Add multibounce compensation

src/materials/PhysicalPathTracingMaterial.js

@@ -810,7 +810,7 @@ export class PhysicalPathTracingMaterial extends MaterialBase {
  // then we can just always assume this is a front face.
  surfaceRec.frontFace = side == 1.0 || transmission == 0.0;
  surfaceRec.eta = material.thinFilm || surfaceRec.frontFace ? 1.0 / material.ior : material.ior;
- surfaceRec.f0 = iorRatioToF0( surfaceRec.eta );
+ surfaceRec.f0 = etaToF0( surfaceRec.eta );
  surfaceRec.thinFilm = material.thinFilm;
 
  // Compute the filtered roughness value to use during specular reflection computations.

src/shader/shaderGGXFunctions.js

@@ -96,5 +96,35 @@ float ggxPDF( vec3 wi, vec3 halfVector, float roughness ) {
 
  return D * G1 * max( 0.0, dot( wi, halfVector ) ) / wi.z;
 
+}
+
+// https://github.com/AcademySoftwareFoundation/MaterialX/blob/main/libraries/pbrlib/genglsl/lib/mx_microfacet_specular.glsl#L113
+// Rational quadratic fit to Monte Carlo data for GGX directional albedo.
+vec3 ggxDirAlbedoAnalytic( float NdotV, float alpha, vec3 F0, vec3 F90 ) {
+
+ float x = NdotV;
+ float y = alpha;
+ float x2 = x * x;
+ float y2 = y * y;
+ vec4 r =
+ vec4( 0.1003, 0.9345, 1.0, 1.0 ) +
+ vec4( - 0.6303, - 2.323, - 1.765, 0.2281 ) * x +
+ vec4( 9.748, 2.229, 8.263, 15.94 ) * y +
+ vec4( - 2.038, - 3.748, 11.53, - 55.83 ) * x * y +
+ vec4( 29.34, 1.424, 28.96, 13.08 ) * x2 +
+ vec4( - 8.245, - 0.7684, - 7.507, 41.26 ) * y2 +
+ vec4( - 26.44, 1.436, - 36.11, 54.9 ) * x2 * y +
+ vec4( 19.99, 0.2913, 15.86, 300.2 ) * x * y2 +
+ vec4( - 5.448, 0.6286, 33.37, -285.1 ) * x2 * y2;
+ vec2 AB = clamp( r.xy / r.zw, 0.0, 1.0 );
+ return F0 * AB.x + F90 * AB.y;
+
+}
+
+vec3 ggxEnergyCompensation( float NdotV, float alpha, vec3 Fss ) {
+
+ float Ess = ggxDirAlbedoAnalytic( NdotV, alpha, vec3( 1.0 ), vec3( 1.0 ) ).r;
+ return 1.0 + Fss * ( 1.0 - Ess ) / Ess;
+
 }
 `;

src/shader/shaderMaterialSampling.js

@@ -129,14 +129,15 @@ float specularEval( vec3 wo, vec3 wi, vec3 wh, SurfaceRec surf, out vec3 color )
  vec3 iridescenceF = evalIridescence( 1.0, surf.iridescenceIor, dot( wi, wh ), surf.iridescenceThickness, vec3( f0 ) );
  vec3 iridescenceMix = mix( vec3( FM ), iridescenceF, surf.iridescence );
  vec3 F = mix( specColor, vec3( 1.0 ), iridescenceMix );
+ vec3 comp = ggxEnergyCompensation( dot( wo, wh ), filteredRoughness, F );
 
- color = mix( surf.specularIntensity, 1.0, surf.metalness ) * wi.z * F * G * D / ( 4.0 * abs( wi.z * wo.z ) );
+ color = mix( surf.specularIntensity, 1.0, surf.metalness ) * comp * wi.z * F * G * D / ( 4.0 * abs( wi.z * wo.z ) );
 
  // PDF
  // See 14.1.1 Microfacet BxDFs in https://www.pbr-book.org/
  float incidentTheta = acos( wo.z );
  float G1 = ggxShadowMaskG1( incidentTheta, filteredRoughness );
- float ggxPdf = D * G1 * max( 0.0, abs( dot( wo, wh ) ) ) / abs ( wo.z );
+ float ggxPdf = D * G1 * max( 0.0, abs( dot( wo, wh ) ) ) / abs( wo.z );
  return ggxPdf / ( 4.0 * dot( wo, wh ) );
 
 }
@@ -242,11 +243,11 @@ vec3 transmissionDirection( vec3 wo, SurfaceRec surf ) {
 float clearcoatEval( vec3 wo, vec3 wi, vec3 wh, SurfaceRec surf, inout vec3 color ) {
 
  float ior = 1.5;
- float f0 = iorRatioToF0( ior );
  bool frontFace = surf.frontFace;
  float filteredClearcoatRoughness = surf.filteredClearcoatRoughness;
 
  float eta = frontFace ? 1.0 / ior : ior;
+ float f0 = etaToF0( eta );
  float G = ggxShadowMaskG2( wi, wo, filteredClearcoatRoughness );
  float D = ggxDistribution( wh, filteredClearcoatRoughness );
  float F = schlickFresnel( dot( wi, wh ), f0 );

src/shader/shaderUtils.js

@@ -11,13 +11,15 @@ export const shaderUtils = /* glsl */`
  // https://google.github.io/filament/Filament.md.html#materialsystem/diffusebrdf
  float schlickFresnel( float cosine, float f0 ) {
 
- return f0 + ( 1.0 - f0 ) * pow( 1.0 - cosine, 5.0 );
+ float f = pow( 1.0 - cosine, 5.0 );
+ return f + f0 * ( 1.0 - f );
 
  }
 
  vec3 schlickFresnel( float cosine, vec3 f0 ) {
 
- return f0 + ( 1.0 - f0 ) * pow( 1.0 - cosine, 5.0 );
+ float f = pow( 1.0 - cosine, 5.0 );
+ return f + f0 * ( 1.0 - f );
 
  }
 
@@ -45,10 +47,10 @@ export const shaderUtils = /* glsl */`
 
  }
 
- // https://raytracing.github.io/books/RayTracingInOneWeekend.html#dielectrics/schlickapproximation
- float iorRatioToF0( float eta ) {
+ // https://google.github.io/filament/Filament.html#materialsystem/specularbrdf/fresnel(specularf)
+ float etaToF0( float eta ) {
 
- return pow( ( 1.0 - eta ) / ( 1.0 + eta ), 2.0 );
+ return pow( eta - 1.0, 2.0 ) / pow( eta + 1.0, 2.0 );
 
  }