#define PI 3.14159265359
#define PI2 6.28318530718
#define PI_HALF 1.5707963267949
#define RECIPROCAL_PI 0.31830988618
#define RECIPROCAL_PI2 0.15915494
#define LOG2 1.442695
#define EPSILON 1e-6

#define saturate(a) clamp( a, 0.0, 1.0 )
#define whiteCompliment(a) ( 1.0 - saturate( a ) )

float pow2( const in float x ) { return x*x; }
float pow3( const in float x ) { return x*x*x; }
float pow4( const in float x ) { float x2 = x*x; return x2*x2; }
float average( const in vec3 color ) { return dot( color, vec3( 0.3333 ) ); }
// expects values in the range of [0,1]x[0,1], returns values in the [0,1] range.
// do not collapse into a single function per: http://byteblacksmith.com/improvements-to-the-canonical-one-liner-glsl-rand-for-opengl-es-2-0/

highp float rand( const in vec2 uv ) {
	const highp float a = 12.9898, b = 78.233, c = 43758.5453;
	highp float dt = dot( uv.xy, vec2( a,b ) ), sn = mod( dt, PI );
	return fract(sin(sn) * c);
}

struct IncidentLight {
	vec3 color;
	vec3 direction;
	bool visible;
};

struct ReflectedLight {
	vec3 directDiffuse;
	vec3 directSpecular;
	vec3 indirectDiffuse;
	vec3 indirectSpecular;
};

struct GeometricContext {
	vec3 position;
	vec3 normal;
	vec3 viewDir;
};

vec3 transformDirection( in vec3 dir, in mat4 matrix ) {

	return normalize( ( matrix * vec4( dir, 0.0 ) ).xyz );

}

// http://en.wikibooks.org/wiki/GLSL_Programming/Applying_Matrix_Transformations

vec3 inverseTransformDirection( in vec3 dir, in mat4 matrix ) {

	return normalize( ( vec4( dir, 0.0 ) * matrix ).xyz );

}

vec3 projectOnPlane(in vec3 point, in vec3 pointOnPlane, in vec3 planeNormal ) {

	float distance = dot( planeNormal, point - pointOnPlane );

	return - distance * planeNormal + point;

}

float sideOfPlane( in vec3 point, in vec3 pointOnPlane, in vec3 planeNormal ) {

	return sign( dot( point - pointOnPlane, planeNormal ) );

}

vec3 linePlaneIntersect( in vec3 pointOnLine, in vec3 lineDirection, in vec3 pointOnPlane, in vec3 planeNormal ) {

	return lineDirection * ( dot( planeNormal, pointOnPlane - pointOnLine ) / dot( planeNormal, lineDirection ) ) + pointOnLine;

}

mat3 transposeMat3( const in mat3 m ) {

	mat3 tmp;

	tmp[ 0 ] = vec3( m[ 0 ].x, m[ 1 ].x, m[ 2 ].x );
	tmp[ 1 ] = vec3( m[ 0 ].y, m[ 1 ].y, m[ 2 ].y );
	tmp[ 2 ] = vec3( m[ 0 ].z, m[ 1 ].z, m[ 2 ].z );

	return tmp;

}

// https://en.wikipedia.org/wiki/Relative_luminance

float linearToRelativeLuminance( const in vec3 color ) {

	vec3 weights = vec3( 0.2126, 0.7152, 0.0722 );

	return dot( weights, color.rgb );

}

#if defined( USE_MAP ) || defined( USE_BUMPMAP ) || defined( USE_NORMALMAP ) || defined( USE_SPECULARMAP ) || defined( USE_ALPHAMAP ) || defined( USE_EMISSIVEMAP ) || defined( USE_ROUGHNESSMAP ) || defined( USE_METALNESSMAP )

	varying vec2 vUv;
	uniform mat3 uvTransform;

#endif

#if defined( USE_LIGHTMAP ) || defined( USE_AOMAP )

	attribute vec2 uv2;
	varying vec2 vUv2;

#endif

#ifdef USE_DISPLACEMENTMAP

	uniform sampler2D displacementMap;
	uniform float displacementScale;
	uniform float displacementBias;

#endif

#ifdef USE_ENVMAP

	#if defined( USE_BUMPMAP ) || defined( USE_NORMALMAP ) || defined( PHONG )
		varying vec3 vWorldPosition;

	#else

		varying vec3 vReflect;
		uniform float refractionRatio;

	#endif

#endif

#ifdef USE_COLOR

	varying vec3 vColor;

#endif

#ifdef USE_FOG

  varying float fogDepth;

#endif

#ifdef USE_MORPHTARGETS

	#ifndef USE_MORPHNORMALS

	uniform float morphTargetInfluences[ 8 ];

	#else

	uniform float morphTargetInfluences[ 4 ];

	#endif

#endif

#ifdef USE_SKINNING

	uniform mat4 bindMatrix;
	uniform mat4 bindMatrixInverse;

