PBR（基于物理的渲染）学习笔记

PBR基本介绍

PBR代表基于物理的渲染，本质上还是

gl_FragColor = Emssive + Ambient + Diffuse + Specular

可能高级一些在考虑下AO也就是环境光遮蔽就是下面的情况

vec4 generalColor = （Ambient + Diffuse + Specular）；
gl_FragColor = Emssive +  mix(color, color * ao, u_OcclusionStrength)

在非PBR模式下，这种光照方式往往看着不真实，为啥呢，专家说因为能量不守恒，跟人眼在客观世界看到的不一样；然后就出现了基于物理的渲染。这种渲染模式呢，大方向模块还是以上那个。但是在各个模块计算过程中充分考虑了能量守恒，各个模块的计算式经过一系列复杂的数学推导计算出来。比如下面这个

•  L(P,V)是经过P点反射（diffuse或specular）后进入视点V的光
•  L(P,-V)是从-V方向射入P点的光

•  R是对应的BRDF（双向反射分布函数）函数，会考虑各种物理现象（能量守恒Energy conservation、粗糙度Roughness、材质的次表面散射subsurface scattering、材质折射率各向异性Fresnel、绝缘度（这玩意用来调整diffuse和specular的能量分配）metallic）

最讨厌这种公式，看着就让人烦，我们这里只要记住，BRDF就是从能量守恒角度考虑的一个计算公式，这个玩意具体公式是做实验做出来的，有好多个，最常用的一个叫Cook-Torrance。一般来说PBR计算过程是比较复杂的，直接在实时渲染里面计算式很耗费时间的，所以数学家有做了一堆拆分，让某些计算因子可以提前进行预处理，放在几个纹理中。对于工程师来说，我不想了解后面具体的物理学和数学推导，我只想知道怎么用来做项目。所以，一言不合看源码（源码来自luma.gl）。

vec4 pbr_filterColor(vec4 colorUnused)
{
  // Metallic and Roughness material properties are packed together
  // In glTF, these factors can be specified by fixed scalar values
  // or from a metallic-roughness map
  float perceptualRoughness = u_MetallicRoughnessValues.y;
  float metallic = u_MetallicRoughnessValues.x;
#ifdef HAS_METALROUGHNESSMAP
  // Roughness is stored in the 'g' channel, metallic is stored in the 'b' channel.
  // This layout intentionally reserves the 'r' channel for (optional) occlusion map data
  vec4 mrSample = texture2D(u_MetallicRoughnessSampler, pbr_vUV);
  perceptualRoughness = mrSample.g * perceptualRoughness;
  metallic = mrSample.b * metallic;
#endif
  perceptualRoughness = clamp(perceptualRoughness, c_MinRoughness, 1.0);
  metallic = clamp(metallic, 0.0, 1.0);
  // Roughness is authored as perceptual roughness; as is convention,
  // convert to material roughness by squaring the perceptual roughness [2].
  float alphaRoughness = perceptualRoughness * perceptualRoughness;

  // The albedo may be defined from a base texture or a flat color
#ifdef HAS_BASECOLORMAP
  vec4 baseColor = SRGBtoLINEAR(texture2D(u_BaseColorSampler, pbr_vUV)) * u_BaseColorFactor;
#else
  vec4 baseColor = u_BaseColorFactor;
#endif

#ifdef ALPHA_CUTOFF
  if (baseColor.a < u_AlphaCutoff) {
    discard;
  }
#endif

  vec3 f0 = vec3(0.04);
  vec3 diffuseColor = baseColor.rgb * (vec3(1.0) - f0);
  diffuseColor *= 1.0 - metallic;
  vec3 specularColor = mix(f0, baseColor.rgb, metallic);

  // Compute reflectance.
  float reflectance = max(max(specularColor.r, specularColor.g), specularColor.b);

  // For typical incident reflectance range (between 4% to 100%) set the grazing
  // reflectance to 100% for typical fresnel effect.
  // For very low reflectance range on highly diffuse objects (below 4%),
  // incrementally reduce grazing reflecance to 0%.
  float reflectance90 = clamp(reflectance * 25.0, 0.0, 1.0);
  vec3 specularEnvironmentR0 = specularColor.rgb;
  vec3 specularEnvironmentR90 = vec3(1.0, 1.0, 1.0) * reflectance90;

  vec3 n = getNormal();                          // normal at surface point
  vec3 v = normalize(u_Camera - pbr_vPosition);  // Vector from surface point to camera

  float NdotV = clamp(abs(dot(n, v)), 0.001, 1.0);
  vec3 reflection = -normalize(reflect(v, n));

