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Differential D3592 Diff 11529 intern/cycles/kernel/closure/bsdf_microfacet.h

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intern/cycles/kernel/closure/bsdf_microfacet.h

Show First 20 Lines • Show All 249 Lines • ▼ Show 20 Lines if(use_fresnel) {
float F0 = fresnel_dielectric_cos(1.0f, bsdf->ior); float F0 = fresnel_dielectric_cos(1.0f, bsdf->ior);
F = interpolate_fresnel_color(L, H, bsdf->ior, F0, bsdf->extra->cspec0); F = interpolate_fresnel_color(L, H, bsdf->ior, F0, bsdf->extra->cspec0);
} }
return F; return F;
} }
ccl_device_forceinline float D_GTR1(float NdotH, float alpha)
/* GGX microfacet distribution functions:
* Here, GTR refers to the Generalized Trowbridge-Reitz model from "Physically Based Shading at Disney".
* GTR with falloff parameter 2 corresponds to GGX, while GTR1 is used for the clearcoat component of the Principled BSDF.
*/
ccl_device_forceinline float D_GTR1(float NdotH, float alpha2)
{ {
if(alpha >= 1.0f) return M_1_PI_F; if(alpha2 >= 1.0f) return M_1_PI_F;
float alpha2 = alpha*alpha; float t = 1.0f + (alpha2 - 1.0f) * sqr(NdotH);
float t = 1.0f + (alpha2 - 1.0f) * NdotH*NdotH;
return (alpha2 - 1.0f) / (M_PI_F * logf(alpha2) * t); return (alpha2 - 1.0f) / (M_PI_F * logf(alpha2) * t);
} }
ccl_device_forceinline float D_GTR2(float NdotM, float alpha2)
{
return alpha2 / (M_PI_F * sqr(1.0f + (alpha2 - 1.0f)*sqr(NdotM)));
}
ccl_device_forceinline float D_GTR2_aniso(float MdotX, float MdotY, float MdotZ, float alpha_x, float alpha_y, float alpha2)
{
float slope_x = MdotX/(MdotZ*alpha_x);
float slope_y = MdotY/(MdotZ*alpha_y);
float slope_len = 1 + sqr(slope_x) + sqr(slope_y);
return 1.0f / (sqr(slope_len * sqr(MdotZ)) * M_PI_F * alpha2);
}
/* GGX geometric shadowing terms.
*
* Note on the implementation:
* In the final BSDF equation, NdotO and NdotI appear in the denominator.
* Since Cycles returns the product of BSDF and NdotI by convention, NdotI cancels out.
* In the formulation of G1 that is used here, the NdotD factor appears in the numerator,
* so we can avoid dividing by NdotO in the BSDF by letting it cancel out with NdotO in the G1o term.
*
* Therefore, G1o actually returns G1/NdotO while G1i returns G1.