	#ifdef BONE_TEXTURE

		uniform sampler2D boneTexture;
		uniform int boneTextureSize;

		mat4 getBoneMatrix( const in float i ) {

			float j = i * 4.0;
			float x = mod( j, float( boneTextureSize ) );
			float y = floor( j / float( boneTextureSize ) );

			float dx = 1.0 / float( boneTextureSize );
			float dy = 1.0 / float( boneTextureSize );

			y = dy * ( y + 0.5 );

			vec4 v1 = texture2D( boneTexture, vec2( dx * ( x + 0.5 ), y ) );
			vec4 v2 = texture2D( boneTexture, vec2( dx * ( x + 1.5 ), y ) );
			vec4 v3 = texture2D( boneTexture, vec2( dx * ( x + 2.5 ), y ) );
			vec4 v4 = texture2D( boneTexture, vec2( dx * ( x + 3.5 ), y ) );

			mat4 bone = mat4( v1, v2, v3, v4 );

			return bone;

		}

	#else

		uniform mat4 boneMatrices[ MAX_BONES ];

		mat4 getBoneMatrix( const in float i ) {

			mat4 bone = boneMatrices[ int(i) ];
			return bone;

		}

	#endif

#endif

#ifdef USE_SHADOWMAP

	#if NUM_DIR_LIGHTS > 0

		uniform mat4 directionalShadowMatrix[ NUM_DIR_LIGHTS ];
		varying vec4 vDirectionalShadowCoord[ NUM_DIR_LIGHTS ];

	#endif

	#if NUM_SPOT_LIGHTS > 0

		uniform mat4 spotShadowMatrix[ NUM_SPOT_LIGHTS ];
		varying vec4 vSpotShadowCoord[ NUM_SPOT_LIGHTS ];

	#endif

	#if NUM_POINT_LIGHTS > 0

		uniform mat4 pointShadowMatrix[ NUM_POINT_LIGHTS ];
		varying vec4 vPointShadowCoord[ NUM_POINT_LIGHTS ];

	#endif

	/*
	#if NUM_RECT_AREA_LIGHTS > 0

		// TODO (abelnation): uniforms for area light shadows

	#endif
	*/

#endif

#ifdef USE_LOGDEPTHBUF

	#ifdef USE_LOGDEPTHBUF_EXT

		varying float vFragDepth;

	#endif

	uniform float logDepthBufFC;

#endif

#if NUM_CLIPPING_PLANES > 0 && ! defined( PHYSICAL ) && ! defined( PHONG )
	varying vec3 vViewPosition;
#endif

#define PI 3.14159265359
#define PI2 6.28318530718
#define PI_HALF 1.5707963267949
#define RECIPROCAL_PI 0.31830988618
#define RECIPROCAL_PI2 0.15915494
#define LOG2 1.442695
#define EPSILON 1e-6

#define saturate(a) clamp( a, 0.0, 1.0 )
#define whiteCompliment(a) ( 1.0 - saturate( a ) )

float pow2( const in float x ) { return x*x; }
float pow3( const in float x ) { return x*x*x; }
float pow4( const in float x ) { float x2 = x*x; return x2*x2; }
float average( const in vec3 color ) { return dot( color, vec3( 0.3333 ) ); }
// expects values in the range of [0,1]x[0,1], returns values in the [0,1] range.
// do not collapse into a single function per: http://byteblacksmith.com/improvements-to-the-canonical-one-liner-glsl-rand-for-opengl-es-2-0/

highp float rand( const in vec2 uv ) {
	const highp float a = 12.9898, b = 78.233, c = 43758.5453;
	highp float dt = dot( uv.xy, vec2( a,b ) ), sn = mod( dt, PI );
	return fract(sin(sn) * c);
}

struct IncidentLight {
	vec3 color;
	vec3 direction;
	bool visible;
};

struct ReflectedLight {
	vec3 directDiffuse;
	vec3 directSpecular;
	vec3 indirectDiffuse;
	vec3 indirectSpecular;
};

struct GeometricContext {
	vec3 position;
	vec3 normal;
	vec3 viewDir;
};

vec3 transformDirection( in vec3 dir, in mat4 matrix ) {

	return normalize( ( matrix * vec4( dir, 0.0 ) ).xyz );

}

// http://en.wikibooks.org/wiki/GLSL_Programming/Applying_Matrix_Transformations

vec3 inverseTransformDirection( in vec3 dir, in mat4 matrix ) {

	return normalize( ( vec4( dir, 0.0 ) * matrix ).xyz );

}

vec3 projectOnPlane(in vec3 point, in vec3 pointOnPlane, in vec3 planeNormal ) {

	float distance = dot( planeNormal, point - pointOnPlane );

	return - distance * planeNormal + point;

}

float sideOfPlane( in vec3 point, in vec3 pointOnPlane, in vec3 planeNormal ) {

	return sign( dot( point - pointOnPlane, planeNormal ) );

}

vec3 linePlaneIntersect( in vec3 pointOnLine, in vec3 lineDirection, in vec3 pointOnPlane, in vec3 planeNormal ) {

	return lineDirection * ( dot( planeNormal, pointOnPlane - pointOnLine ) / dot( planeNormal, lineDirection ) ) + pointOnLine;

}

mat3 transposeMat3( const in mat3 m ) {

	mat3 tmp;

	tmp[ 0 ] = vec3( m[ 0 ].x, m[ 1 ].x, m[ 2 ].x );
	tmp[ 1 ] = vec3( m[ 0 ].y, m[ 1 ].y, m[ 2 ].y );
	tmp[ 2 ] = vec3( m[ 0 ].z, m[ 1 ].z, m[ 2 ].z );

	return tmp;

}

// https://en.wikipedia.org/wiki/Relative_luminance

float linearToRelativeLuminance( const in vec3 color ) {

	vec3 weights = vec3( 0.2126, 0.7152, 0.0722 );

	return dot( weights, color.rgb );