  PBRInfo pbrInputs = PBRInfo(
    0.0, // NdotL
    NdotV,
    0.0, // NdotH
    0.0, // LdotH
    0.0, // VdotH
    perceptualRoughness,
    metallic,
    specularEnvironmentR0,
    specularEnvironmentR90,
    alphaRoughness,
    diffuseColor,
    specularColor,
    n,
    v
  );

  vec3 color = vec3(, , );

#ifdef USE_LIGHTS
  // Apply ambient light
  PBRInfo_setAmbientLight(pbrInputs);
  color += calculateFinalColor(pbrInputs, lighting_uAmbientLight.color);

  // Apply directional light
  SMART_FOR(int i = , i < MAX_LIGHTS, i < lighting_uDirectionalLightCount, i++) {
    if (i < lighting_uDirectionalLightCount) {
      PBRInfo_setDirectionalLight(pbrInputs, lighting_uDirectionalLight[i].direction);
      color += calculateFinalColor(pbrInputs, lighting_uDirectionalLight[i].color);
    }
  }

  // Apply point light
  SMART_FOR(int i = , i < MAX_LIGHTS, i < lighting_uPointLightCount, i++) {
    if (i < lighting_uPointLightCount) {
      PBRInfo_setPointLight(pbrInputs, lighting_uPointLight[i]);
      float attenuation = getPointLightAttenuation(lighting_uPointLight[i], distance(lighting_uPointLight[i].position, pbr_vPosition));
      color += calculateFinalColor(pbrInputs, lighting_uPointLight[i].color / attenuation);
    }
  }
#endif

  // Calculate lighting contribution from image based lighting source (IBL)
#ifdef USE_IBL
  color += getIBLContribution(pbrInputs, n, reflection);
#endif

  // Apply optional PBR terms for additional (optional) shading
#ifdef HAS_OCCLUSIONMAP
  float ao = texture2D(u_OcclusionSampler, pbr_vUV).r;
  color = mix(color, color * ao, u_OcclusionStrength);
#endif

#ifdef HAS_EMISSIVEMAP
  vec3 emissive = SRGBtoLINEAR(texture2D(u_EmissiveSampler, pbr_vUV)).rgb * u_EmissiveFactor;
  color += emissive;
#endif

  // This section uses mix to override final color for reference app visualization
  // of various parameters in the lighting equation.
#ifdef PBR_DEBUG
  // TODO: Figure out how to debug multiple lights

  // color = mix(color, F, u_ScaleFGDSpec.x);
  // color = mix(color, vec3(G), u_ScaleFGDSpec.y);
  // color = mix(color, vec3(D), u_ScaleFGDSpec.z);
  // color = mix(color, specContrib, u_ScaleFGDSpec.w);

  // color = mix(color, diffuseContrib, u_ScaleDiffBaseMR.x);
  color = mix(color, baseColor.rgb, u_ScaleDiffBaseMR.y);
  color = mix(color, vec3(metallic), u_ScaleDiffBaseMR.z);
  color = mix(color, vec3(perceptualRoughness), u_ScaleDiffBaseMR.w);
#endif

  return vec4(pow(color,vec3(1.0/2.2)), baseColor.a);
}

一堆数学计算看不懂。。。没关系，慢慢拆分

如果模型采用PBR材质，最少需要两个两张纹理：albedo和metalRoughness。Albedo对应该模型的纹理，就是我们常用的的baseColor。metalRoughness对应rgba的g和b两位，范围是[0,1]，对应模型的g(roughness)和b(metallic)。这个metallic属性，用来描述该模型对应P点在绝缘体和金属之间的一个度，金属的反射率相对较高，该系数用来调整diffuse和specular的能量分配。那么这一部分，主要目的是求一个粗糙度和绝缘系数。

// Metallic and Roughness material properties are packed together
  // In glTF, these factors can be specified by fixed scalar values
  // or from a metallic-roughness map
  float perceptualRoughness = u_MetallicRoughnessValues.y;
  float metallic = u_MetallicRoughnessValues.x;
#ifdef HAS_METALROUGHNESSMAP
  // Roughness is stored in the 'g' channel, metallic is stored in the 'b' channel.
  // This layout intentionally reserves the 'r' channel for (optional) occlusion map data
  vec4 mrSample = texture2D(u_MetallicRoughnessSampler, pbr_vUV);
  perceptualRoughness = mrSample.g * perceptualRoughness;
  metallic = mrSample.b * metallic;
#endif
  perceptualRoughness = clamp(perceptualRoughness, c_MinRoughness, 1.0);
  metallic = clamp(metallic, 0.0, 1.0);
  // Roughness is authored as perceptual roughness; as is convention,
  // convert to material roughness by squaring the perceptual roughness [2].
  float alphaRoughness = perceptualRoughness * perceptualRoughness;