*/
ccl_device_forceinline float GGX_G1o(float NdotO, float alpha2)
{
return 2.0f / (NdotO + safe_sqrtf(sqr(NdotO) * (1.0f - alpha2) + alpha2));
}
ccl_device_forceinline float GGX_G1i(float NdotI, float alpha2)
{
return 2.0f * NdotI / (NdotI + safe_sqrtf(sqr(NdotI) * (1.0f - alpha2) + alpha2));
}
ccl_device_forceinline float GGX_G1o_aniso(float XdotD, float YdotD, float NdotD, float alpha_x, float alpha_y)
{
float alphaI2 = sqr(XdotD*alpha_x) + sqr(YdotD*alpha_y);
return 2.0f / (NdotD + safe_sqrtf(sqr(NdotD) + alphaI2));
}
ccl_device_forceinline float GGX_G1i_aniso(float XdotD, float YdotD, float NdotD, float alpha_x, float alpha_y)
{
float alphaI2 = sqr(XdotD*alpha_x) + sqr(YdotD*alpha_y);
return 2.0f * NdotD / (NdotD + safe_sqrtf(sqr(NdotD) + alphaI2));
}
/* GGX microfacet with Smith shadow-masking from: /* GGX microfacet with Smith shadow-masking from:
* *
* Microfacet Models for Refraction through Rough Surfaces * Microfacet Models for Refraction through Rough Surfaces
* B. Walter, S. R. Marschner, H. Li, K. E. Torrance, EGSR 2007 * B. Walter, S. R. Marschner, H. Li, K. E. Torrance, EGSR 2007
* *
* Anisotropic from: * Anisotropic from:
* *
* Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs * Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs
▲ Show 20 Lines • Show All 117 Lines • ▼ Show 20 Linesccl_device void bsdf_microfacet_ggx_blur(ShaderClosure *sc, float roughness)
bsdf->alpha_y = fmaxf(roughness, bsdf->alpha_y); bsdf->alpha_y = fmaxf(roughness, bsdf->alpha_y);
} }
ccl_device float3 bsdf_microfacet_ggx_eval_reflect(const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf) ccl_device float3 bsdf_microfacet_ggx_eval_reflect(const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf)
{ {
const MicrofacetBsdf *bsdf = (const MicrofacetBsdf*)sc; const MicrofacetBsdf *bsdf = (const MicrofacetBsdf*)sc;
float alpha_x = bsdf->alpha_x; float alpha_x = bsdf->alpha_x;
float alpha_y = bsdf->alpha_y; float alpha_y = bsdf->alpha_y;
float alpha2 = alpha_x * alpha_y;
bool m_refractive = bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID; bool m_refractive = bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
float3 N = bsdf->N; float3 N = bsdf->N;
if(m_refractive || alpha_x*alpha_y <= 1e-7f) if(m_refractive || alpha_x*alpha_y <= 1e-7f) {
return make_float3(0.0f, 0.0f, 0.0f); return make_float3(0.0f, 0.0f, 0.0f);
}
float cosNO = dot(N, I); float cosNO = dot(N, I);
float cosNI = dot(N, omega_in); float cosNI = dot(N, omega_in);
if(cosNI > 0 && cosNO > 0) { if(cosNI <= 0 && cosNO <= 0) {
/* get half vector */ /* This might happen due to e.g. normal mapping - not supported here, so just give up and return black. */
return make_float3(0.0f, 0.0f, 0.0f);
}
/* Calculate the half vector as the average of the incoming and outgoing direction. */
float3 m = normalize(omega_in + I); float3 m = normalize(omega_in + I);
float alpha2 = alpha_x * alpha_y;
float D, G1o, G1i; float D, G1o, G1i;
/* Calculation of D and G1 can be simplified for the common isotropic case. */
if(alpha_x == alpha_y) { if(alpha_x == alpha_y) {
/* isotropic
* eq. 20: (F*G*D)/(4*in*on)
* eq. 33: first we calculate D(m) */
float cosThetaM = dot(N, m); float cosThetaM = dot(N, m);
float cosThetaM2 = cosThetaM * cosThetaM;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
float tanThetaM2 = (1 - cosThetaM2) / cosThetaM2;
if(bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID) { if(bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID) {
/* use GTR1 for clearcoat */ /* Use the GTR1 model for clearcoat reflection. */
D = D_GTR1(cosThetaM, bsdf->alpha_x); D = D_GTR1(cosThetaM, alpha2);
/* the alpha value for clearcoat is a fixed 0.25 => alpha2 = 0.25 * 0.25 */ /* The alpha value for clearcoat is a fixed 0.25. */
alpha2 = 0.0625f; alpha2 = 0.0625f;
} }
else { else {
/* use GTR2 otherwise */ /* Use GTR2 (aka GGX) otherwise. */
D = alpha2 / (M_PI_F * cosThetaM4 * (alpha2 + tanThetaM2) * (alpha2 + tanThetaM2)); D = D_GTR2(cosThetaM, alpha2);
} }
/* eq. 34: now calculate G1(i,m) and G1(o,m) */ /* Calculate the geometric terms (note the comment about the functions above). */
G1o = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNO * cosNO) / (cosNO * cosNO))); G1o = GGX_G1o(cosNO, alpha2);
G1i = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNI * cosNI) / (cosNI * cosNI))); G1i = GGX_G1i(cosNI, alpha2);
} }
else { else {
/* anisotropic */ /* Construct orthonormal system from the given tangent.
