three
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JavaScript 3D library
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JavaScript
export default /* glsl */`
struct PhysicalMaterial {
vec3 diffuseColor;
float roughness;
vec3 specularColor;
float specularF90;
float dispersion;
float clearcoat;
float clearcoatRoughness;
vec3 clearcoatF0;
float clearcoatF90;
float iridescence;
float iridescenceIOR;
float iridescenceThickness;
vec3 iridescenceFresnel;
vec3 iridescenceF0;
vec3 sheenColor;
float sheenRoughness;
float ior;
float transmission;
float transmissionAlpha;
float thickness;
float attenuationDistance;
vec3 attenuationColor;
float anisotropy;
float alphaT;
vec3 anisotropyT;
vec3 anisotropyB;
};
// temporary
vec3 clearcoatSpecularDirect = vec3( 0.0 );
vec3 clearcoatSpecularIndirect = vec3( 0.0 );
vec3 sheenSpecularDirect = vec3( 0.0 );
vec3 sheenSpecularIndirect = vec3(0.0 );
vec3 Schlick_to_F0( const in vec3 f, const in float f90, const in float dotVH ) {
float x = clamp( 1.0 - dotVH, 0.0, 1.0 );
float x2 = x * x;
float x5 = clamp( x * x2 * x2, 0.0, 0.9999 );
return ( f - vec3( f90 ) * x5 ) / ( 1.0 - x5 );
}
// Moving Frostbite to Physically Based Rendering 3.0 - page 12, listing 2
// https://seblagarde.files.wordpress.com/2015/07/course_notes_moving_frostbite_to_pbr_v32.pdf
float V_GGX_SmithCorrelated( const in float alpha, const in float dotNL, const in float dotNV ) {
float a2 = pow2( alpha );
float gv = dotNL * sqrt( a2 + ( 1.0 - a2 ) * pow2( dotNV ) );
float gl = dotNV * sqrt( a2 + ( 1.0 - a2 ) * pow2( dotNL ) );
return 0.5 / max( gv + gl, EPSILON );
}
// Microfacet Models for Refraction through Rough Surfaces - equation (33)
// http://graphicrants.blogspot.com/2013/08/specular-brdf-reference.html
// alpha is "roughness squared" in Disney’s reparameterization
float D_GGX( const in float alpha, const in float dotNH ) {
float a2 = pow2( alpha );
float denom = pow2( dotNH ) * ( a2 - 1.0 ) + 1.0; // avoid alpha = 0 with dotNH = 1
return RECIPROCAL_PI * a2 / pow2( denom );
}
// https://google.github.io/filament/Filament.md.html#materialsystem/anisotropicmodel/anisotropicspecularbrdf
float V_GGX_SmithCorrelated_Anisotropic( const in float alphaT, const in float alphaB, const in float dotTV, const in float dotBV, const in float dotTL, const in float dotBL, const in float dotNV, const in float dotNL ) {
float gv = dotNL * length( vec3( alphaT * dotTV, alphaB * dotBV, dotNV ) );
float gl = dotNV * length( vec3( alphaT * dotTL, alphaB * dotBL, dotNL ) );
float v = 0.5 / ( gv + gl );
return saturate(v);
}
float D_GGX_Anisotropic( const in float alphaT, const in float alphaB, const in float dotNH, const in float dotTH, const in float dotBH ) {
float a2 = alphaT * alphaB;
highp vec3 v = vec3( alphaB * dotTH, alphaT * dotBH, a2 * dotNH );
highp float v2 = dot( v, v );
float w2 = a2 / v2;
return RECIPROCAL_PI * a2 * pow2 ( w2 );
}
// GGX Distribution, Schlick Fresnel, GGX_SmithCorrelated Visibility
vec3 BRDF_GGX_Clearcoat( const in vec3 lightDir, const in vec3 viewDir, const in vec3 normal, const in PhysicalMaterial material) {
vec3 f0 = material.clearcoatF0;
float f90 = material.clearcoatF90;
float roughness = material.clearcoatRoughness;
float alpha = pow2( roughness ); // UE4's roughness
vec3 halfDir = normalize( lightDir + viewDir );
float dotNL = saturate( dot( normal, lightDir ) );
float dotNV = saturate( dot( normal, viewDir ) );
float dotNH = saturate( dot( normal, halfDir ) );
float dotVH = saturate( dot( viewDir, halfDir ) );
