ustring sample(const Vec3 &Ng,
const Vec3 &omega_out, const Vec3 &domega_out_dx, const Vec3 &domega_out_dy,
float randu, float randv,
Vec3 &omega_in, Vec3 &domega_in_dx, Vec3 &domega_in_dy,
float &pdf, Color3 &eval) const
{
// we are viewing the surface from the right side - send a ray out with cosine
// distribution over the hemisphere
sample_cos_hemisphere(m_N, omega_out, randu, randv, omega_in, pdf);
if (Ng.dot(omega_in) > 0) {
// TODO: account for sheen when sampling
float cosNO = m_N.dot(omega_out);
float sinNO2 = 1 - cosNO * cosNO;
float westin = sinNO2 > 0 ? powf(sinNO2, 0.5f * m_edginess) * pdf : 0;
eval.setValue(westin, westin, westin);
// TODO: find a better approximation for the diffuse bounce
domega_in_dx = (2 * m_N.dot(domega_out_dx)) * m_N - domega_out_dx;
domega_in_dy = (2 * m_N.dot(domega_out_dy)) * m_N - domega_out_dy;
domega_in_dx *= 125;
domega_in_dy *= 125;
}
else {
pdf = 0;
}
return Labels::REFLECT;
}
ustring sample (const Vec3 &Ng,
const Vec3 &omega_out, const Vec3 &domega_out_dx, const Vec3 &domega_out_dy,
float randu, float randv,
Vec3 &omega_in, Vec3 &domega_in_dx, Vec3 &domega_in_dy,
float &pdf, Color3 &eval) const
{
Vec3 R, dRdx, dRdy;
Vec3 T, dTdx, dTdy;
bool inside;
fresnel_dielectric(m_eta, m_N,
omega_out, domega_out_dx, domega_out_dy,
R, dRdx, dRdy,
T, dTdx, dTdy,
inside);
if (!inside) {
pdf = 1;
eval.setValue(1.0f, 1.0f, 1.0f);
omega_in = T;
domega_in_dx = dTdx;
domega_in_dy = dTdy;
}
return Labels::TRANSMIT;
}
ustring sample (const Vec3 &Ng,
const Vec3 &omega_out, const Vec3 &domega_out_dx, const Vec3 &domega_out_dy,
float randu, float randv,
Vec3 &omega_in, Vec3 &domega_in_dx, Vec3 &domega_in_dy,
float &pdf, Color3 &eval) const
{
// we are viewing the surface from the right side - send a ray out with cosine
// distribution over the hemisphere
sample_cos_hemisphere (m_N, omega_out, randu, randv, omega_in, pdf);
if (Ng.dot(omega_in) > 0) {
eval.setValue(pdf, pdf, pdf);
// TODO: find a better approximation for the diffuse bounce
domega_in_dx = (2 * m_N.dot(domega_out_dx)) * m_N - domega_out_dx;
domega_in_dy = (2 * m_N.dot(domega_out_dy)) * m_N - domega_out_dy;
domega_in_dx *= 125;
domega_in_dy *= 125;
} else
pdf = 0;
return Labels::REFLECT;
}
ustring sample(const Vec3 &Ng,
const Vec3 &omega_out, const Vec3 &domega_out_dx, const Vec3 &domega_out_dy,
float randu, float randv,
Vec3 &omega_in, Vec3 &domega_in_dx, Vec3 &domega_in_dy,
float &pdf, Color3 &eval) const
{
float cosNO = m_N.dot(omega_out);
if (cosNO > 0) {
domega_in_dx = domega_out_dx;
domega_in_dy = domega_out_dy;
Vec3 T, B;
make_orthonormals(omega_out, T, B);
float phi = 2 * (float) M_PI * randu;
float cosTheta = powf(randv, 1 / (m_invroughness + 1));
float sinTheta2 = 1 - cosTheta * cosTheta;
float sinTheta = sinTheta2 > 0 ? sqrtf(sinTheta2) : 0;
omega_in = (cosf(phi) * sinTheta) * T +
(sinf(phi) * sinTheta) * B +
(cosTheta) * omega_out;
if (Ng.dot(omega_in) > 0)
{
// common terms for pdf and eval
float cosNI = m_N.dot(omega_in);
// make sure the direction we chose is still in the right hemisphere
if (cosNI > 0)
{
pdf = 0.5f * (float) M_1_PI * powf(cosTheta, m_invroughness);
pdf = (m_invroughness + 1) * pdf;
eval.setValue(pdf, pdf, pdf);
// Since there is some blur to this reflection, make the
// derivatives a bit bigger. In theory this varies with the
// exponent but the exact relationship is complex and
// requires more ops than are practical.