*
* TODO(lukas): Check whether making bsdf->T orthonormal to bsdf->N in the setup code and just getting
* the bitangent with a single cross() here is faster since it can be reused. */
float3 X, Y, Z = N; float3 X, Y, Z = N;
make_orthonormals_tangent(Z, bsdf->T, &X, &Y); make_orthonormals_tangent(Z, bsdf->T, &X, &Y);
/* distribution */ /* Evaluate distribution and geometric terms. */
float3 local_m = make_float3(dot(X, m), dot(Y, m), dot(Z, m)); D = D_GTR2_aniso(dot(X, m), dot(Y, m), dot(Z, m), alpha_x, alpha_y, alpha2);
float slope_x = -local_m.x/(local_m.z*alpha_x); G1o = GGX_G1o_aniso(dot(I, X), dot(I, Y), cosNO, alpha_x, alpha_y);
float slope_y = -local_m.y/(local_m.z*alpha_y); G1i = GGX_G1i_aniso(dot(omega_in, X), dot(omega_in, Y), cosNI, alpha_x, alpha_y);
float slope_len = 1 + slope_x*slope_x + slope_y*slope_y;
float cosThetaM = local_m.z;
float cosThetaM2 = cosThetaM * cosThetaM;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
D = 1 / ((slope_len * slope_len) * M_PI_F * alpha2 * cosThetaM4);
/* G1(i,m) and G1(o,m) */
float tanThetaO2 = (1 - cosNO * cosNO) / (cosNO * cosNO);
float cosPhiO = dot(I, X);
float sinPhiO = dot(I, Y);
float alphaO2 = (cosPhiO*cosPhiO)*(alpha_x*alpha_x) + (sinPhiO*sinPhiO)*(alpha_y*alpha_y);
alphaO2 /= cosPhiO*cosPhiO + sinPhiO*sinPhiO;
G1o = 2 / (1 + safe_sqrtf(1 + alphaO2 * tanThetaO2));
float tanThetaI2 = (1 - cosNI * cosNI) / (cosNI * cosNI);
float cosPhiI = dot(omega_in, X);
float sinPhiI = dot(omega_in, Y);
float alphaI2 = (cosPhiI*cosPhiI)*(alpha_x*alpha_x) + (sinPhiI*sinPhiI)*(alpha_y*alpha_y);
alphaI2 /= cosPhiI*cosPhiI + sinPhiI*sinPhiI;
G1i = 2 / (1 + safe_sqrtf(1 + alphaI2 * tanThetaI2));
} }
float G = G1o * G1i; /* The full BSDF is f = F*D*G1o*G1i / (4*cosNO*cosNI).
* In Cycles we return f*cosNI and 1/cosNO is included in G1o, so the result here is F*D*G1i*G1i / 4.
/* eq. 20 */ * F and G1i are not included in the importance sampling, so the PDF is D*G1o / 4.
