def microfacetNoExp(mu_o, mu_i, eta_, alpha, phi_d):
sinThetaI = f.safe_sqrt(1.0 - mu_i * mu_i)
sinThetaO = f.safe_sqrt(1.0 - mu_o * mu_o)
cosPhi = math.cos(phi_d)
sinPhi = math.sin(phi_d)
wi = np.array([-sinThetaI, 0.0, -mu_i])
wo = np.array([sinThetaO * cosPhi, sinThetaO * sinPhi, mu_o])
reflect = (-mu_i * mu_o) > 0
if (mu_o == 0.0) or (mu_i == 0.0):
return 0.0
conductor = eta_.imag != 0.0
if conductor and not reflect:
return 0.0
eta = eta_
if not (-mu_i > 0 or conductor):
eta = (complex(1.0, 0.0) / eta_)
scalingFactor = 1.0
if not reflect:
scalingFactor = eta.real
H = wi + wo * scalingFactor
H /= np.linalg.norm(H)
H *= np.sign(H[2]) # math::signum(Frame::cosTheta(H));
cosThetaH2 = H[2] * H[2]
D = 1.0 / (math.pi * alpha * alpha * cosThetaH2 * cosThetaH2)
# Calculate the fresnel term
F = 0.0
if not conductor:
F, _ = fresnelDielectric(np.dot(wi, H), 0, eta_.real)
else:
F = fresnelConductor(np.abs(np.dot(wi, H)), eta)
G = smithG1(wi, H, alpha) * smithG1(wo, H, alpha)
if reflect:
return F * D * G / (4.0 * np.abs(mu_i * mu_o))
else:
sqrtDenom = np.dot(wi, H) + eta.real * np.dot(wo, H)
return np.abs(((1 - F) * D * G * eta.real * eta.real * np.dot(wi, H) * np.dot(wo, H)) / (
mu_i * mu_o * sqrtDenom * sqrtDenom))
def getAB(mu_i, mu_o, eta, alpha):
reflect = (-mu_i * mu_o) > 0
sinMu2 = f.safe_sqrt((1.0 - mu_i * mu_i) * (1.0 - mu_o * mu_o))
if reflect:
temp = 1.0 / (alpha * (mu_i - mu_o))
A = (mu_i * mu_i + mu_o * mu_o - 2) * temp * temp
B = 2.0 * sinMu2 * temp * temp
else:
temp = 1.0 / (alpha * (mu_i - eta.real * mu_o))
A = (mu_i * mu_i - 1.0 + eta.real * eta.real * (mu_o * mu_o - 1.0)) * temp * temp
B = 2 * eta.real * sinMu2 * temp * temp
return A, B
def fresnelConductor(cosThetaI, eta_):
eta = eta_.real
k = eta_.imag
cosThetaI2 = cosThetaI * cosThetaI
sinThetaI2 = 1.0 - cosThetaI2
sinThetaI4 = sinThetaI2 * sinThetaI2
temp1 = eta * eta - k * k - sinThetaI2
a2pb2 = f.safe_sqrt(temp1 * temp1 + 4 * k * k * eta * eta)
a = f.safe_sqrt(0.5 * (a2pb2 + temp1))
term1 = a2pb2 + cosThetaI2
term2 = 2 * a * cosThetaI
Rs2 = (term1 - term2) / (term1 + term2)
term3 = a2pb2 * cosThetaI2 + sinThetaI4
term4 = term2 * sinThetaI2
Rp2 = Rs2 * (term3 - term4) / (term3 + term4)
return 0.5 * (Rp2 + Rs2)
def microfacetNoExpFourierSeries(mu_o, mu_i, etaC, alpha, n, phiMax):
# const
nEvals = 200
eps = 10e-4
def foo(a):
return microfacetNoExp(mu_o, mu_i, etaC, alpha, a)
reflect = - mu_o * mu_i > 0.0
sinMu2 = f.safe_sqrt((1.0 - mu_i * mu_i) * (1.0 - mu_o * mu_o))
phiCritical = 0.0
conductor = etaC.imag != 0.0
if -mu_i > 0.0 or conductor:
eta = etaC
else:
eta = complex(1.0, 0.0) / etaC
if reflect:
if not conductor:
if sinMu2 == 0:
temp = -1.0
else:
temp = (2.0 * eta.real * eta.real - mu_i * mu_o - 1.0) / sinMu2
phiCritical = f.safe_acos(temp)
elif not reflect:
if eta.real > 1.0:
etaDenser = eta.real
else:
etaDenser = 1.0 / eta.real
if sinMu2 == 0:
temp = -1.0
else:
temp = (1.0 - etaDenser * mu_i * mu_o) / (etaDenser * sinMu2)
phiCritical = f.safe_acos(temp)
if reflect:
if phiCritical > eps and phiCritical < phiMax - eps:
b1 = filonIntegrate(foo, n, nEvals, 0.0, phiCritical)
b2 = filonIntegrate(foo, n, nEvals, phiCritical, phiMax)
b = np.concatenate((b1, b2), axis=0)
else:
b = filonIntegrate(foo, n, nEvals, 0.0, phiMax)
else:
b = filonIntegrate(foo, n, nEvals, 0.0, min(phiCritical, phiMax))
# ToDo: if (phiMax < math::Pi - math::Epsilon) SVD stuff
return b