Merge pull request #9928 from erichlof/dev

Optimize SkyShader.js with pre-calculated consts

examples/js/SkyShader.js

@@ -41,39 +41,41 @@ THREE.ShaderLib[ 'sky' ] = {
 		"varying vec3 vBetaM;",
 		"varying float vSunE;",
 
-		"const vec3 up = vec3(0.0, 1.0, 0.0);",
+		"const vec3 up = vec3( 0.0, 1.0, 0.0 );",
 
 		// constants for atmospheric scattering
 		"const float e = 2.71828182845904523536028747135266249775724709369995957;",
 		"const float pi = 3.141592653589793238462643383279502884197169;",
 
+		// wavelength of used primaries, according to preetham
+		"const vec3 lambda = vec3( 680E-9, 550E-9, 450E-9 );",
+		// this pre-calcuation replaces older TotalRayleigh(vec3 lambda) function:
+		// (8.0 * pow(pi, 3.0) * pow(pow(n, 2.0) - 1.0, 2.0) * (6.0 + 3.0 * pn)) / (3.0 * N * pow(lambda, vec3(4.0)) * (6.0 - 7.0 * pn))
+		"const vec3 totalRayleigh = vec3( 5.804542996261093E-6, 1.3562911419845635E-5, 3.0265902468824876E-5 );",
+		
 		// mie stuff
 		// K coefficient for the primaries
 		"const float v = 4.0;",
-		"const vec3 K = vec3(0.686, 0.678, 0.666);",
-
-		// see http://blenderartists.org/forum/showthread.php?321110-Shaders-and-Skybox-madness
-		// A simplied version of the total Reayleigh scattering to works on browsers that use ANGLE
-		"const vec3 simplifiedRayleigh = 0.0005 / vec3(94, 40, 18);",
-
-		// wavelength of used primaries, according to preetham
-		"const vec3 lambda = vec3(680E-9, 550E-9, 450E-9);",
+		"const vec3 K = vec3( 0.686, 0.678, 0.666 );",
+		// MieConst = pi * pow( ( 2.0 * pi ) / lambda, vec3( v - 2.0 ) ) * K
+		"const vec3 MieConst = vec3( 1.8399918514433978E14, 2.7798023919660528E14, 4.0790479543861094E14 );",
 
 		// earth shadow hack
-		"const float cutoffAngle = pi/1.95;",
+		// cutoffAngle = pi / 1.95;
+		"const float cutoffAngle = 1.6110731556870734;",
 		"const float steepness = 1.5;",
 		"const float EE = 1000.0;",
 
-		"float sunIntensity(float zenithAngleCos)",
+		"float sunIntensity( float zenithAngleCos )",
 		"{",
-			"zenithAngleCos = clamp(zenithAngleCos, -1.0, 1.0);",
-			"return EE * max(0.0, 1.0 - pow(e, -((cutoffAngle - acos(zenithAngleCos))/steepness)));",
+			"zenithAngleCos = clamp( zenithAngleCos, -1.0, 1.0 );",
+			"return EE * max( 0.0, 1.0 - pow( e, -( ( cutoffAngle - acos( zenithAngleCos ) ) / steepness ) ) );",
 		"}",
 
-		"vec3 totalMie(vec3 lambda, float T)",
+		"vec3 totalMie( float T )",
 		"{",
-			"float c = (0.2 * T ) * 10E-18;",
-			"return 0.434 * c * pi * pow((2.0 * pi) / lambda, vec3(v - 2.0)) * K;",
+			"float c = ( 0.2 * T ) * 10E-18;",
+			"return 0.434 * c * MieConst;",
 		"}",
 
 		"void main() {",
@@ -83,20 +85,20 @@ THREE.ShaderLib[ 'sky' ] = {
 
 			"gl_Position = projectionMatrix * modelViewMatrix * vec4( position, 1.0 );",
 
-			"vSunDirection = normalize(sunPosition);",
+			"vSunDirection = normalize( sunPosition );",
 
-			"vSunE = sunIntensity(dot(vSunDirection, up));",
+			"vSunE = sunIntensity( dot( vSunDirection, up ) );",
 
-			"vSunfade = 1.0-clamp(1.0-exp((sunPosition.y/450000.0)),0.0,1.0);",
+			"vSunfade = 1.0 - clamp( 1.0 - exp( ( sunPosition.y / 450000.0 ) ), 0.0, 1.0 );",
 
-			"float rayleighCoefficient = rayleigh - (1.0 * (1.0-vSunfade));",
+			"float rayleighCoefficient = rayleigh - ( 1.0 * ( 1.0 - vSunfade ) );",
 