}

vec3 packNormalToRGB( const in vec3 normal ) {
	return normalize( normal ) * 0.5 + 0.5;
}

vec3 unpackRGBToNormal( const in vec3 rgb ) {
	return 2.0 * rgb.xyz - 1.0;
}

const float PackUpscale = 256. / 255.; // fraction -> 0..1 (including 1)
const float UnpackDownscale = 255. / 256.; // 0..1 -> fraction (excluding 1)

const vec3 PackFactors = vec3( 256. * 256. * 256., 256. * 256.,  256. );
const vec4 UnpackFactors = UnpackDownscale / vec4( PackFactors, 1. );

const float ShiftRight8 = 1. / 256.;

vec4 packDepthToRGBA( const in float v ) {
	vec4 r = vec4( fract( v * PackFactors ), v );
	r.yzw -= r.xyz * ShiftRight8; // tidy overflow
	return r * PackUpscale;
}

float unpackRGBAToDepth( const in vec4 v ) {
	return dot( v, UnpackFactors );
}

// NOTE: viewZ/eyeZ is < 0 when in front of the camera per OpenGL conventions

float viewZToOrthographicDepth( const in float viewZ, const in float near, const in float far ) {
	return ( viewZ + near ) / ( near - far );
}
float orthographicDepthToViewZ( const in float linearClipZ, const in float near, const in float far ) {
	return linearClipZ * ( near - far ) - near;
}

float viewZToPerspectiveDepth( const in float viewZ, const in float near, const in float far ) {
	return (( near + viewZ ) * far ) / (( far - near ) * viewZ );
}
float perspectiveDepthToViewZ( const in float invClipZ, const in float near, const in float far ) {
	return ( near * far ) / ( ( far - near ) * invClipZ - far );
}

#if defined( DITHERING )

	// based on https://www.shadertoy.com/view/MslGR8

	vec3 dithering( vec3 color ) {
		//Calculate grid position
		float grid_position = rand( gl_FragCoord.xy );

		//Shift the individual colors differently, thus making it even harder to see the dithering pattern
		vec3 dither_shift_RGB = vec3( 0.25 / 255.0, -0.25 / 255.0, 0.25 / 255.0 );

		//modify shift acording to grid position.
		dither_shift_RGB = mix( 2.0 * dither_shift_RGB, -2.0 * dither_shift_RGB, grid_position );

		//shift the color by dither_shift
		return color + dither_shift_RGB;
	}

#endif

#ifdef USE_COLOR

	varying vec3 vColor;

#endif

#if defined( USE_MAP ) || defined( USE_BUMPMAP ) || defined( USE_NORMALMAP ) || defined( USE_SPECULARMAP ) || defined( USE_ALPHAMAP ) || defined( USE_EMISSIVEMAP ) || defined( USE_ROUGHNESSMAP ) || defined( USE_METALNESSMAP )

	varying vec2 vUv;

#endif

#if defined( USE_LIGHTMAP ) || defined( USE_AOMAP )

	varying vec2 vUv2;

#endif

#ifdef USE_MAP

	uniform sampler2D map;

#endif

#ifdef USE_ALPHAMAP

	uniform sampler2D alphaMap;

#endif

#ifdef USE_AOMAP

	uniform sampler2D aoMap;
	uniform float aoMapIntensity;

#endif

#ifdef USE_LIGHTMAP

	uniform sampler2D lightMap;
	uniform float lightMapIntensity;

#endif

#ifdef USE_EMISSIVEMAP

	uniform sampler2D emissiveMap;

#endif

#if defined( USE_ENVMAP ) || defined( PHYSICAL )
	uniform float reflectivity;
	uniform float envMapIntensity;
#endif

#ifdef USE_ENVMAP

	#if ! defined( PHYSICAL ) && ( defined( USE_BUMPMAP ) || defined( USE_NORMALMAP ) || defined( PHONG ) )
		varying vec3 vWorldPosition;
	#endif

	#ifdef ENVMAP_TYPE_CUBE
		uniform samplerCube envMap;
	#else
		uniform sampler2D envMap;
	#endif
	uniform float flipEnvMap;
	uniform int maxMipLevel;

	#if defined( USE_BUMPMAP ) || defined( USE_NORMALMAP ) || defined( PHONG ) || defined( PHYSICAL )
		uniform float refractionRatio;
	#else
		varying vec3 vReflect;
	#endif

#endif

#ifdef TOON

	uniform sampler2D gradientMap;

	vec3 getGradientIrradiance( vec3 normal, vec3 lightDirection ) {

		// dotNL will be from -1.0 to 1.0
		float dotNL = dot( normal, lightDirection );
		vec2 coord = vec2( dotNL * 0.5 + 0.5, 0.0 );

		#ifdef USE_GRADIENTMAP

			return texture2D( gradientMap, coord ).rgb;

		#else

			return ( coord.x < 0.7 ) ? vec3( 0.7 ) : vec3( 1.0 );

		#endif


	}

#endif

#ifdef USE_FOG

	uniform vec3 fogColor;
	varying float fogDepth;

	#ifdef FOG_EXP2

		uniform float fogDensity;

	#else

		uniform float fogNear;
		uniform float fogFar;