float common = D * 0.25f / cosNO; *
* Note that since the PDF is normalized and F*G1i is never >1, this formulation doesn't conserve energy. */
float common = 0.25f * G1o * D;
float3 F = reflection_color(bsdf, omega_in, m); float3 F = reflection_color(bsdf, omega_in, m);
if(bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID) { if(bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID) {
F *= 0.25f * bsdf->extra->clearcoat; F *= 0.25f * bsdf->extra->clearcoat;
} }
float3 out = F * G * common; *pdf = common;
return G1i * common * F;
/* eq. 2 in distribution of visible normals sampling
* pm = Dw = G1o * dot(m, I) * D / dot(N, I); */
/* eq. 38 - but see also:
* eq. 17 in http://www.graphics.cornell.edu/~bjw/wardnotes.pdf
* pdf = pm * 0.25 / dot(m, I); */
*pdf = G1o * common;
return out;
}
return make_float3(0.0f, 0.0f, 0.0f);
} }
ccl_device float3 bsdf_microfacet_ggx_eval_transmit(const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf) ccl_device float3 bsdf_microfacet_ggx_eval_transmit(const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf)
{ {
const MicrofacetBsdf *bsdf = (const MicrofacetBsdf*)sc; const MicrofacetBsdf *bsdf = (const MicrofacetBsdf*)sc;
float alpha_x = bsdf->alpha_x; float alpha_x = bsdf->alpha_x;
float alpha_y = bsdf->alpha_y; float alpha_y = bsdf->alpha_y;
float m_eta = bsdf->ior; float m_eta = bsdf->ior;
bool m_refractive = bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID; bool m_refractive = bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
float3 N = bsdf->N; float3 N = bsdf->N;
if(!m_refractive || alpha_x*alpha_y <= 1e-7f) float alpha2 = alpha_x * alpha_y;
if(!m_refractive || alpha2 <= 1e-7f) {
return make_float3(0.0f, 0.0f, 0.0f); return make_float3(0.0f, 0.0f, 0.0f);
}
float cosNO = dot(N, I); float cosNO = dot(N, I);
float cosNI = dot(N, omega_in); float cosNI = dot(N, omega_in);
if(cosNO <= 0 || cosNI >= 0) if(cosNO <= 0 || cosNI >= 0) {
return make_float3(0.0f, 0.0f, 0.0f); /* vectors on same side -- not possible */ /* This might happen due to e.g. normal mapping - not supported here, so just give up and return black. */
return make_float3(0.0f, 0.0f, 0.0f);
}
/* compute half-vector of the refraction (eq. 16) */ /* Compute half-vector of the refraction (eq. 16). */
float3 ht = -(m_eta * omega_in + I); float3 ht = -(m_eta * omega_in + I);
float3 Ht = normalize(ht); float ht_inv_len = 1.0f / sqrtf(dot(ht, ht));
float3 Ht = ht * ht_inv_len;
float cosHO = dot(Ht, I); float cosHO = dot(Ht, I);
float cosHI = dot(Ht, omega_in); float cosHI = dot(Ht, omega_in);
float D, G1o, G1i; /* Evaluate distribution and geometric terms. */
float D = D_GTR2(dot(Ht, N), alpha2);
/* eq. 33: first we calculate D(m) with m=Ht: */ float G1o = GGX_G1o(cosNO, alpha2);
float alpha2 = alpha_x * alpha_y; float G1i = GGX_G1i(-cosNI, alpha2);
float cosThetaM = dot(N, Ht);
float cosThetaM2 = cosThetaM * cosThetaM; /* For the refraction case, the BSDF is abs(cosHI * cosHO) * eta^2 * G1o * G1i * D / (cosNO * cosNI * Ht2).