vec3 F = F_Schlick( f0, f90, dotVH );
float V = V_GGX_SmithCorrelated( alpha, dotNL, dotNV );
float D = D_GGX( alpha, dotNH );
return F * ( V * D );
}
vec3 BRDF_GGX( const in vec3 lightDir, const in vec3 viewDir, const in vec3 normal, const in PhysicalMaterial material ) {
vec3 f0 = material.specularColor;
float f90 = material.specularF90;
float roughness = material.roughness;
float alpha = pow2( roughness ); // UE4's roughness
vec3 halfDir = normalize( lightDir + viewDir );
float dotNL = saturate( dot( normal, lightDir ) );
float dotNV = saturate( dot( normal, viewDir ) );
float dotNH = saturate( dot( normal, halfDir ) );
float dotVH = saturate( dot( viewDir, halfDir ) );
vec3 F = F_Schlick( f0, f90, dotVH );
F = mix( F, material.iridescenceFresnel, material.iridescence );
float dotTL = dot( material.anisotropyT, lightDir );
float dotTV = dot( material.anisotropyT, viewDir );
float dotTH = dot( material.anisotropyT, halfDir );
float dotBL = dot( material.anisotropyB, lightDir );
float dotBV = dot( material.anisotropyB, viewDir );
float dotBH = dot( material.anisotropyB, halfDir );
float V = V_GGX_SmithCorrelated_Anisotropic( material.alphaT, alpha, dotTV, dotBV, dotTL, dotBL, dotNV, dotNL );
float D = D_GGX_Anisotropic( material.alphaT, alpha, dotNH, dotTH, dotBH );
float V = V_GGX_SmithCorrelated( alpha, dotNL, dotNV );
float D = D_GGX( alpha, dotNH );
return F * ( V * D );
}
// Rect Area Light
// Real-Time Polygonal-Light Shading with Linearly Transformed Cosines
// by Eric Heitz, Jonathan Dupuy, Stephen Hill and David Neubelt
// code: https://github.com/selfshadow/ltc_code/
vec2 LTC_Uv( const in vec3 N, const in vec3 V, const in float roughness ) {
const float LUT_SIZE = 64.0;
const float LUT_SCALE = ( LUT_SIZE - 1.0 ) / LUT_SIZE;
const float LUT_BIAS = 0.5 / LUT_SIZE;
float dotNV = saturate( dot( N, V ) );
// texture parameterized by sqrt( GGX alpha ) and sqrt( 1 - cos( theta ) )
vec2 uv = vec2( roughness, sqrt( 1.0 - dotNV ) );
uv = uv * LUT_SCALE + LUT_BIAS;
return uv;
}
float LTC_ClippedSphereFormFactor( const in vec3 f ) {
// Real-Time Area Lighting: a Journey from Research to Production (p.102)
// An approximation of the form factor of a horizon-clipped rectangle.
float l = length( f );
return max( ( l * l + f.z ) / ( l + 1.0 ), 0.0 );
}
vec3 LTC_EdgeVectorFormFactor( const in vec3 v1, const in vec3 v2 ) {
float x = dot( v1, v2 );
float y = abs( x );
// rational polynomial approximation to theta / sin( theta ) / 2PI
float a = 0.8543985 + ( 0.4965155 + 0.0145206 * y ) * y;
float b = 3.4175940 + ( 4.1616724 + y ) * y;
float v = a / b;
float theta_sintheta = ( x > 0.0 ) ? v : 0.5 * inversesqrt( max( 1.0 - x * x, 1e-7 ) ) - v;
return cross( v1, v2 ) * theta_sintheta;
}
vec3 LTC_Evaluate( const in vec3 N, const in vec3 V, const in vec3 P, const in mat3 mInv, const in vec3 rectCoords[ 4 ] ) {
// bail if point is on back side of plane of light
// assumes ccw winding order of light vertices
vec3 v1 = rectCoords[ 1 ] - rectCoords[ 0 ];
vec3 v2 = rectCoords[ 3 ] - rectCoords[ 0 ];
vec3 lightNormal = cross( v1, v2 );
if( dot( lightNormal, P - rectCoords[ 0 ] ) < 0.0 ) return vec3( 0.0 );
// construct orthonormal basis around N
vec3 T1, T2;
T1 = normalize( V - N * dot( V, N ) );
T2 = - cross( N, T1 ); // negated from paper; possibly due to a different handedness of world coordinate system
// compute transform
mat3 mat = mInv * transposeMat3( mat3( T1, T2, N ) );
// transform rect
vec3 coords[ 4 ];
