Switch MX conductor to spi way for MS

Turquin style multiple scattering is very simple, but also way noiser
than using a diffuse lobe for MS. This is because sampling microfacets
for reflection is far from ideal at high roughnesses. I don't have any
proof of one model being closer to reality than the other. They are
close, and at low roughness I like Turquin look better. But in my
production experience cleaner means faster renders and therefore better.

So I suggest adopting a non-reciprocal flavor of the diffuse lobe with
the original coloring based on the series summation. This is still very
simple, cleaner and also recovers saturation. The computation cost
itself is almost identical. Given that many times we'll be sampling a
diffuse lobe instead of microfacets it could even be faster.

I'm using the simplification of F_avg = F_ss, similar to Turquin to skip
fitting anything, let the render average it.

Signed-off-by: Alejandro Conty <[email protected]>

Author: aconty

src/libbsdl/include/BSDL/MTX/bsdf_conductor_decl.h

@@ -2,7 +2,6 @@
 // SPDX-License-Identifier: BSD-3-Clause
 // https://github.com/AcademySoftwareFoundation/OpenShadingLanguage
 
-
 #pragma once
 
 #include <BSDL/bsdf_decl.h>
@@ -69,6 +68,7 @@ template<typename BSDF_ROOT> struct ConductorLobe : public Lobe<BSDF_ROOT> {
     GGXDist dist;
     ConductorFresnel fresnel;
     float E_ms;
+    float E_ms_avg;
 };
 
 }  // namespace mtx

src/libbsdl/include/BSDL/MTX/bsdf_conductor_impl.h

@@ -2,7 +2,6 @@
 // SPDX-License-Identifier: BSD-3-Clause
 // https://github.com/AcademySoftwareFoundation/OpenShadingLanguage
 
-
 #pragma once
 
 #include <BSDL/MTX/bsdf_conductor_decl.h>
@@ -103,7 +102,8 @@ ConductorLobe<BSDF_ROOT>::ConductorLobe(T* lobe, const BsdfGlobals& globals,
     fresnel = ConductorFresnel(globals.wave(data.IOR),
                                globals.wave(data.extinction), globals.lambda_0);
     TabulatedEnergyCurve<spi::MiniMicrofacetGGX> curve(roughness, 0.0f);
-    E_ms = curve.Emiss_eval(cosNO);
+    E_ms     = curve.Emiss_eval(cosNO);
+    E_ms_avg = curve.get_Emiss_avg();
     Base::set_roughness(roughness);
 }
 
@@ -112,7 +112,8 @@ BSDL_INLINE_METHOD Sample
 ConductorLobe<BSDF_ROOT>::eval_impl(const Imath::V3f& wo,
                                     const Imath::V3f& wi) const
 {
-    Sample s    = eval_turquin_microms_reflection(dist, fresnel, E_ms, wo, wi);
+    Sample s    = eval_spi_microms_reflection(dist, fresnel, E_ms, E_ms_avg, wo,
+                                              wi);
     s.roughness = Base::roughness();
     return s;
 }
@@ -122,15 +123,10 @@ BSDL_INLINE_METHOD Sample
 ConductorLobe<BSDF_ROOT>::sample_impl(const Imath::V3f& wo,
                                       const Imath::V3f& rnd) const
 {
-    const float cosNO = wo.z;
-    if (cosNO <= 0)
-        return {};
-
-    // sample microfacet (half vector)
-    // generate outgoing direction
-    Imath::V3f wi = reflect(wo, dist.sample(wo, rnd.x, rnd.y));
-    // evaluate brdf on outgoing direction
-    return eval_impl(wo, wi);
+    Sample s = sample_spi_microms_reflection(dist, fresnel, E_ms, E_ms_avg, wo,
+                                             rnd);
+    s.roughness = Base::roughness();
+    return s;
 }
 
 }  // namespace mtx

src/libbsdl/include/BSDL/microfacet_tools_decl.h

@@ -2,7 +2,6 @@
 // SPDX-License-Identifier: BSD-3-Clause
 // https://github.com/AcademySoftwareFoundation/OpenShadingLanguage
 
