ca, cb)
# Python appears to handle the branch cuts
# differently from Enoki, C, and Mathematica..
a = ek.asin(C(i, j + 0.1))
b = C(cmath.asin(complex(i, j + 0.1)))
assert ek.allclose(a, b)
a = ek.acos(C(i, j + 0.1))
b = C(cmath.acos(complex(i, j + 0.1)))
assert ek.allclose(a, b)
if abs(j) != 1 or i != 0:
a = ek.atan(C(i, j))
b = C(cmath.atan(complex(i, j)))
assert ek.allclose(a, b, atol=1e-7)
def fallof(self, cosTheta):
# delta = (cosTheta - self.cosTotalWidth)/(self.cosFallOffStart - self.cosTotalWidth)
delta = (self.cutOffAngle -
ek.acos(cosTheta)) * self.m_invTransitionWidth
delta = ek.select(cosTheta > self.cosFallOffStart,
ek.full(type(delta), 1), delta)
delta = ek.select(cosTheta < self.cosTotalWidth, ek.zero(type(delta)),
delta)
return delta
def test04_snell(variant_packet_rgb):
from mitsuba.render import fresnel
# Snell's law
theta_i = ek.linspace(Float, 0, ek.pi / 2, 20)
F, cos_theta_t, _, _ = fresnel(ek.cos(theta_i), 1.5)
theta_t = ek.acos(cos_theta_t)
assert ek.allclose(ek.sin(theta_i) - 1.5 * ek.sin(theta_t),
Float.zero(20),
atol=1e-5)
def test_sample_direction(variant_scalar_spectral, spectrum_key, it_pos,
wavelength_sample, cutoff_angle, lookat):
# Check the correctness of the sample_direction() method
import math
from mitsuba.core import sample_shifted, Transform4f
from mitsuba.render import SurfaceInteraction3f
cutoff_angle_rad = math.radians(cutoff_angle)
beam_width_rad = cutoff_angle_rad * 0.75
inv_transition_width = 1 / (cutoff_angle_rad - beam_width_rad)
emitter, spectrum = create_emitter_and_spectrum(lookat, cutoff_angle,
spectrum_key)
eval_t = 0.3
trafo = Transform4f(emitter.world_transform().eval(eval_t))
# Create a surface iteration
it = SurfaceInteraction3f.zero()
it.p = it_pos
it.time = eval_t
# Sample a wavelength from spectrum
wav, spec = spectrum.sample(it, sample_shifted(wavelength_sample))
it.wavelengths = wav
# Direction from the position to the point emitter
d = -it.p + lookat["pos"]
dist = ek.norm(d)
d /= dist
# Calculate angle between lookat direction and ray direction
angle = ek.acos((trafo.inverse().transform_vector(-d))[2])
angle = ek.select(
ek.abs(angle - beam_width_rad) < 1e-3, beam_width_rad, angle)
angle = ek.select(
ek.abs(angle - cutoff_angle_rad) < 1e-3, cutoff_angle_rad, angle)
# Sample a direction from the emitter
ds, res = emitter.sample_direction(it, [0, 0])
# Evalutate the spectrum
spec = spectrum.eval(it)
spec = ek.select(
angle <= beam_width_rad, spec,
spec * ((cutoff_angle_rad - angle) * inv_transition_width))
spec = ek.select(angle <= cutoff_angle_rad, spec, 0)
assert ds.time == it.time
assert ds.pdf == 1.0
assert ds.delta
assert ek.allclose(ds.d, d)
assert ek.allclose(res, spec / (dist**2))
def acos_(a0):
if not a0.IsFloat:
raise Exception("acos(): requires floating point operands!")
ar, sr = _check1(a0)
if not a0.IsSpecial:
for i in range(sr):
ar[i] = _ek.acos(a0[i])
elif a0.IsSpecial:
tmp = _ek.sqrt(1 - _ek.sqr(a0))
tmp = _ek.log(a0 + type(a0)(-tmp.imag, tmp.real))
ar.real = tmp.imag
ar.imag = -tmp.real
else:
raise Exception("acos(): unsupported array type!")