coords[ 0 ] = mat * ( rectCoords[ 0 ] - P );
coords[ 1 ] = mat * ( rectCoords[ 1 ] - P );
coords[ 2 ] = mat * ( rectCoords[ 2 ] - P );
coords[ 3 ] = mat * ( rectCoords[ 3 ] - P );
// project rect onto sphere
coords[ 0 ] = normalize( coords[ 0 ] );
coords[ 1 ] = normalize( coords[ 1 ] );
coords[ 2 ] = normalize( coords[ 2 ] );
coords[ 3 ] = normalize( coords[ 3 ] );
// calculate vector form factor
vec3 vectorFormFactor = vec3( 0.0 );
vectorFormFactor += LTC_EdgeVectorFormFactor( coords[ 0 ], coords[ 1 ] );
vectorFormFactor += LTC_EdgeVectorFormFactor( coords[ 1 ], coords[ 2 ] );
vectorFormFactor += LTC_EdgeVectorFormFactor( coords[ 2 ], coords[ 3 ] );
vectorFormFactor += LTC_EdgeVectorFormFactor( coords[ 3 ], coords[ 0 ] );
// adjust for horizon clipping
float result = LTC_ClippedSphereFormFactor( vectorFormFactor );
/*
// alternate method of adjusting for horizon clipping (see reference)
// refactoring required
float len = length( vectorFormFactor );
float z = vectorFormFactor.z / len;
const float LUT_SIZE = 64.0;
const float LUT_SCALE = ( LUT_SIZE - 1.0 ) / LUT_SIZE;
const float LUT_BIAS = 0.5 / LUT_SIZE;
// tabulated horizon-clipped sphere, apparently...
vec2 uv = vec2( z * 0.5 + 0.5, len );
uv = uv * LUT_SCALE + LUT_BIAS;
float scale = texture2D( ltc_2, uv ).w;
float result = len * scale;
*/
return vec3( result );
}
// End Rect Area Light
// https://github.com/google/filament/blob/master/shaders/src/brdf.fs
float D_Charlie( float roughness, float dotNH ) {
float alpha = pow2( roughness );
// Estevez and Kulla 2017, "Production Friendly Microfacet Sheen BRDF"
float invAlpha = 1.0 / alpha;
float cos2h = dotNH * dotNH;
float sin2h = max( 1.0 - cos2h, 0.0078125 ); // 2^(-14/2), so sin2h^2 > 0 in fp16
return ( 2.0 + invAlpha ) * pow( sin2h, invAlpha * 0.5 ) / ( 2.0 * PI );
}
// https://github.com/google/filament/blob/master/shaders/src/brdf.fs
float V_Neubelt( float dotNV, float dotNL ) {
// Neubelt and Pettineo 2013, "Crafting a Next-gen Material Pipeline for The Order: 1886"
return saturate( 1.0 / ( 4.0 * ( dotNL + dotNV - dotNL * dotNV ) ) );
}
vec3 BRDF_Sheen( const in vec3 lightDir, const in vec3 viewDir, const in vec3 normal, vec3 sheenColor, const in float sheenRoughness ) {
vec3 halfDir = normalize( lightDir + viewDir );
float dotNL = saturate( dot( normal, lightDir ) );
float dotNV = saturate( dot( normal, viewDir ) );
float dotNH = saturate( dot( normal, halfDir ) );
float D = D_Charlie( sheenRoughness, dotNH );
float V = V_Neubelt( dotNV, dotNL );
return sheenColor * ( D * V );
}
// This is a curve-fit approximation to the "Charlie sheen" BRDF integrated over the hemisphere from
// Estevez and Kulla 2017, "Production Friendly Microfacet Sheen BRDF". The analysis can be found
// in the Sheen section of https://drive.google.com/file/d/1T0D1VSyR4AllqIJTQAraEIzjlb5h4FKH/view?usp=sharing
float IBLSheenBRDF( const in vec3 normal, const in vec3 viewDir, const in float roughness ) {
float dotNV = saturate( dot( normal, viewDir ) );
float r2 = roughness * roughness;
float a = roughness < 0.25 ? -339.2 * r2 + 161.4 * roughness - 25.9 : -8.48 * r2 + 14.3 * roughness - 9.95;
float b = roughness < 0.25 ? 44.0 * r2 - 23.7 * roughness + 3.26 : 1.97 * r2 - 3.27 * roughness + 0.72;
float DG = exp( a * dotNV + b ) + ( roughness < 0.25 ? 0.0 : 0.1 * ( roughness - 0.25 ) );
return saturate( DG * RECIPROCAL_PI );
}
// Analytical approximation of the DFG LUT, one half of the
// split-sum approximation used in indirect specular lighting.
