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
y2 = np.zeros(n)
mu_i = -0.6
mu_o = 0.5
alpha = 0.05
eta = 1.5
for i in range(n):
curPhi = phi[i]
etaC = complex(eta, 0)
y[i] = microfacetNoExp(mu_o, mu_i, etaC, alpha, curPhi)
def f(a):
return microfacetNoExp(mu_o, mu_i, etaC, alpha, a)
# compute the fourier approx
b = filonIntegrate(f, nCoeff, nEvals, a, b)
for i in range(n):
curPhi = phi[i]
for l in range(nCoeff):
y2[i] += b[l] * np.cos(float(l) * curPhi)
plt.figure()
plt.plot(phi, y, 'b')
plt.plot(phi, y2, 'r--')
err = np.sum(np.abs(y - y2)) / n
plt.title("Error " + str(err) + " with " + str(nCoeff) + " coefficients")
#plt.show()
plt.savefig("Microfacetgraph.pdf")