float tanThetaM2 = (1 - cosThetaM2) / cosThetaM2; * Again, G1i includes cosNO and cosNI cancels out in Cycles, so by grouping some terms we get:
float cosThetaM4 = cosThetaM2 * cosThetaM2; * abs(cosHI * cosHO) * G1o * G1i * (eta * (1 / Ht))^2
D = alpha2 / (M_PI_F * cosThetaM4 * (alpha2 + tanThetaM2) * (alpha2 + tanThetaM2)); *
* The PDF here is abs(cosHI * cosHO) * G1o * (eta * (1 / Ht))^2. */
/* eq. 34: now calculate G1(i,m) and G1(o,m) */ float common = G1o * D * fabsf(cosHI * cosHO) * sqr(m_eta * ht_inv_len);
G1o = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNO * cosNO) / (cosNO * cosNO))); float out = G1i * common;
G1i = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNI * cosNI) / (cosNI * cosNI))); *pdf = common;
float G = G1o * G1i;
/* probability */
float Ht2 = dot(ht, ht);
/* eq. 2 in distribution of visible normals sampling
* pm = Dw = G1o * dot(m, I) * D / dot(N, I); */
/* out = fabsf(cosHI * cosHO) * (m_eta * m_eta) * G * D / (cosNO * Ht2)
* pdf = pm * (m_eta * m_eta) * fabsf(cosHI) / Ht2 */
float common = D * (m_eta * m_eta) / (cosNO * Ht2);
float out = G * fabsf(cosHI * cosHO) * common;
*pdf = G1o * fabsf(cosHO * cosHI) * common;
return make_float3(out, out, out); return make_float3(out, out, out);
} }
ccl_device int bsdf_microfacet_ggx_sample(KernelGlobals *kg, const ShaderClosure *sc, float3 Ng, float3 I, float3 dIdx, float3 dIdy, float randu, float randv, float3 *eval, float3 *omega_in, float3 *domega_in_dx, float3 *domega_in_dy, float *pdf) ccl_device int bsdf_microfacet_ggx_sample(KernelGlobals *kg, const ShaderClosure *sc, float3 Ng, float3 I, float3 dIdx, float3 dIdy, float randu, float randv, float3 *eval, float3 *omega_in, float3 *domega_in_dx, float3 *domega_in_dy, float *pdf)
{ {
const MicrofacetBsdf *bsdf = (const MicrofacetBsdf*)sc; const MicrofacetBsdf *bsdf = (const MicrofacetBsdf*)sc;
float alpha_x = bsdf->alpha_x; float alpha_x = bsdf->alpha_x;
float alpha_y = bsdf->alpha_y; float alpha_y = bsdf->alpha_y;
bool m_refractive = bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID; bool m_refractive = bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID;
float3 N = bsdf->N; float3 N = bsdf->N;
int label; int label;
float alpha2 = alpha_x * alpha_y;
float cosNO = dot(N, I); float cosNO = dot(N, I);
if(cosNO > 0) { if(cosNO > 0) {
float3 X, Y, Z = N; float3 X, Y, Z = N;
if(alpha_x == alpha_y) if(alpha_x == alpha_y)
make_orthonormals(Z, &X, &Y); make_orthonormals(Z, &X, &Y);
else else
make_orthonormals_tangent(Z, bsdf->T, &X, &Y); make_orthonormals_tangent(Z, bsdf->T, &X, &Y);
/* importance sampling with distribution of visible normals. vectors are /* Sample half-vector from the distribution of visible normals.
* transformed to local space before and after */ *
* Sampling happens in local coordinates, so transform I before calling
* and then transform the result back. */
float3 local_I = make_float3(dot(X, I), dot(Y, I), cosNO); float3 local_I = make_float3(dot(X, I), dot(Y, I), cosNO);
float3 local_m;
float G1o;
local_m = microfacet_sample_stretched(kg, local_I, alpha_x, alpha_y, float G1o;