// via 'environmentBRDF' from "Physically Based Shading on Mobile"
// https://www.unrealengine.com/blog/physically-based-shading-on-mobile
vec2 DFGApprox( const in vec3 normal, const in vec3 viewDir, const in float roughness ) {
float dotNV = saturate( dot( normal, viewDir ) );
const vec4 c0 = vec4( - 1, - 0.0275, - 0.572, 0.022 );
const vec4 c1 = vec4( 1, 0.0425, 1.04, - 0.04 );
vec4 r = roughness * c0 + c1;
float a004 = min( r.x * r.x, exp2( - 9.28 * dotNV ) ) * r.x + r.y;
vec2 fab = vec2( - 1.04, 1.04 ) * a004 + r.zw;
return fab;
}
vec3 EnvironmentBRDF( const in vec3 normal, const in vec3 viewDir, const in vec3 specularColor, const in float specularF90, const in float roughness ) {
vec2 fab = DFGApprox( normal, viewDir, roughness );
return specularColor * fab.x + specularF90 * fab.y;
}
// Fdez-Agüera's "Multiple-Scattering Microfacet Model for Real-Time Image Based Lighting"
// Approximates multiscattering in order to preserve energy.
// http://www.jcgt.org/published/0008/01/03/
void computeMultiscatteringIridescence( const in vec3 normal, const in vec3 viewDir, const in vec3 specularColor, const in float specularF90, const in float iridescence, const in vec3 iridescenceF0, const in float roughness, inout vec3 singleScatter, inout vec3 multiScatter ) {
void computeMultiscattering( const in vec3 normal, const in vec3 viewDir, const in vec3 specularColor, const in float specularF90, const in float roughness, inout vec3 singleScatter, inout vec3 multiScatter ) {
vec2 fab = DFGApprox( normal, viewDir, roughness );
vec3 Fr = mix( specularColor, iridescenceF0, iridescence );
vec3 Fr = specularColor;
vec3 FssEss = Fr * fab.x + specularF90 * fab.y;
float Ess = fab.x + fab.y;
float Ems = 1.0 - Ess;
vec3 Favg = Fr + ( 1.0 - Fr ) * 0.047619; // 1/21
vec3 Fms = FssEss * Favg / ( 1.0 - Ems * Favg );
singleScatter += FssEss;
multiScatter += Fms * Ems;
}
void RE_Direct_RectArea_Physical( const in RectAreaLight rectAreaLight, const in vec3 geometryPosition, const in vec3 geometryNormal, const in vec3 geometryViewDir, const in vec3 geometryClearcoatNormal, const in PhysicalMaterial material, inout ReflectedLight reflectedLight ) {
vec3 normal = geometryNormal;
vec3 viewDir = geometryViewDir;
vec3 position = geometryPosition;
vec3 lightPos = rectAreaLight.position;
vec3 halfWidth = rectAreaLight.halfWidth;
vec3 halfHeight = rectAreaLight.halfHeight;
vec3 lightColor = rectAreaLight.color;
float roughness = material.roughness;
vec3 rectCoords[ 4 ];
rectCoords[ 0 ] = lightPos + halfWidth - halfHeight; // counterclockwise; light shines in local neg z direction
rectCoords[ 1 ] = lightPos - halfWidth - halfHeight;
rectCoords[ 2 ] = lightPos - halfWidth + halfHeight;
rectCoords[ 3 ] = lightPos + halfWidth + halfHeight;
vec2 uv = LTC_Uv( normal, viewDir, roughness );
vec4 t1 = texture2D( ltc_1, uv );
vec4 t2 = texture2D( ltc_2, uv );
mat3 mInv = mat3(
vec3( t1.x, 0, t1.y ),
vec3( 0, 1, 0 ),
vec3( t1.z, 0, t1.w )
);
// LTC Fresnel Approximation by Stephen Hill
// http://blog.selfshadow.com/publications/s2016-advances/s2016_ltc_fresnel.pdf
vec3 fresnel = ( material.specularColor * t2.x + ( vec3( 1.0 ) - material.specularColor ) * t2.y );
reflectedLight.directSpecular += lightColor * fresnel * LTC_Evaluate( normal, viewDir, position, mInv, rectCoords );
reflectedLight.directDiffuse += lightColor * material.diffuseColor * LTC_Evaluate( normal, viewDir, position, mat3( 1.0 ), rectCoords );
