cg:pbr

float r = lightRadius; vec3 L = lightPosition - vertexPosition; float dist = length(L); float d = max( dist - r, 0.0 ); L /= dist; float denom = d / r + 1.0; float attenuation = 1.0 / (denom*denom); float cutoff = 0.0052; attenuation = (attenuation - cutoff) / (1.0 - cutoff); attenuation = max(attenuation, 0.0); return attenuation;

vec3 N = normalize( vNormal ); vec3 V = normalize( uCamPosition - vPosition ); vec3 L = normalize( uLightPosition - vPosition ); vec3 H = normalize(V + L);

float attenuation = getAttenuation( uLightPosition, vPosition, uLightRadius ); float D = D_GGX(uRoughness,NoH); float Vis = Vis_Smith(uRoughness,NoV,NoL); vec3 F = F_Schlick(specularColor,VoH);

float a = Roughness * Roughness; float Phi = 2 * PI * Xi.x; float CosTheta = sqrt( (1 - Xi.y) / ( 1 + (a*a - 1) * Xi.y ) ); float SinTheta = sqrt( 1 - CosTheta * CosTheta ); float3 H; H.x = SinTheta * cos( Phi ); H.y = SinTheta * sin( Phi ); H.z = CosTheta; float3 UpVector = abs(N.z) < 0.999 ? float3(0,0,1) : float3(1,0,0); float3 TangentX = normalize( cross( UpVector , N ) ); float3 TangentY = cross( N, TangentX ); // Tangent to world space return TangentX * H.x + TangentY * H.y + N * H.z;

float3 SpecularLighting = 0; const uint NumSamples = 1024; for( uint i = 0; i < NumSamples; i++ ) { float2 Xi = Hammersley( i, NumSamples ); float3 H = ImportanceSampleGGX( Xi, Roughness , N ); float3 L = 2 * dot( V, H ) * H - V; float NoV = saturate( dot( N, V ) ); float NoL = saturate( dot( N, L ) ); float NoH = saturate( dot( N, H ) ); float VoH = saturate( dot( V, H ) ); if( NoL > 0 ) { float3 SampleColor = EnvMap.SampleLevel( EnvMapSampler , L, 0 ).rgb; float G = G_Smith( Roughness , NoV, NoL ); float Fc = pow( 1 - VoH, 5 ); float3 F = (1 - Fc) * SpecularColor + Fc; // Incident light = SampleColor * NoL // Microfacet specular = D*G*F / (4*NoL*NoV) // pdf = D * NoH / (4 * VoH) SpecularLighting += SampleColor * F * G * VoH / (NoH * NoV); } } return SpecularLighting / NumSamples;

float3 N = R; float3 V = R; float3 PrefilteredColor = 0; const uint NumSamples = 1024; for( uint i = 0; i < NumSamples; i++ ) { float2 Xi = Hammersley( i, NumSamples ); float3 H = ImportanceSampleGGX( Xi, Roughness , N ); float3 L = 2 * dot( V, H ) * H - V; float NoL = saturate( dot( N, L ) ); if( NoL > 0 ) { PrefilteredColor += EnvMap.SampleLevel( EnvMapSampler , L, 0 ).rgb * NoL; TotalWeight += NoL; } } return PrefilteredColor / TotalWeight;

if (NoL > 0){ float Vis = Vis_SmithJointApprox(Roughness, NoV, NoL); //#Incident light = NoL //#pdf = D * NoH / (4 * VoH) //#NoL * Vis / pdf float NoL_Vis_PDF = NoL * Vis * (4 * VoH / NoH); float Fc = pow(1 - VoH, 5); A += (1 - Fc) * NoL_Vis_PDF; B += Fc * NoL_Vis_PDF; } } return Vector2(A / NumSamples, B / NumSamples);

//# [ Lazarov 2013, "Getting More Physical in Call of Duty: Black Ops II" ] //# Adaptation to fit our G term. Vector4 c0 = Vector4(-1, -0.0275, -0.572, 0.022); Vector4 c1 = Vector4(1, 0.0425, 1.04, -0.04); Vector4 r = c0 * (Roughness) + c1; float a004 = min(r.x * r.x, pow(2, -9.28 * NoV)) * r.x + r.y; Vector2 AB = Vector2(-1.04, 1.04)*(a004) + Vector2(r.z, r.w); return AB;

Vector4 DiffuseLighting; unsigned NumSamples = 4096 * 2; //for i in range(NumSamples) : for (unsigned int i = 0; i < NumSamples; i++){ Vector2 E = Hammersley(i, NumSamples, Random); Vector3 C = CosineSampleHemisphere(E); Vector3 L = TangentToWorld(C, N);

float NoL = saturate(N.dot(L));; //#print("NoL", NoL); if (NoL > 0){ Vector2 uv2 = pos2uv(L); Vector4 result = img.getPixel32Int(uv2.x * img.width, uv2.y * img.height); //#lambert = DiffuseColor * NoL / PI //#pdf = NoL / PI float e = 1.0; if (hdr) { e = result.w - 128.0; e = pow(2, e); } DiffuseLighting.x += result.x * e; DiffuseLighting.y += result.y * e; DiffuseLighting.z += result.z * e; DiffuseLighting.w += 255; } } float Weight = 1.0 / NumSamples; DiffuseLighting = DiffuseLighting * (Weight); return DiffuseLighting;