	#endif

#endif

float punctualLightIntensityToIrradianceFactor( const in float lightDistance, const in float cutoffDistance, const in float decayExponent ) {

	if( decayExponent > 0.0 ) {

#if defined ( PHYSICALLY_CORRECT_LIGHTS )

		// based upon Frostbite 3 Moving to Physically-based Rendering
		// page 32, equation 26: E[window1]
		// https://seblagarde.files.wordpress.com/2015/07/course_notes_moving_frostbite_to_pbr_v32.pdf

		// this is intended to be used on spot and point lights who are represented as luminous intensity
		// but who must be converted to luminous irradiance for surface lighting calculation
		float distanceFalloff = 1.0 / max( pow( lightDistance, decayExponent ), 0.01 );
		float maxDistanceCutoffFactor = pow2( saturate( 1.0 - pow4( lightDistance / cutoffDistance ) ) );
		return distanceFalloff * maxDistanceCutoffFactor;

#else

		return pow( saturate( -lightDistance / cutoffDistance + 1.0 ), decayExponent );

#endif

	}

	return 1.0;

}

vec3 BRDF_Diffuse_Lambert( const in vec3 diffuseColor ) {

	return RECIPROCAL_PI * diffuseColor;

} // validated

vec3 F_Schlick( const in vec3 specularColor, const in float dotLH ) {

	// Original approximation by Christophe Schlick '94
	// float fresnel = pow( 1.0 - dotLH, 5.0 );

	// Optimized variant (presented by Epic at SIGGRAPH '13)
	// https://cdn2.unrealengine.com/Resources/files/2013SiggraphPresentationsNotes-26915738.pdf

	float fresnel = exp2( ( -5.55473 * dotLH - 6.98316 ) * dotLH );

	return ( 1.0 - specularColor ) * fresnel + specularColor;

} // validated

// Microfacet Models for Refraction through Rough Surfaces - equation (34)
// http://graphicrants.blogspot.com/2013/08/specular-brdf-reference.html

// alpha is "roughness squared" in Disney’s reparameterization
float G_GGX_Smith( const in float alpha, const in float dotNL, const in float dotNV ) {

	// geometry term (normalized) = G(l)⋅G(v) / 4(n⋅l)(n⋅v)
	// also see #12151

	float a2 = pow2( alpha );

	float gl = dotNL + sqrt( a2 + ( 1.0 - a2 ) * pow2( dotNL ) );
	float gv = dotNV + sqrt( a2 + ( 1.0 - a2 ) * pow2( dotNV ) );

	return 1.0 / ( gl * gv );

} // validated

// 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 G_GGX_SmithCorrelated( const in float alpha, const in float dotNL, const in float dotNV ) {

	float a2 = pow2( alpha );

	// dotNL and dotNV are explicitly swapped. This is not a mistake.
	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 );

}

// GGX Distribution, Schlick Fresnel, GGX-Smith Visibility
vec3 BRDF_Specular_GGX( const in IncidentLight incidentLight, const in GeometricContext geometry, const in vec3 specularColor, const in float roughness ) {

	float alpha = pow2( roughness ); // UE4's roughness

	vec3 halfDir = normalize( incidentLight.direction + geometry.viewDir );

	float dotNL = saturate( dot( geometry.normal, incidentLight.direction ) );
	float dotNV = saturate( dot( geometry.normal, geometry.viewDir ) );
	float dotNH = saturate( dot( geometry.normal, halfDir ) );
	float dotLH = saturate( dot( incidentLight.direction, halfDir ) );

	vec3 F = F_Schlick( specularColor, dotLH );

	float G = G_GGX_SmithCorrelated( alpha, dotNL, dotNV );

	float D = D_GGX( alpha, dotNH );

	return F * ( G * D );

} // validated

// 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 referece)
	// 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

// ref: https://www.unrealengine.com/blog/physically-based-shading-on-mobile - environmentBRDF for GGX on mobile

vec3 BRDF_Specular_GGX_Environment( const in GeometricContext geometry, const in vec3 specularColor, const in float roughness ) {

	float dotNV = saturate( dot( geometry.normal, geometry.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 AB = vec2( -1.04, 1.04 ) * a004 + r.zw;

	return specularColor * AB.x + AB.y;

} // validated


float G_BlinnPhong_Implicit( /* const in float dotNL, const in float dotNV */ ) {

	// geometry term is (n dot l)(n dot v) / 4(n dot l)(n dot v)
	return 0.25;

}

float D_BlinnPhong( const in float shininess, const in float dotNH ) {

	return RECIPROCAL_PI * ( shininess * 0.5 + 1.0 ) * pow( dotNH, shininess );

}

vec3 BRDF_Specular_BlinnPhong( const in IncidentLight incidentLight, const in GeometricContext geometry, const in vec3 specularColor, const in float shininess ) {

	vec3 halfDir = normalize( incidentLight.direction + geometry.viewDir );

	//float dotNL = saturate( dot( geometry.normal, incidentLight.direction ) );
	//float dotNV = saturate( dot( geometry.normal, geometry.viewDir ) );
	float dotNH = saturate( dot( geometry.normal, halfDir ) );
	float dotLH = saturate( dot( incidentLight.direction, halfDir ) );

	vec3 F = F_Schlick( specularColor, dotLH );

	float G = G_BlinnPhong_Implicit( /* dotNL, dotNV */ );

	float D = D_BlinnPhong( shininess, dotNH );

	return F * ( G * D );