}
void RE_Direct_Physical( const in IncidentLight directLight, const in vec3 geometryPosition, const in vec3 geometryNormal, const in vec3 geometryViewDir, const in vec3 geometryClearcoatNormal, const in PhysicalMaterial material, inout ReflectedLight reflectedLight ) {
float dotNL = saturate( dot( geometryNormal, directLight.direction ) );
vec3 irradiance = dotNL * directLight.color;
float dotNLcc = saturate( dot( geometryClearcoatNormal, directLight.direction ) );
vec3 ccIrradiance = dotNLcc * directLight.color;
clearcoatSpecularDirect += ccIrradiance * BRDF_GGX_Clearcoat( directLight.direction, geometryViewDir, geometryClearcoatNormal, material );
sheenSpecularDirect += irradiance * BRDF_Sheen( directLight.direction, geometryViewDir, geometryNormal, material.sheenColor, material.sheenRoughness );
reflectedLight.directSpecular += irradiance * BRDF_GGX( directLight.direction, geometryViewDir, geometryNormal, material );
reflectedLight.directDiffuse += irradiance * BRDF_Lambert( material.diffuseColor );
}
void RE_IndirectDiffuse_Physical( const in vec3 irradiance, const in vec3 geometryPosition, const in vec3 geometryNormal, const in vec3 geometryViewDir, const in vec3 geometryClearcoatNormal, const in PhysicalMaterial material, inout ReflectedLight reflectedLight ) {
reflectedLight.indirectDiffuse += irradiance * BRDF_Lambert( material.diffuseColor );
}
void RE_IndirectSpecular_Physical( const in vec3 radiance, const in vec3 irradiance, const in vec3 clearcoatRadiance, const in vec3 geometryPosition, const in vec3 geometryNormal, const in vec3 geometryViewDir, const in vec3 geometryClearcoatNormal, const in PhysicalMaterial material, inout ReflectedLight reflectedLight) {
clearcoatSpecularIndirect += clearcoatRadiance * EnvironmentBRDF( geometryClearcoatNormal, geometryViewDir, material.clearcoatF0, material.clearcoatF90, material.clearcoatRoughness );
sheenSpecularIndirect += irradiance * material.sheenColor * IBLSheenBRDF( geometryNormal, geometryViewDir, material.sheenRoughness );
// Both indirect specular and indirect diffuse light accumulate here
vec3 singleScattering = vec3( 0.0 );
vec3 multiScattering = vec3( 0.0 );
vec3 cosineWeightedIrradiance = irradiance * RECIPROCAL_PI;
computeMultiscatteringIridescence( geometryNormal, geometryViewDir, material.specularColor, material.specularF90, material.iridescence, material.iridescenceFresnel, material.roughness, singleScattering, multiScattering );
computeMultiscattering( geometryNormal, geometryViewDir, material.specularColor, material.specularF90, material.roughness, singleScattering, multiScattering );
vec3 totalScattering = singleScattering + multiScattering;
vec3 diffuse = material.diffuseColor * ( 1.0 - max( max( totalScattering.r, totalScattering.g ), totalScattering.b ) );
reflectedLight.indirectSpecular += radiance * singleScattering;
reflectedLight.indirectSpecular += multiScattering * cosineWeightedIrradiance;
reflectedLight.indirectDiffuse += diffuse * cosineWeightedIrradiance;
}
// ref: https://seblagarde.files.wordpress.com/2015/07/course_notes_moving_frostbite_to_pbr_v32.pdf
float computeSpecularOcclusion( const in float dotNV, const in float ambientOcclusion, const in float roughness ) {
return saturate( pow( dotNV + ambientOcclusion, exp2( - 16.0 * roughness - 1.0 ) ) - 1.0 + ambientOcclusion );
}
`;