def microfacetFourierSeries(mu_o, mu_i, etaC, alpha, n, relerr=10e-4):
A, B = getAB(mu_i, mu_o, etaC, alpha)
if sp.i0e(B) * np.exp(A+B) < 1e-10:
return [0.0]
B_max = Bmax(n, relerr)
if B > B_max:
A = A + B - B_max + math.log(sp.i0e(B) / sp.i0e(B_max))
B = B_max
expcos_coeffs = expcos_fseries(A, B, relerr)
if B == 0.0:
phiMax = f.safe_acos(-1.0)
else:
phiMax = f.safe_acos(1.0 + np.log(relerr) / B)
lowfreq_coeffs = microfacetNoExpFourierSeries(mu_o, mu_i, etaC, alpha, 12, phiMax)
result = fseries_convolve(lowfreq_coeffs, len(lowfreq_coeffs), expcos_coeffs, len(expcos_coeffs))
for i in range(len(result)):
if result[i] == 0 or np.abs(result[i]) < result[0] * relerr:
result = result[:i]
break
return result
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