 			// extinction (absorbtion + out scattering)
 			// rayleigh coefficients
-			"vBetaR = simplifiedRayleigh * rayleighCoefficient;",
+			"vBetaR = totalRayleigh * rayleighCoefficient;",
 
 			// mie coefficients
-			"vBetaM = totalMie(lambda, turbidity) * mieCoefficient;",
+			"vBetaM = totalMie( turbidity ) * mieCoefficient;",
 
 		"}"
 
@@ -114,7 +116,7 @@ THREE.ShaderLib[ 'sky' ] = {
 		"uniform float luminance;",
 		"uniform float mieDirectionalG;",
 
-		"const vec3 cameraPos = vec3(0., 0., 0.);",
+		"const vec3 cameraPos = vec3( 0.0, 0.0, 0.0 );",
 
 		// constants for atmospheric scattering
 		"const float pi = 3.141592653589793238462643383279502884197169;",
@@ -126,19 +128,25 @@ THREE.ShaderLib[ 'sky' ] = {
 		// optical length at zenith for molecules
 		"const float rayleighZenithLength = 8.4E3;",
 		"const float mieZenithLength = 1.25E3;",
-		"const vec3 up = vec3(0.0, 1.0, 0.0);",
-
-		"const float sunAngularDiameterCos = 0.999956676946448443553574619906976478926848692873900859324;",
+		"const vec3 up = vec3( 0.0, 1.0, 0.0 );",
 		// 66 arc seconds -> degrees, and the cosine of that
+		"const float sunAngularDiameterCos = 0.999956676946448443553574619906976478926848692873900859324;",
+
+		// 3.0 / ( 16.0 * pi )
+		"const float THREE_OVER_SIXTEENPI = 0.05968310365946075;",
+		// 1.0 / ( 4.0 * pi )
+		"const float ONE_OVER_FOURPI = 0.07957747154594767;",
 
-		"float rayleighPhase(float cosTheta)",
+		"float rayleighPhase( float cosTheta )",
 		"{",
-			"return (3.0 / (16.0*pi)) * (1.0 + pow(cosTheta, 2.0));",
+			"return THREE_OVER_SIXTEENPI * ( 1.0 + pow( cosTheta, 2.0 ) );",
 		"}",
 
-		"float hgPhase(float cosTheta, float g)",
+		"float hgPhase( float cosTheta, float g )",
 		"{",
-			"return (1.0 / (4.0*pi)) * ((1.0 - pow(g, 2.0)) / pow(1.0 - 2.0*g*cosTheta + pow(g, 2.0), 1.5));",
+			"float g2 = pow( g, 2.0 );",
+			"float inverse = 1.0 / pow( 1.0 - 2.0 * g * cosTheta + g2, 1.5 );",
+			"return ONE_OVER_FOURPI * ( ( 1.0 - g2 ) * inverse );",
 		"}",
 
 		// Filmic ToneMapping http://filmicgames.com/archives/75
@@ -151,9 +159,9 @@ THREE.ShaderLib[ 'sky' ] = {
 
 		"const float whiteScale = 1.0748724675633854;", // 1.0 / Uncharted2Tonemap(1000.0)
 
-		"vec3 Uncharted2Tonemap(vec3 x)",
+		"vec3 Uncharted2Tonemap( vec3 x )",
 		"{",
-		   "return ((x*(A*x+C*B)+D*E)/(x*(A*x+B)+D*F))-E/F;",
+			"return ( ( x * ( A * x + C * B ) + D * E ) / ( x * ( A * x + B ) + D * F ) ) - E / F;",
 		"}",
 
 
@@ -161,42 +169,43 @@ THREE.ShaderLib[ 'sky' ] = {
 		"{",
 			// optical length
 			// cutoff angle at 90 to avoid singularity in next formula.
-			"float zenithAngle = acos(max(0.0, dot(up, normalize(vWorldPosition - cameraPos))));",
-			"float sR = rayleighZenithLength / (cos(zenithAngle) + 0.15 * pow(93.885 - ((zenithAngle * 180.0) / pi), -1.253));",
-			"float sM = mieZenithLength / (cos(zenithAngle) + 0.15 * pow(93.885 - ((zenithAngle * 180.0) / pi), -1.253));",
+			"float zenithAngle = acos( max( 0.0, dot( up, normalize( vWorldPosition - cameraPos ) ) ) );",
+			"float inverse = 1.0 / ( cos( zenithAngle ) + 0.15 * pow( 93.885 - ( ( zenithAngle * 180.0 ) / pi ), -1.253 ) );",
+			"float sR = rayleighZenithLength * inverse;",
+			"float sM = mieZenithLength * inverse;",
 