} // validated

// source: http://simonstechblog.blogspot.ca/2011/12/microfacet-brdf.html

float GGXRoughnessToBlinnExponent( const in float ggxRoughness ) {
	return ( 2.0 / pow2( ggxRoughness + 0.0001 ) - 2.0 );
}

float BlinnExponentToGGXRoughness( const in float blinnExponent ) {
	return sqrt( 2.0 / ( blinnExponent + 2.0 ) );
}

uniform vec3 ambientLightColor;

vec3 getAmbientLightIrradiance( const in vec3 ambientLightColor ) {

	vec3 irradiance = ambientLightColor;

	#ifndef PHYSICALLY_CORRECT_LIGHTS

		irradiance *= PI;

	#endif

	return irradiance;

}

#if NUM_DIR_LIGHTS > 0

	struct DirectionalLight {
		vec3 direction;
		vec3 color;

		int shadow;
		float shadowBias;
		float shadowRadius;
		vec2 shadowMapSize;
	};

	uniform DirectionalLight directionalLights[ NUM_DIR_LIGHTS ];

	void getDirectionalDirectLightIrradiance( const in DirectionalLight directionalLight, const in GeometricContext geometry, out IncidentLight directLight ) {

		directLight.color = directionalLight.color;
		directLight.direction = directionalLight.direction;
		directLight.visible = true;

	}

#endif


#if NUM_POINT_LIGHTS > 0

	struct PointLight {
		vec3 position;
		vec3 color;
		float distance;
		float decay;

		int shadow;
		float shadowBias;
		float shadowRadius;
		vec2 shadowMapSize;
		float shadowCameraNear;
		float shadowCameraFar;
	};

	uniform PointLight pointLights[ NUM_POINT_LIGHTS ];

	// directLight is an out parameter as having it as a return value caused compiler errors on some devices
	void getPointDirectLightIrradiance( const in PointLight pointLight, const in GeometricContext geometry, out IncidentLight directLight ) {

		vec3 lVector = pointLight.position - geometry.position;
		directLight.direction = normalize( lVector );

		float lightDistance = length( lVector );

		directLight.color = pointLight.color;
		directLight.color *= punctualLightIntensityToIrradianceFactor( lightDistance, pointLight.distance, pointLight.decay );
		directLight.visible = ( directLight.color != vec3( 0.0 ) );

	}

#endif


#if NUM_SPOT_LIGHTS > 0

	struct SpotLight {
		vec3 position;
		vec3 direction;
		vec3 color;
		float distance;
		float decay;
		float coneCos;
		float penumbraCos;

		int shadow;
		float shadowBias;
		float shadowRadius;
		vec2 shadowMapSize;
	};

	uniform SpotLight spotLights[ NUM_SPOT_LIGHTS ];

	// directLight is an out parameter as having it as a return value caused compiler errors on some devices
	void getSpotDirectLightIrradiance( const in SpotLight spotLight, const in GeometricContext geometry, out IncidentLight directLight  ) {

		vec3 lVector = spotLight.position - geometry.position;
		directLight.direction = normalize( lVector );

		float lightDistance = length( lVector );
		float angleCos = dot( directLight.direction, spotLight.direction );

		if ( angleCos > spotLight.coneCos ) {

			float spotEffect = smoothstep( spotLight.coneCos, spotLight.penumbraCos, angleCos );

			directLight.color = spotLight.color;
			directLight.color *= spotEffect * punctualLightIntensityToIrradianceFactor( lightDistance, spotLight.distance, spotLight.decay );
			directLight.visible = true;

		} else {

			directLight.color = vec3( 0.0 );
			directLight.visible = false;

		}
	}

#endif


#if NUM_RECT_AREA_LIGHTS > 0

	struct RectAreaLight {
		vec3 color;
		vec3 position;
		vec3 halfWidth;
		vec3 halfHeight;
	};

	// Pre-computed values of LinearTransformedCosine approximation of BRDF
	// BRDF approximation Texture is 64x64
	uniform sampler2D ltc_1; // RGBA Float
	uniform sampler2D ltc_2; // RGBA Float

	uniform RectAreaLight rectAreaLights[ NUM_RECT_AREA_LIGHTS ];

#endif


#if NUM_HEMI_LIGHTS > 0

	struct HemisphereLight {
		vec3 direction;
		vec3 skyColor;
		vec3 groundColor;
	};

	uniform HemisphereLight hemisphereLights[ NUM_HEMI_LIGHTS ];

	vec3 getHemisphereLightIrradiance( const in HemisphereLight hemiLight, const in GeometricContext geometry ) {

		float dotNL = dot( geometry.normal, hemiLight.direction );
		float hemiDiffuseWeight = 0.5 * dotNL + 0.5;

		vec3 irradiance = mix( hemiLight.groundColor, hemiLight.skyColor, hemiDiffuseWeight );

		#ifndef PHYSICALLY_CORRECT_LIGHTS

			irradiance *= PI;

		#endif

		return irradiance;

	}

#endif

varying vec3 vViewPosition;

#ifndef FLAT_SHADED

	varying vec3 vNormal;

#endif


struct BlinnPhongMaterial {

	vec3	diffuseColor;
	vec3	specularColor;
	float	specularShininess;
	float	specularStrength;

};

void RE_Direct_BlinnPhong( const in IncidentLight directLight, const in GeometricContext geometry, const in BlinnPhongMaterial material, inout ReflectedLight reflectedLight ) {

