def test_spherical(self, theta, phi):
st = np.sin(theta)
ct = np.cos(theta)
v = geo.spherical_direction(st, ct, phi)
theta_ret = geo.spherical_theta(v)
phi_ret = geo.spherical_phi(v)
assert_almost_eq(theta, theta_ret)
assert_almost_eq(phi, phi_ret)
def sample(self, u1: FLOAT, u2: FLOAT) -> ['geo.Point', 'geo.Normal']: """ account for partial sphere """ from pytracer.montecarlo import uniform_sample_sphere v = uniform_sample_sphere(u1, u2) phi = geo.spherical_theta(v) * self.phiMax * INV_2PI theta = self.thetaMin + geo.spherical_theta(v) * (self.thetaMax - self.thetaMin) v = geo.spherical_direction(np.sin(theta), np.cos(theta), phi) * self.radius v.z = self.zmin + v.z * (self.zmax - self.zmin) p = geo.Point.from_arr(v) Ns = geo.normalize(self.o2w(geo.Normal(p.x, p.y, p.z))) if self.ro: Ns *= -1. return [self.o2w(p), Ns]
def sample_hg(w: 'geo.Vector', g: FLOAT, u1: FLOAT, u2: FLOAT) -> 'geo.Vector':
"""
sample_hg()
Sampling from Henyey-Greestein
phase function, i.e.,
$$
\cos(\theta) = \frac{1}{2g}\left(1 + g^2 - \left( \frac{1-g^2}{1-g+2g\zeta} \right) ^2 \right))
$$
"""
if np.fabs(g) < EPS:
ct = 1. - 2. * u1
else:
sqr = (1. - g * g) / (1. - g + 2. * g * u1)
ct = (1. + g * g - sqr * sqr) / (2. * g)
st = np.sqrt(max(0., 1 - ct * ct))
phi = 2. * PI * u2
_, v1, v2 = geo.coordinate_system(w)
return geo.spherical_direction(st, ct, phi, v1, v2, w)
def sample_f(self, wo: 'geo.Vector', u1: FLOAT,
u2: FLOAT) -> [FLOAT, 'geo.Vector']:
# compute sampled half-angle vector
ct = np.power(u1, 1. / (self.e + 1))
st = np.sqrt(max(0., 1. - ct * ct))
phi = u2 * 2. * PI
wh = geo.spherical_direction(st, ct, phi)
if wo.z * wh.z <= 0.:
wh *= -1.
# incident direction by reflection
wi = -wo + 2. * wo.dot(wh) * wh
# pdf
pdf = ((self.e + 1.) * np.power(ct, self.e)) / \
(2. * PI * 4. * wo.dot(wh))
if wo.dot(wh) <= 0.:
pdf = 0.
return [pdf, wi]
def sample_f(self, wo: 'geo.Vector', u1: FLOAT,
u2: FLOAT) -> [FLOAT, 'geo.Vector']:
# sample from first quadrant and remap to hemisphere to sample w_h
if u1 < .25:
phi, ct = self.__sample_first_quad(4. * u1, u2)
elif u1 < .5:
u1 = 4. * (.5 - u1)
phi, ct = self.__sample_first_quad(u1, u2)
phi = PI - phi
elif u1 < .75:
u1 = 4. * (u1 - .5)
phi, ct = self.__sample_first_quad(u1, u2)
phi += PI
else:
u1 = 4. * (1. - u1)
phi, ct = self.__sample_first_quad(u1, u2)
phi = 2. * PI - phi
st = np.sqrt(max(0., 1. - ct * ct))
wh = geo.spherical_direction(st, ct, phi)
if wo.z * wh.z <= 0.:
wh *= -1.
# incident direction by reflection
wi = -wo + 2. * wo.dot(wh) * wh
# compute pdf for w_i
ct = abs_cos_theta(wh)
ds = 1. - ct * ct
if ds > 0. and wo.dot(wh) > 0.:
return [(np.sqrt((self.ex + 1.) * (self.ey + 1.)) * INV_2PI * np.power(ct,
(
self.ex * wh.x * wh.x + self.ey * wh.y * wh.y) / ds)) / \
(4. * wo.dot(wh)), wi]
else:
return [0., wi]