float3 local_m = microfacet_sample_stretched(kg, local_I, alpha_x, alpha_y,
randu, randv, false, &G1o); randu, randv, false, &G1o);
float3 m = X*local_m.x + Y*local_m.y + Z*local_m.z; float3 m = X*local_m.x + Y*local_m.y + Z*local_m.z;
float cosThetaM = local_m.z; float cosThetaM = local_m.z;
/* reflection or refraction? */ /* Reflection or refraction? */
if(!m_refractive) { if(!m_refractive) {
float cosMO = dot(m, I); float cosMO = dot(m, I);
label = LABEL_REFLECT | LABEL_GLOSSY; label = LABEL_REFLECT | LABEL_GLOSSY;
if(cosMO > 0) { if(cosMO > 0) {
/* eq. 39 - compute actual reflected direction */ /* Compute reflected direction. */
*omega_in = 2 * cosMO * m - I; *omega_in = 2 * cosMO * m - I;
if(dot(Ng, *omega_in) > 0) { if(dot(Ng, *omega_in) > 0) {
if(alpha_x*alpha_y <= 1e-7f) { if(alpha_x*alpha_y <= 1e-7f) {
/* some high number for MIS */ /* some high number for MIS */
*pdf = 1e6f; *pdf = 1e6f;
*eval = make_float3(1e6f, 1e6f, 1e6f); *eval = make_float3(1e6f, 1e6f, 1e6f);
bool use_fresnel = (bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_FRESNEL_ID bool use_fresnel = (bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_FRESNEL_ID
|| bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID || bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID
|| bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_ANISO_FRESNEL_ID); || bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_ANISO_FRESNEL_ID);
/* if fresnel is used, calculate the color with reflection_color(...) */ /* if fresnel is used, calculate the color with reflection_color(...) */
if(use_fresnel) { if(use_fresnel) {
*eval *= reflection_color(bsdf, *omega_in, m); *eval *= reflection_color(bsdf, *omega_in, m);
} }
label = LABEL_REFLECT | LABEL_SINGULAR; label = LABEL_REFLECT | LABEL_SINGULAR;
} }
else { else {
/* microfacet normal is visible to this ray */
/* eq. 33 */
float alpha2 = alpha_x * alpha_y;
float D, G1i; float D, G1i;
if(alpha_x == alpha_y) { if(alpha_x == alpha_y) {
/* isotropic */
float cosThetaM2 = cosThetaM * cosThetaM;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
float tanThetaM2 = 1/(cosThetaM2) - 1;
/* eval BRDF*cosNI */
float cosNI = dot(N, *omega_in);
if(bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID) { if(bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID) {
/* use GTR1 for clearcoat */ /* Use the GTR1 model for clearcoat reflection. */
D = D_GTR1(cosThetaM, bsdf->alpha_x); D = D_GTR1(cosThetaM, alpha2);
/* the alpha value for clearcoat is a fixed 0.25 => alpha2 = 0.25 * 0.25 */ /* The alpha value for clearcoat is a fixed 0.25. */
alpha2 = 0.0625f; alpha2 = 0.0625f;
/* recalculate G1o */ /* Recalculate G1o since the previous value is based on a different alpha. */
G1o = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNO * cosNO) / (cosNO * cosNO))); G1o = GGX_G1o(cosNO, alpha2);
} }
else { else {
/* use GTR2 otherwise */ /* Use GTR2 (aka GGX) otherwise. */
D = alpha2 / (M_PI_F * cosThetaM4 * (alpha2 + tanThetaM2) * (alpha2 + tanThetaM2)); D = D_GTR2(cosThetaM, alpha2);
} }
/* eq. 34: now calculate G1(i,m) */ /* G1o is already known, so we only need to evaluate G1i here. */