domega_in_dx *= 10;
domega_in_dy *= 10;
}
}
}
return Labels::REFLECT;
}
ustring sample(const Vec3 &Ng,
const Vec3 &omega_out, const Vec3 &domega_out_dx, const Vec3 &domega_out_dy,
float randu, float randv,
Vec3 &omega_in, Vec3 &domega_in_dx, Vec3 &domega_in_dy,
float &pdf, Color3 &eval) const
{
float cosNO = m_N.dot(omega_out);
if (cosNO > 0) {
Vec3 X, Y, Z = m_N;
make_orthonormals(Z, X, Y);
// generate a random microfacet normal m
// eq. 35,36:
// we take advantage of cos(atan(x)) == 1/sqrt(1+x^2)
// and sin(atan(x)) == x/sqrt(1+x^2)
float alpha2 = m_ab * m_ab;
float tanThetaM = sqrtf(-alpha2 * logf(1 - randu));
float cosThetaM = 1 / sqrtf(1 + tanThetaM * tanThetaM);
float sinThetaM = cosThetaM * tanThetaM;
float phiM = 2 * float(M_PI) * randv;
Vec3 m = (cosf(phiM) * sinThetaM) * X +
(sinf(phiM) * sinThetaM) * Y +
cosThetaM * Z;
if (Refractive == 0) {
float cosMO = m.dot(omega_out);
if (cosMO > 0) {
// eq. 39 - compute actual reflected direction
omega_in = 2 * cosMO * m - omega_out;
if (Ng.dot(omega_in) > 0) {
// microfacet normal is visible to this ray
// eq. 25
float cosThetaM2 = cosThetaM * cosThetaM;
float tanThetaM2 = tanThetaM * tanThetaM;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
float D = expf(-tanThetaM2 / alpha2) / (float(M_PI) * alpha2 * cosThetaM4);
// eq. 24
float pm = D * cosThetaM;
// convert into pdf of the sampled direction
// eq. 38 - but see also:
// eq. 17 in http://www.graphics.cornell.edu/~bjw/wardnotes.pdf
pdf = pm * 0.25f / cosMO;
// Eval BRDF*cosNI
float cosNI = m_N.dot(omega_in);
// eq. 26, 27: now calculate G1(i,m) and G1(o,m)
float ao = 1 / (m_ab * sqrtf((1 - cosNO * cosNO) / (cosNO * cosNO)));
float ai = 1 / (m_ab * sqrtf((1 - cosNI * cosNI) / (cosNI * cosNI)));
float G1o = ao < 1.6f ? (3.535f * ao + 2.181f * ao * ao) / (1 + 2.276f * ao + 2.577f * ao * ao) : 1.0f;
float G1i = ai < 1.6f ? (3.535f * ai + 2.181f * ai * ai) / (1 + 2.276f * ai + 2.577f * ai * ai) : 1.0f;
float G = G1o * G1i;
// eq. 20: (F*G*D)/(4*in*on)
float out = (G * D) * 0.25f / cosNO;
eval.setValue(out, out, out);
domega_in_dx = (2 * m.dot(domega_out_dx)) * m - domega_out_dx;
domega_in_dy = (2 * m.dot(domega_out_dy)) * m - domega_out_dy;
/* disabled for now - gives texture filtering problems */
#if 0
// Since there is some blur to this reflection, make the
// derivatives a bit bigger. In theory this varies with the
// roughness but the exact relationship is complex and
// requires more ops than are practical.
domega_in_dx *= 10;
domega_in_dy *= 10;
#endif
}
}
}
else {
// CAUTION: the i and o variables are inverted relative to the paper
// eq. 39 - compute actual refractive direction
Vec3 R, dRdx, dRdy;
Vec3 T, dTdx, dTdy;
bool inside;
fresnel_dielectric(m_eta, m, omega_out, domega_out_dx, domega_out_dy,
R, dRdx, dRdy,
T, dTdx, dTdy,
inside);
if (!inside) {
omega_in = T;
domega_in_dx = dTdx;
domega_in_dy = dTdy;
// eq. 33
float cosThetaM2 = cosThetaM * cosThetaM;
float tanThetaM2 = tanThetaM * tanThetaM;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
float D = expf(-tanThetaM2 / alpha2) / (float(M_PI) * alpha2 * cosThetaM4);
// eq. 24
float pm = D * cosThetaM;
// eval BRDF*cosNI
float cosNI = m_N.dot(omega_in);
// eq. 26, 27: now calculate G1(i,m) and G1(o,m)
float ao = 1 / (m_ab * sqrtf((1 - cosNO * cosNO) / (cosNO * cosNO)));
float ai = 1 / (m_ab * sqrtf((1 - cosNI * cosNI) / (cosNI * cosNI)));
float G1o = ao < 1.6f ? (3.535f * ao + 2.181f * ao * ao) / (1 + 2.276f * ao + 2.577f * ao * ao) : 1.0f;
float G1i = ai < 1.6f ? (3.535f * ai + 2.181f * ai * ai) / (1 + 2.276f * ai + 2.577f * ai * ai) : 1.0f;
float G = G1o * G1i;
// eq. 21
float cosHI = m.dot(omega_in);
float cosHO = m.dot(omega_out);
float Ht2 = m_eta * cosHI + cosHO;
Ht2 *= Ht2;
float out = (fabsf(cosHI * cosHO) * (m_eta * m_eta) * (G * D)) / (cosNO * Ht2);
// eq. 38 and eq. 17
pdf = pm * (m_eta * m_eta) * fabsf(cosHI) / Ht2;
eval.setValue(out, out, out);
/* disabled for now - gives texture filtering problems */
#if 0
// Since there is some blur to this refraction, make the
// derivatives a bit bigger. In theory this varies with the
// roughness but the exact relationship is complex and
// requires more ops than are practical.
domega_in_dx *= 10;
domega_in_dy *= 10;
#endif
}
}
}
return Refractive ? Labels::TRANSMIT : Labels::REFLECT;
}