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\mathrm{n} \cdot \mathrm{h})^2(\alpha ^2-1)+1)^2} [/latex]</p> <h1> 4.遮挡项G </h1> G称为双向阴影遮挡函数，也就是v会被其他的微面元遮挡，G主要受粗糙度影响，是用Smith GGX分布<p/> Geometry Factor Smith GGX <p style=“text-align: center;”>[latex] \alpha = Roughness^2 [/latex]</p> <p style=“text-align: center;”>[latex] G_{GGX}(\mathrm{k})=\frac{2(\mathrm{n} \cdot \mathrm{k})}{(\mathrm{n} \cdot \mathrm{k}) + \sqrt{\alpha^2+(1-\alpha^2)(\mathrm{n} \cdot \mathrm{k})^2 }} [/latex]</p> <p style=“text-align: center;”>[latex] G(\mathrm{l},\mathrm{v},\mathrm{h})=G_1(\mathrm{l})G_1(\mathrm{v}) [/latex]</p> <h1> 5.漫反射Diffuse </h1> Lambert模型 <p style=“text-align: center;”>[latex] f_d(\mathrm{l},\mathrm{v}) = \frac{c_\mathrm{diff}}{\pi} [/latex]</p> <h1> 6.UE4材质模型 </h1> <h5> 6.1 Basecolor </h5> Basecolor就是材质的基础颜色，也就是材质的漫反射颜色，即漫反射公式中的[latex]c_{diff}[/latex]，漫反射颜色的本质是，光线在照射材质后，光线进入材质内部经过复杂散射后出来的光，这个散射后的光丧失了方向。与之对应的是高光，高光直接在材质上反射，映射的直接是光的颜色 <h5> 6.2 Roughness </h5> 粗糙度是影响D和G的重要参数 <h5> 6.3 Metallic </h5> 金属是个很特殊的参数，影响的是漫反射diff和菲涅尔项F，当材质为纯金属的时候原来漫反射为0（可理解为纯金属的时候进入材质的的光和金属发生光电反应，全部以热能的形式消耗掉），而此时[latex]F_0[/latex]就是diff。<p/> 非金属的情况，当完全是非金属的时候，漫反射就是diff，此时[latex]F_0[/latex]就是下面的Specular <h5> 6.4 Specular </h5> 由金属的参数性质可知，Specular只有在非金属的情况才生效，根据非金属的菲涅尔的图标可以看出[latex]F_0[/latex]的范围大致在0.03到0.08之间<p/> <p/> <p/> 根据6.3和6.4可得出 <p style=“text-align: center;”>[latex] diffuseColor = baseColor*(1-metallic) [/latex]</p> <p style=“text-align: center;”>[latex] specularColor = mix(0.08*specular,baseColor,metallic) [/latex]</p> <h1> 7.精确光源 </h1> <p style=“text-align: center;”>[latex] f=f_d+f_r [/latex]</p> <p style=“text-align: center;”>[latex] =\frac{c_{diff}}{\pi } + \frac{FDG}{4 (n\cdot l) (n \cdot v)} [/latex]</p> <p style=“text-align: center;”>[latex] =\frac{c_{diff}}{\pi } + (F_0+(1-F_0)(1-v\cdot h)^5)(\frac{\alpha ^2}{\pi ((\mathrm{n} \cdot \mathrm{h})^2(\alpha ^2-1)+1)^2})((\frac{2(\mathrm{n} \cdot \mathrm{l})}{(\mathrm{n} \cdot \mathrm{l}) + \sqrt{\alpha^2+(1-\alpha^2)(\mathrm{n} \cdot \mathrm{l})^2 }})(\frac{2(\mathrm{n} \cdot \mathrm{v})}{(\mathrm{n} \cdot \mathrm{v}) + \sqrt{\alpha^2+(1-\alpha^2)(\mathrm{n} \cdot \mathrm{v})^2 }}

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\mathrm{n} \cdot \mathrm{h})^2(\alpha ^2-1)+1)^2})((\frac{1}{(\mathrm{n} \cdot \mathrm{l}) + \sqrt{\alpha^2+(1-\alpha^2)(\mathrm{n} \cdot \mathrm{l})^2 }})(\frac{1}{(\mathrm{n} \cdot \mathrm{v}) + \sqrt{\alpha^2+(1-\alpha^2)(\mathrm{n} \cdot \mathrm{v})^2 }}