	#ifdef TOON

		vec3 irradiance = getGradientIrradiance( geometry.normal, directLight.direction ) * directLight.color;

	#else

		float dotNL = saturate( dot( geometry.normal, directLight.direction ) );
		vec3 irradiance = dotNL * directLight.color;

	#endif

	#ifndef PHYSICALLY_CORRECT_LIGHTS

		irradiance *= PI; // punctual light

	#endif

	reflectedLight.directDiffuse += irradiance * BRDF_Diffuse_Lambert( material.diffuseColor );

	reflectedLight.directSpecular += irradiance * BRDF_Specular_BlinnPhong( directLight, geometry, material.specularColor, material.specularShininess ) * material.specularStrength;

}

void RE_IndirectDiffuse_BlinnPhong( const in vec3 irradiance, const in GeometricContext geometry, const in BlinnPhongMaterial material, inout ReflectedLight reflectedLight ) {

	reflectedLight.indirectDiffuse += irradiance * BRDF_Diffuse_Lambert( material.diffuseColor );

}

#define RE_Direct				RE_Direct_BlinnPhong
#define RE_IndirectDiffuse		RE_IndirectDiffuse_BlinnPhong

#define Material_LightProbeLOD( material )	(0)

#ifdef USE_SHADOWMAP

	#if NUM_DIR_LIGHTS > 0

		uniform sampler2D directionalShadowMap[ NUM_DIR_LIGHTS ];
		varying vec4 vDirectionalShadowCoord[ NUM_DIR_LIGHTS ];

	#endif

	#if NUM_SPOT_LIGHTS > 0

		uniform sampler2D spotShadowMap[ NUM_SPOT_LIGHTS ];
		varying vec4 vSpotShadowCoord[ NUM_SPOT_LIGHTS ];

	#endif

	#if NUM_POINT_LIGHTS > 0

		uniform sampler2D pointShadowMap[ NUM_POINT_LIGHTS ];
		varying vec4 vPointShadowCoord[ NUM_POINT_LIGHTS ];

	#endif

	/*
	#if NUM_RECT_AREA_LIGHTS > 0

		// TODO (abelnation): create uniforms for area light shadows

	#endif
	*/

	float texture2DCompare( sampler2D depths, vec2 uv, float compare ) {

		return step( compare, unpackRGBAToDepth( texture2D( depths, uv ) ) );

	}

	float texture2DShadowLerp( sampler2D depths, vec2 size, vec2 uv, float compare ) {

		const vec2 offset = vec2( 0.0, 1.0 );

		vec2 texelSize = vec2( 1.0 ) / size;
		vec2 centroidUV = floor( uv * size + 0.5 ) / size;

		float lb = texture2DCompare( depths, centroidUV + texelSize * offset.xx, compare );
		float lt = texture2DCompare( depths, centroidUV + texelSize * offset.xy, compare );
		float rb = texture2DCompare( depths, centroidUV + texelSize * offset.yx, compare );
		float rt = texture2DCompare( depths, centroidUV + texelSize * offset.yy, compare );

		vec2 f = fract( uv * size + 0.5 );

		float a = mix( lb, lt, f.y );
		float b = mix( rb, rt, f.y );
		float c = mix( a, b, f.x );

		return c;

	}

	float getShadow( sampler2D shadowMap, vec2 shadowMapSize, float shadowBias, float shadowRadius, vec4 shadowCoord ) {

		float shadow = 1.0;

		shadowCoord.xyz /= shadowCoord.w;
		shadowCoord.z += shadowBias;

		// if ( something && something ) breaks ATI OpenGL shader compiler
		// if ( all( something, something ) ) using this instead

		bvec4 inFrustumVec = bvec4 ( shadowCoord.x >= 0.0, shadowCoord.x <= 1.0, shadowCoord.y >= 0.0, shadowCoord.y <= 1.0 );
		bool inFrustum = all( inFrustumVec );

		bvec2 frustumTestVec = bvec2( inFrustum, shadowCoord.z <= 1.0 );

		bool frustumTest = all( frustumTestVec );

		if ( frustumTest ) {

		#if defined( SHADOWMAP_TYPE_PCF )

			vec2 texelSize = vec2( 1.0 ) / shadowMapSize;

			float dx0 = - texelSize.x * shadowRadius;
			float dy0 = - texelSize.y * shadowRadius;
			float dx1 = + texelSize.x * shadowRadius;
			float dy1 = + texelSize.y * shadowRadius;

			shadow = (
				texture2DCompare( shadowMap, shadowCoord.xy + vec2( dx0, dy0 ), shadowCoord.z ) +
				texture2DCompare( shadowMap, shadowCoord.xy + vec2( 0.0, dy0 ), shadowCoord.z ) +
				texture2DCompare( shadowMap, shadowCoord.xy + vec2( dx1, dy0 ), shadowCoord.z ) +
				texture2DCompare( shadowMap, shadowCoord.xy + vec2( dx0, 0.0 ), shadowCoord.z ) +
				texture2DCompare( shadowMap, shadowCoord.xy, shadowCoord.z ) +
				texture2DCompare( shadowMap, shadowCoord.xy + vec2( dx1, 0.0 ), shadowCoord.z ) +
				texture2DCompare( shadowMap, shadowCoord.xy + vec2( dx0, dy1 ), shadowCoord.z ) +
				texture2DCompare( shadowMap, shadowCoord.xy + vec2( 0.0, dy1 ), shadowCoord.z ) +
				texture2DCompare( shadowMap, shadowCoord.xy + vec2( dx1, dy1 ), shadowCoord.z )
			) * ( 1.0 / 9.0 );