G1i = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNI * cosNI) / (cosNI * cosNI))); G1i = GGX_G1i(dot(Z, *omega_in), alpha2);
} }
else { else {
/* anisotropic distribution */ /* Use the anisotropic distribution. */
float3 local_m = make_float3(dot(X, m), dot(Y, m), dot(Z, m)); D = D_GTR2_aniso(dot(X, m), dot(Y, m), dot(Z, m), alpha_x, alpha_y, alpha2);
float slope_x = -local_m.x/(local_m.z*alpha_x); G1i = GGX_G1i_aniso(dot(X, *omega_in), dot(Y, *omega_in), dot(Z, *omega_in), alpha_x, alpha_y);
float slope_y = -local_m.y/(local_m.z*alpha_y);
float slope_len = 1 + slope_x*slope_x + slope_y*slope_y;
float cosThetaM = local_m.z;
float cosThetaM2 = cosThetaM * cosThetaM;
float cosThetaM4 = cosThetaM2 * cosThetaM2;
D = 1 / ((slope_len * slope_len) * M_PI_F * alpha2 * cosThetaM4);
/* calculate G1(i,m) */
float cosNI = dot(N, *omega_in);
float tanThetaI2 = (1 - cosNI * cosNI) / (cosNI * cosNI);
float cosPhiI = dot(*omega_in, X);
float sinPhiI = dot(*omega_in, Y);
float alphaI2 = (cosPhiI*cosPhiI)*(alpha_x*alpha_x) + (sinPhiI*sinPhiI)*(alpha_y*alpha_y);
alphaI2 /= cosPhiI*cosPhiI + sinPhiI*sinPhiI;
G1i = 2 / (1 + safe_sqrtf(1 + alphaI2 * tanThetaI2));
} }
/* see eval function for derivation */ /* The BSDF calculation here follows the evaluation code, with the exception that here G1o doesn't
float common = (G1o * D) * 0.25f / cosNO; * contain the 1/cosNO factor already. */
float common = 0.25f * D * G1o / cosNO;
*pdf = common; *pdf = common;
float3 F = reflection_color(bsdf, *omega_in, m); float3 F = reflection_color(bsdf, *omega_in, m);
*eval = G1i * common * F; *eval = G1i * common * F;
} }
if(bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID) { if(bsdf->type == CLOSURE_BSDF_MICROFACET_GGX_CLEARCOAT_ID) {
*eval *= 0.25f * bsdf->extra->clearcoat; *eval *= 0.25f * bsdf->extra->clearcoat;
} }
#ifdef __RAY_DIFFERENTIALS__ #ifdef __RAY_DIFFERENTIALS__
*domega_in_dx = (2 * dot(m, dIdx)) * m - dIdx; *domega_in_dx = (2 * dot(m, dIdx)) * m - dIdx;
*domega_in_dy = (2 * dot(m, dIdy)) * m - dIdy; *domega_in_dy = (2 * dot(m, dIdy)) * m - dIdy;
#endif #endif
} }
} }
} }
else { else {
label = LABEL_TRANSMIT | LABEL_GLOSSY; label = LABEL_TRANSMIT | LABEL_GLOSSY;
/* CAUTION: the i and o variables are inverted relative to the paper /* Compute the refracted direction and make sure that no TIR occurs. */
* eq. 39 - compute actual refractive direction */ float3 T;
float3 R, T;
#ifdef __RAY_DIFFERENTIALS__ #ifdef __RAY_DIFFERENTIALS__
float3 dRdx, dRdy, dTdx, dTdy; float3 dTdx, dTdy;
#endif #endif
float m_eta = bsdf->ior, fresnel; float m_eta = bsdf->ior;
bool inside; if(refract_dielectric(m_eta, m, I,
fresnel = fresnel_dielectric(m_eta, m, I, &R, &T,
#ifdef __RAY_DIFFERENTIALS__ #ifdef __RAY_DIFFERENTIALS__
dIdx, dIdy, &dRdx, &dRdy, &dTdx, &dTdy, dIdx, dIdy, &dTdx, &dTdy,
#endif #endif
&inside); &T))
{
if(!inside && fresnel != 1.0f) {
*omega_in = T; *omega_in = T;
#ifdef __RAY_DIFFERENTIALS__ #ifdef __RAY_DIFFERENTIALS__
*domega_in_dx = dTdx; *domega_in_dx = dTdx;
*domega_in_dy = dTdy; *domega_in_dy = dTdy;
#endif #endif
if(alpha_x*alpha_y <= 1e-7f || fabsf(m_eta - 1.0f) < 1e-4f) { if(alpha2 <= 1e-7f || fabsf(m_eta - 1.0f) < 1e-4f) {