-
 #pragma once
 
 #include <BSDL/config.h>
@@ -137,4 +136,17 @@ eval_turquin_microms_reflection(const Dist& dist, const Fresnel& fresnel,
                                 float E_ms, const Imath::V3f& wo,
                                 const Imath::V3f& wi);
 
+// SPI style microfacet with multiple scattering
+template<typename Dist, typename Fresnel>
+BSDL_INLINE Sample
+eval_spi_microms_reflection(const Dist& dist, const Fresnel& fresnel,
+                            float E_ms, float E_ms_avg, const Imath::V3f& wo,
+                            const Imath::V3f& wi);
+
+template<typename Dist, typename Fresnel>
+BSDL_INLINE Sample
+sample_spi_microms_reflection(const Dist& dist, const Fresnel& fresnel,
+                              float E_ms, float E_ms_avg, const Imath::V3f& wo,
+                              const Imath::V3f& rnd);
+
 BSDL_LEAVE_NAMESPACE

src/libbsdl/include/BSDL/microfacet_tools_impl.h

@@ -2,7 +2,6 @@
 // SPDX-License-Identifier: BSD-3-Clause
 // https://github.com/AcademySoftwareFoundation/OpenShadingLanguage
 
-
 #pragma once
 
 #include <BSDL/config.h>
@@ -329,4 +328,67 @@ eval_turquin_microms_reflection(const Dist& dist, const Fresnel& fresnel,
     return { wi, O, s_pdf, -1 /* roughness set by caller */ };
 }
 
+// SPI style microfacet with multiple scattering, with a diffuse lobe
+template<typename Dist, typename Fresnel>
+BSDL_INLINE Sample
+eval_spi_microms_reflection(const Dist& dist, const Fresnel& fresnel,
+                            float E_ms, float E_ms_avg, const Imath::V3f& wo,
+                            const Imath::V3f& wi)
+{
+    const float cosNO = wo.z;
+    const float cosNI = wi.z;
+    if (cosNI <= 0 || cosNO <= 0)
+        return {};
+
+    // get half vector
+    Imath::V3f m    = (wo + wi).normalized();
+    float cosMO     = m.dot(wo);
+    const float D   = dist.D(m);
+    const float G1  = dist.G1(wo);
+    const float out = dist.G2_G1(wi, wo);
+    float s_pdf     = (G1 * D) / (4.0f * cosNO);
+    // fresnel term between outgoing direction and microfacet
+    const Power F = fresnel.eval(cosMO);
+    const Power O = out * F;
+
+    const Power one = Power(1, 1);
+    // Like Turquin we are using F_avg = F instead of an average fresnel, the
+    // render integrator has an average effect for high roughness.
+    //const Power F0 = fresnel.F0();
+    const Power F_avg = F;
+    // Evaluate multiple scattering lobe, roughness set by caller. The
+    // 1 / (1 - F_avg * E_ms_avg) term comes from the series summation.
+    const Power O_ms = SQR(F_avg) * (1 - E_ms_avg) / (one - F_avg * E_ms_avg);
+
+    Sample ec = { wi, O_ms, E_ms * cosNI * ONEOVERPI, -1 };
+    ec.update(O, s_pdf, 1 - E_ms);
+
+    return ec;
+}
+
+template<typename Dist, typename Fresnel>
+BSDL_INLINE Sample
+sample_spi_microms_reflection(const Dist& dist, const Fresnel& fresnel,
+                              float E_ms, float E_ms_avg, const Imath::V3f& wo,
+                              const Imath::V3f& rnd)
+{
+    const float cosNO = wo.z;
+    if (cosNO <= 0)
+        return {};
+
+    Imath::V3f wi;
+    if (rnd.z < E_ms) {
+        // sample diffuse energy compensation lobe
+        wi = sample_cos_hemisphere(rnd.x, rnd.y);
+    } else {
+        // sample microfacet (half vector)
+        // generate outgoing direction
+        wi = reflect(wo, dist.sample(wo, rnd.x, rnd.y));
+        if (wi.z <= 0)
+            return {};
+    }
+    // evaluate brdf on outgoing direction
+    return eval_spi_microms_reflection(dist, fresnel, E_ms, E_ms_avg, wo, wi);
+}
+
 BSDL_LEAVE_NAMESPACE