 			// combined extinction factor
-			"vec3 Fex = exp(-(vBetaR * sR + vBetaM * sM));",
+			"vec3 Fex = exp( -( vBetaR * sR + vBetaM * sM ) );",
 
 			// in scattering
-			"float cosTheta = dot(normalize(vWorldPosition - cameraPos), vSunDirection);",
+			"float cosTheta = dot( normalize( vWorldPosition - cameraPos ), vSunDirection );",
 
-			"float rPhase = rayleighPhase(cosTheta*0.5+0.5);",
+			"float rPhase = rayleighPhase( cosTheta * 0.5 + 0.5 );",
 			"vec3 betaRTheta = vBetaR * rPhase;",
 
-			"float mPhase = hgPhase(cosTheta, mieDirectionalG);",
+			"float mPhase = hgPhase( cosTheta, mieDirectionalG );",
 			"vec3 betaMTheta = vBetaM * mPhase;",
 
-			"vec3 Lin = pow(vSunE * ((betaRTheta + betaMTheta) / (vBetaR + vBetaM)) * (1.0 - Fex),vec3(1.5));",
-			"Lin *= mix(vec3(1.0),pow(vSunE * ((betaRTheta + betaMTheta) / (vBetaR + vBetaM)) * Fex,vec3(1.0/2.0)),clamp(pow(1.0-dot(up, vSunDirection),5.0),0.0,1.0));",
+			"vec3 Lin = pow( vSunE * ( ( betaRTheta + betaMTheta ) / ( vBetaR + vBetaM ) ) * ( 1.0 - Fex ), vec3( 1.5 ) );",
+			"Lin *= mix( vec3( 1.0 ), pow( vSunE * ( ( betaRTheta + betaMTheta ) / ( vBetaR + vBetaM ) ) * Fex, vec3( 1.0 / 2.0 ) ), clamp( pow( 1.0 - dot( up, vSunDirection ), 5.0 ), 0.0, 1.0 ) );",
 
 			//nightsky
-			"vec3 direction = normalize(vWorldPosition - cameraPos);",
-			"float theta = acos(direction.y); // elevation --> y-axis, [-pi/2, pi/2]",
-			"float phi = atan(direction.z, direction.x); // azimuth --> x-axis [-pi/2, pi/2]",
-			"vec2 uv = vec2(phi, theta) / vec2(2.0*pi, pi) + vec2(0.5, 0.0);",
-			"vec3 L0 = vec3(0.1) * Fex;",
+			"vec3 direction = normalize( vWorldPosition - cameraPos );",
+			"float theta = acos( direction.y ); // elevation --> y-axis, [-pi/2, pi/2]",
+			"float phi = atan( direction.z, direction.x ); // azimuth --> x-axis [-pi/2, pi/2]",
+			"vec2 uv = vec2( phi, theta ) / vec2( 2.0 * pi, pi ) + vec2( 0.5, 0.0 );",
+			"vec3 L0 = vec3( 0.1 ) * Fex;",
 
 			// composition + solar disc
-			"float sundisk = smoothstep(sunAngularDiameterCos,sunAngularDiameterCos+0.00002,cosTheta);",
-			"L0 += (vSunE * 19000.0 * Fex)*sundisk;",
+			"float sundisk = smoothstep( sunAngularDiameterCos, sunAngularDiameterCos + 0.00002, cosTheta );",
+			"L0 += ( vSunE * 19000.0 * Fex ) * sundisk;",
 
-			"vec3 texColor = (Lin+L0) * 0.04 + vec3(0.0, 0.0003, 0.00075);",
+			"vec3 texColor = ( Lin + L0 ) * 0.04 + vec3( 0.0, 0.0003, 0.00075 );",
 
-			"vec3 curr = Uncharted2Tonemap((log2(2.0/pow(luminance,4.0)))*texColor);",
-			"vec3 color = curr*whiteScale;",
+			"vec3 curr = Uncharted2Tonemap( ( log2( 2.0 / pow( luminance, 4.0 ) ) ) * texColor );",
+			"vec3 color = curr * whiteScale;",
 
-			"vec3 retColor = pow(color,vec3(1.0/(1.2+(1.2*vSunfade))));",
+			"vec3 retColor = pow( color, vec3( 1.0 / ( 1.2 + ( 1.2 * vSunfade ) ) ) );",
 
 			"gl_FragColor.rgb = retColor;",