/* some high number for MIS */ /* some high number for MIS */
*pdf = 1e6f; *pdf = 1e6f;
*eval = make_float3(1e6f, 1e6f, 1e6f); *eval = make_float3(1e6f, 1e6f, 1e6f);
label = LABEL_TRANSMIT | LABEL_SINGULAR; label = LABEL_TRANSMIT | LABEL_SINGULAR;
} }
else { else {
/* eq. 33 */ /* Evaluate distribution and geometric term - G1o is already known from the half-vector sampling. */
float alpha2 = alpha_x * alpha_y; float D = D_GTR2(cosThetaM, alpha2);
float cosThetaM2 = cosThetaM * cosThetaM; float G1i = GGX_G1i(-dot(N, *omega_in), alpha2);
float cosThetaM4 = cosThetaM2 * cosThetaM2;
float tanThetaM2 = 1/(cosThetaM2) - 1;
float D = alpha2 / (M_PI_F * cosThetaM4 * (alpha2 + tanThetaM2) * (alpha2 + tanThetaM2));
/* eval BRDF*cosNI */
float cosNI = dot(N, *omega_in);
/* eq. 34: now calculate G1(i,m) */
float G1i = 2 / (1 + safe_sqrtf(1 + alpha2 * (1 - cosNI * cosNI) / (cosNI * cosNI)));
/* eq. 21 */ /* eq. 21 */
float cosHI = dot(m, *omega_in); float cosHI = dot(m, *omega_in);
float cosHO = dot(m, I); float cosHO = dot(m, I);
float Ht2 = m_eta * cosHI + cosHO; float Ht2 = m_eta * cosHI + cosHO;
Ht2 *= Ht2;
/* see eval function for derivation */ /* The BSDF calculation here follows the evaluation code, with the exception that here G1o doesn't
float common = (G1o * D) * (m_eta * m_eta) / (cosNO * Ht2); * contain the 1/cosNO factor already. */
float out = G1i * fabsf(cosHI * cosHO) * common; float common = D * G1o * fabsf(cosHI * cosHO) * sqr(m_eta) / (cosNO * sqr(Ht2));
*pdf = cosHO * fabsf(cosHI) * common; float out = G1i * common;
*pdf = common;
*eval = make_float3(out, out, out); *eval = make_float3(out, out, out);
} }
} }
} }
} }
else { else {
label = (m_refractive) ? LABEL_TRANSMIT|LABEL_GLOSSY : LABEL_REFLECT|LABEL_GLOSSY; label = (m_refractive) ? LABEL_TRANSMIT|LABEL_GLOSSY : LABEL_REFLECT|LABEL_GLOSSY;
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} }
} }
} }
else { else {
label = LABEL_TRANSMIT | LABEL_GLOSSY; label = LABEL_TRANSMIT | LABEL_GLOSSY;
/* CAUTION: the i and o variables are inverted relative to the paper /* CAUTION: the i and o variables are inverted relative to the paper
* eq. 39 - compute actual refractive direction */ * eq. 39 - compute actual refractive direction */
float3 R, T; float3 T;
#ifdef __RAY_DIFFERENTIALS__ #ifdef __RAY_DIFFERENTIALS__
float3 dRdx, dRdy, dTdx, dTdy; float3 dTdx, dTdy;
#endif #endif
float m_eta = bsdf->ior, fresnel; float m_eta = bsdf->ior;
bool inside;
fresnel = fresnel_dielectric(m_eta, m, I, &R, &T, if(refract_dielectric(m_eta, m, I,
#ifdef __RAY_DIFFERENTIALS__ #ifdef __RAY_DIFFERENTIALS__
dIdx, dIdy, &dRdx, &dRdy, &dTdx, &dTdy, dIdx, dIdy, &dTdx, &dTdy,
#endif #endif
&inside); &T))
{
if(!inside && fresnel != 1.0f) {
*omega_in = T; *omega_in = T;
#ifdef __RAY_DIFFERENTIALS__ #ifdef __RAY_DIFFERENTIALS__
*domega_in_dx = dTdx; *domega_in_dx = dTdx;
*domega_in_dy = dTdy; *domega_in_dy = dTdy;
#endif #endif
if(alpha_x*alpha_y <= 1e-7f || fabsf(m_eta - 1.0f) < 1e-4f) { if(alpha_x*alpha_y <= 1e-7f || fabsf(m_eta - 1.0f) < 1e-4f) {
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