return ar
def test_sample_ray(variant_packet_spectral, spectrum_key, wavelength_sample,
pos_sample, cutoff_angle, lookat):
# Check the correctness of the sample_ray() method
import math
from mitsuba.core import warp, sample_shifted, Transform4f
from mitsuba.render import SurfaceInteraction3f
cutoff_angle_rad = math.radians(cutoff_angle)
cos_cutoff_angle_rad = math.cos(cutoff_angle_rad)
beam_width_rad = cutoff_angle_rad * 0.75
inv_transition_width = 1 / (cutoff_angle_rad - beam_width_rad)
emitter, spectrum = create_emitter_and_spectrum(lookat, cutoff_angle,
spectrum_key)
eval_t = 0.3
trafo = Transform4f(emitter.world_transform().eval(eval_t))
# Sample a local direction and calculate local angle
dir_sample = pos_sample # not being used anyway
local_dir = warp.square_to_uniform_cone(pos_sample, cos_cutoff_angle_rad)
angle = ek.acos(local_dir[2])
angle = ek.select(
ek.abs(angle - beam_width_rad) < 1e-3, beam_width_rad, angle)
angle = ek.select(
ek.abs(angle - cutoff_angle_rad) < 1e-3, cutoff_angle_rad, angle)
# Sample a ray (position, direction, wavelengths) from the emitter
ray, res = emitter.sample_ray(eval_t, wavelength_sample, pos_sample,
dir_sample)
# Sample wavelengths on the spectrum
it = SurfaceInteraction3f.zero()
wav, spec = spectrum.sample(it, sample_shifted(wavelength_sample))
it.wavelengths = wav
spec = spectrum.eval(it)
spec = ek.select(
angle <= beam_width_rad, spec,
spec * ((cutoff_angle_rad - angle) * inv_transition_width))
spec = ek.select(angle <= cutoff_angle_rad, spec, 0)
assert ek.allclose(
res, spec / warp.square_to_uniform_cone_pdf(
trafo.inverse().transform_vector(ray.d), cos_cutoff_angle_rad))
assert ek.allclose(ray.time, eval_t)
assert ek.all(local_dir.z >= cos_cutoff_angle_rad)
assert ek.allclose(ray.wavelengths, wav)
assert ek.allclose(ray.d, trafo.transform_vector(local_dir))
assert ek.allclose(ray.o, lookat["pos"])
def log_(a0):
if not a0.IsFloat:
raise Exception("log(): requires floating point operands!")
ar, sr = _check1(a0)
if not a0.IsSpecial:
for i in range(sr):
ar[i] = _ek.log(a0[i])
elif a0.IsComplex:
ar.real = .5 * _ek.log(_ek.squared_norm(a0))
ar.imag = _ek.arg(a0)
elif a0.IsQuaternion:
qi_n = _ek.normalize(a0.imag)
rq = _ek.norm(a0)
acos_rq = _ek.acos(a0.real / rq)
log_rq = _ek.log(rq)
ar.imag = qi_n * acos_rq
ar.real = log_rq
else:
raise Exception("log(): unsupported array type!")
return ar
def test04_normal_weighting_scheme(variant_scalar_rgb):
from mitsuba.core import Struct, float_dtype, Vector3f
from mitsuba.render import Mesh
import numpy as np
"""Tests the weighting scheme that is used to compute surface normals."""
vertex_struct = Struct() \
.append("x", Struct.Type.Float32) \
.append("y", Struct.Type.Float32) \
.append("z", Struct.Type.Float32) \
.append("nx", Struct.Type.Float32) \
.append("ny", Struct.Type.Float32) \
.append("nz", Struct.Type.Float32)
index_struct = Struct() \
.append("i0", Struct.Type.UInt32) \
.append("i1", Struct.Type.UInt32) \
.append("i2", Struct.Type.UInt32)
m = Mesh("MyMesh", vertex_struct, 5, index_struct, 2)
v = m.vertices()
a, b = 1.0, 0.5
v['x'] = Float([0, -a, a, -b, b])
v['y'] = Float([0, 1, 1, 0, 0])
v['z'] = Float([0, 0, 0, 1, 1])
n0 = Vector3f(0.0, 0.0, -1.0)
n1 = Vector3f(0.0, 1.0, 0.0)
angle_0 = ek.pi / 2.0
angle_1 = ek.acos(3.0 / 5.0)
n2 = n0 * angle_0 + n1 * angle_1
n2 /= ek.norm(n2)
n = np.vstack([n2, n0, n0, n1, n1])
f = m.faces()
f[0] = (0, 1, 2)
f[1] = (0, 3, 4)
m.recompute_vertex_normals()
assert ek.allclose(v['nx'], n[:, 0], 5e-4)
assert ek.allclose(v['ny'], n[:, 1], 5e-4)
assert ek.allclose(v['nz'], n[:, 2], 5e-4)
def check_fov(camera, sample):
ray, _ = camera.sample_ray(0, 0, sample, 0)
assert ek.allclose(
ek.acos(ek.dot(ray.d, direction)) * 180 / ek.pi, fov / 2)
def check_fov(camera, sample):
# aperture position at the center
ray, _ = camera.sample_ray(0, 0, sample, [0.5, 0.5])
assert ek.allclose(
ek.acos(ek.dot(ray.d, direction)) * 180 / ek.pi, fov / 2)