		#elif defined( SHADOWMAP_TYPE_PCF_SOFT )

			vec2 texelSize = vec2( 1.0 ) / shadowMapSize;

			float dx0 = - texelSize.x * shadowRadius;
			float dy0 = - texelSize.y * shadowRadius;
			float dx1 = + texelSize.x * shadowRadius;
			float dy1 = + texelSize.y * shadowRadius;

			shadow = (
				texture2DShadowLerp( shadowMap, shadowMapSize, shadowCoord.xy + vec2( dx0, dy0 ), shadowCoord.z ) +
				texture2DShadowLerp( shadowMap, shadowMapSize, shadowCoord.xy + vec2( 0.0, dy0 ), shadowCoord.z ) +
				texture2DShadowLerp( shadowMap, shadowMapSize, shadowCoord.xy + vec2( dx1, dy0 ), shadowCoord.z ) +
				texture2DShadowLerp( shadowMap, shadowMapSize, shadowCoord.xy + vec2( dx0, 0.0 ), shadowCoord.z ) +
				texture2DShadowLerp( shadowMap, shadowMapSize, shadowCoord.xy, shadowCoord.z ) +
				texture2DShadowLerp( shadowMap, shadowMapSize, shadowCoord.xy + vec2( dx1, 0.0 ), shadowCoord.z ) +
				texture2DShadowLerp( shadowMap, shadowMapSize, shadowCoord.xy + vec2( dx0, dy1 ), shadowCoord.z ) +
				texture2DShadowLerp( shadowMap, shadowMapSize, shadowCoord.xy + vec2( 0.0, dy1 ), shadowCoord.z ) +
				texture2DShadowLerp( shadowMap, shadowMapSize, shadowCoord.xy + vec2( dx1, dy1 ), shadowCoord.z )
			) * ( 1.0 / 9.0 );

		#else // no percentage-closer filtering:

			shadow = texture2DCompare( shadowMap, shadowCoord.xy, shadowCoord.z );

		#endif

		}

		return shadow;

	}

	// cubeToUV() maps a 3D direction vector suitable for cube texture mapping to a 2D
	// vector suitable for 2D texture mapping. This code uses the following layout for the
	// 2D texture:
	//
	// xzXZ
	//  y Y
	//
	// Y - Positive y direction
	// y - Negative y direction
	// X - Positive x direction
	// x - Negative x direction
	// Z - Positive z direction
	// z - Negative z direction
	//
	// Source and test bed:
	// https://gist.github.com/tschw/da10c43c467ce8afd0c4


	vec2 cubeToUV( vec3 v, float texelSizeY ) {

		// Number of texels to avoid at the edge of each square

		vec3 absV = abs( v );

		// Intersect unit cube

		float scaleToCube = 1.0 / max( absV.x, max( absV.y, absV.z ) );
		absV *= scaleToCube;

		// Apply scale to avoid seams

		// two texels less per square (one texel will do for NEAREST)
		v *= scaleToCube * ( 1.0 - 2.0 * texelSizeY );

		// Unwrap

		// space: -1 ... 1 range for each square
		//
		// #X##		dim    := ( 4 , 2 )
		//  # #		center := ( 1 , 1 )

		vec2 planar = v.xy;

		float almostATexel = 1.5 * texelSizeY;
		float almostOne = 1.0 - almostATexel;

		if ( absV.z >= almostOne ) {

			if ( v.z > 0.0 )
				planar.x = 4.0 - v.x;

		} else if ( absV.x >= almostOne ) {

			float signX = sign( v.x );
			planar.x = v.z * signX + 2.0 * signX;

		} else if ( absV.y >= almostOne ) {

			float signY = sign( v.y );
			planar.x = v.x + 2.0 * signY + 2.0;
			planar.y = v.z * signY - 2.0;

		}

		// Transform to UV space

		// scale := 0.5 / dim
		// translate := ( center + 0.5 ) / dim
		return vec2( 0.125, 0.25 ) * planar + vec2( 0.375, 0.75 );

	}

	float getPointShadow( sampler2D shadowMap, vec2 shadowMapSize, float shadowBias, float shadowRadius, vec4 shadowCoord, float shadowCameraNear, float shadowCameraFar ) {

		vec2 texelSize = vec2( 1.0 ) / ( shadowMapSize * vec2( 4.0, 2.0 ) );

		// for point lights, the uniform @vShadowCoord is re-purposed to hold
		// the vector from the light to the world-space position of the fragment.
		vec3 lightToPosition = shadowCoord.xyz;

		// dp = normalized distance from light to fragment position
		float dp = ( length( lightToPosition ) - shadowCameraNear ) / ( shadowCameraFar - shadowCameraNear ); // need to clamp?
		dp += shadowBias;

		// bd3D = base direction 3D
		vec3 bd3D = normalize( lightToPosition );

		#if defined( SHADOWMAP_TYPE_PCF ) || defined( SHADOWMAP_TYPE_PCF_SOFT )

			vec2 offset = vec2( - 1, 1 ) * shadowRadius * texelSize.y;

			return (
				texture2DCompare( shadowMap, cubeToUV( bd3D + offset.xyy, texelSize.y ), dp ) +
				texture2DCompare( shadowMap, cubeToUV( bd3D + offset.yyy, texelSize.y ), dp ) +
				texture2DCompare( shadowMap, cubeToUV( bd3D + offset.xyx, texelSize.y ), dp ) +
				texture2DCompare( shadowMap, cubeToUV( bd3D + offset.yyx, texelSize.y ), dp ) +
				texture2DCompare( shadowMap, cubeToUV( bd3D, texelSize.y ), dp ) +
				texture2DCompare( shadowMap, cubeToUV( bd3D + offset.xxy, texelSize.y ), dp ) +
				texture2DCompare( shadowMap, cubeToUV( bd3D + offset.yxy, texelSize.y ), dp ) +
				texture2DCompare( shadowMap, cubeToUV( bd3D + offset.xxx, texelSize.y ), dp ) +
				texture2DCompare( shadowMap, cubeToUV( bd3D + offset.yxx, texelSize.y ), dp )
			) * ( 1.0 / 9.0 );

		#else // no percentage-closer filtering

			return texture2DCompare( shadowMap, cubeToUV( bd3D, texelSize.y ), dp );

		#endif

	}

#endif

#ifdef USE_BUMPMAP

	uniform sampler2D bumpMap;
	uniform float bumpScale;

	// Bump Mapping Unparametrized Surfaces on the GPU by Morten S. Mikkelsen
	// http://api.unrealengine.com/attachments/Engine/Rendering/LightingAndShadows/BumpMappingWithoutTangentSpace/mm_sfgrad_bump.pdf


	// Evaluate the derivative of the height w.r.t. screen-space using forward differencing (listing 2)

	vec2 dHdxy_fwd() {

		vec2 dSTdx = dFdx( vUv );
		vec2 dSTdy = dFdy( vUv );

		float Hll = bumpScale * texture2D( bumpMap, vUv ).x;
		float dBx = bumpScale * texture2D( bumpMap, vUv + dSTdx ).x - Hll;
		float dBy = bumpScale * texture2D( bumpMap, vUv + dSTdy ).x - Hll;

		return vec2( dBx, dBy );

	}

	vec3 perturbNormalArb( vec3 surf_pos, vec3 surf_norm, vec2 dHdxy ) {

		// Workaround for Adreno 3XX dFd*( vec3 ) bug. See #9988

		vec3 vSigmaX = vec3( dFdx( surf_pos.x ), dFdx( surf_pos.y ), dFdx( surf_pos.z ) );
		vec3 vSigmaY = vec3( dFdy( surf_pos.x ), dFdy( surf_pos.y ), dFdy( surf_pos.z ) );
		vec3 vN = surf_norm;		// normalized

		vec3 R1 = cross( vSigmaY, vN );
		vec3 R2 = cross( vN, vSigmaX );

		float fDet = dot( vSigmaX, R1 );

		fDet *= ( float( gl_FrontFacing ) * 2.0 - 1.0 );

		vec3 vGrad = sign( fDet ) * ( dHdxy.x * R1 + dHdxy.y * R2 );
		return normalize( abs( fDet ) * surf_norm - vGrad );

	}

#endif

#ifdef USE_NORMALMAP

	uniform sampler2D normalMap;
	uniform vec2 normalScale;

	#ifdef OBJECTSPACE_NORMALMAP

		uniform mat3 normalMatrix;

	#else

		// Per-Pixel Tangent Space Normal Mapping
		// http://hacksoflife.blogspot.ch/2009/11/per-pixel-tangent-space-normal-mapping.html


		vec3 perturbNormal2Arb( vec3 eye_pos, vec3 surf_norm ) {

			// Workaround for Adreno 3XX dFd*( vec3 ) bug. See #9988

			vec3 q0 = vec3( dFdx( eye_pos.x ), dFdx( eye_pos.y ), dFdx( eye_pos.z ) );
			vec3 q1 = vec3( dFdy( eye_pos.x ), dFdy( eye_pos.y ), dFdy( eye_pos.z ) );
			vec2 st0 = dFdx( vUv.st );
			vec2 st1 = dFdy( vUv.st );

			float scale = sign( st1.t * st0.s - st0.t * st1.s ); // we do not care about the magnitude

			vec3 S = normalize( ( q0 * st1.t - q1 * st0.t ) * scale );
			vec3 T = normalize( ( - q0 * st1.s + q1 * st0.s ) * scale );
			vec3 N = normalize( surf_norm );
			mat3 tsn = mat3( S, T, N );

			vec3 mapN = texture2D( normalMap, vUv ).xyz * 2.0 - 1.0;

			mapN.xy *= normalScale;
			mapN.xy *= ( float( gl_FrontFacing ) * 2.0 - 1.0 );

			return normalize( tsn * mapN );

		}

	#endif

#endif

#ifdef USE_SPECULARMAP

	uniform sampler2D specularMap;

#endif

#ifdef USE_LOGDEPTHBUF

	uniform float logDepthBufFC;

	#ifdef USE_LOGDEPTHBUF_EXT

		varying float vFragDepth;

	#endif

#endif

#if NUM_CLIPPING_PLANES > 0

	#if ! defined( PHYSICAL ) && ! defined( PHONG )
		varying vec3 vViewPosition;
	#endif

	uniform vec4 clippingPlanes[ NUM_CLIPPING_PLANES ];

#endif