上面说的albedo从下面的纹理中获取

  // The albedo may be defined from a base texture or a flat color
#ifdef HAS_BASECOLORMAP
  vec4 baseColor = SRGBtoLINEAR(texture2D(u_BaseColorSampler, pbr_vUV)) * u_BaseColorFactor;
#else
  vec4 baseColor = u_BaseColorFactor;
#endif

#ifdef ALPHA_CUTOFF
  if (baseColor.a < u_AlphaCutoff) {
    discard;
  }
#endif

下面代码是求了一个镜像反射系数，这个镜像反射系数为了满足菲涅尔效果，在不同角度下系数不一样（4%~100%）之间。下面的25就是1/0.4的值。specularEnvironmentR0 和 specularEnvironmentR90 我猜是代表视线和法线夹角在0和90的一个反射颜色。

  // Compute reflectance.
  float reflectance = max(max(specularColor.r, specularColor.g), specularColor.b);

  // For typical incident reflectance range (between 4% to 100%) set the grazing
  // reflectance to 100% for typical fresnel effect.
  // For very low reflectance range on highly diffuse objects (below 4%),
  // incrementally reduce grazing reflecance to 0%.
  // 对于典型的入射反射范围(在4%到100%之间)，将掠射反射率设置为100%以获得典型的菲涅耳效果。对于高度漫反射对象上的极低反射范围(低于4%)，请以增量方式将掠过反射减少到0%。
  float reflectance90 = clamp(reflectance * 25.0, 0.0, 1.0);
  vec3 specularEnvironmentR0 = specularColor.rgb;
  vec3 specularEnvironmentR90 = vec3(1.0, 1.0, 1.0) * reflectance90;

根据法线和视线计算出夹角和反射向量。getNormal的计算过程也是涉及到法向量切变空间，这个后续在继续。同时这里要特别注意这个向量的原点在哪里，这是在视空间还是世界空间中的计算。

  vec3 n = getNormal();                          // normal at surface point
  vec3 v = normalize(u_Camera - pbr_vPosition);  // Vector from surface point to camera

  float NdotV = clamp(abs(dot(n, v)), 0.001, 1.0);
  vec3 reflection = -normalize(reflect(v, n));

组装PBRInfo以及设置初始颜色值

PBRInfo pbrInputs = PBRInfo(
    0.0, // NdotL
    NdotV,
    0.0, // NdotH
    0.0, // LdotH
    0.0, // VdotH
    perceptualRoughness,
    metallic,
    specularEnvironmentR0,
    specularEnvironmentR90,
    alphaRoughness,
    diffuseColor,
    specularColor,
    n,
    v
  );

  vec3 color = vec3(0, 0, 0);

根据不同的光源类型，环境光、方向光源、点光源进行光照计算。这个跟普通的光照模式一样

#ifdef USE_LIGHTS
  // Apply ambient light
  PBRInfo_setAmbientLight(pbrInputs);
  color += calculateFinalColor(pbrInputs, lighting_uAmbientLight.color);

  // Apply directional light
  SMART_FOR(int i = 0, i < MAX_LIGHTS, i < lighting_uDirectionalLightCount, i++) {
    if (i < lighting_uDirectionalLightCount) {
      PBRInfo_setDirectionalLight(pbrInputs, lighting_uDirectionalLight[i].direction);
      color += calculateFinalColor(pbrInputs, lighting_uDirectionalLight[i].color);
    }
  }

  // Apply point light
  SMART_FOR(int i = 0, i < MAX_LIGHTS, i < lighting_uPointLightCount, i++) {
    if (i < lighting_uPointLightCount) {
      PBRInfo_setPointLight(pbrInputs, lighting_uPointLight[i]);
      float attenuation = getPointLightAttenuation(lighting_uPointLight[i], distance(lighting_uPointLight[i].position, pbr_vPosition));
      color += calculateFinalColor(pbrInputs, lighting_uPointLight[i].color / attenuation);
    }
  }
#endif

这块可以认为是除了普通的环境光之外，其他来自四面发放的光。光源在环境中经过其他各种物体反射、折射等汇集而来的光。

  // Calculate lighting contribution from image based lighting source (IBL)
#ifdef USE_IBL
  color += getIBLContribution(pbrInputs, n, reflection);
#endif

下面是计算环境光遮蔽的效果，这个也是提前处理在一张纹理上了。环境光遮蔽又是一个专门的话题。

文档：Cesium源码剖析---Ambient Occlusion(?..

链接：http://note.youdao.com/noteshare?id=5d3122657947fcb43010948ea5f7d627&sub=D56577007ABC43A696F84D0CA968EA27

上面这个是安哥写的文章。

  // Apply optional PBR terms for additional (optional) shading
#ifdef HAS_OCCLUSIONMAP
  float ao = texture2D(u_OcclusionSampler, pbr_vUV).r;
  color = mix(color, color * ao, u_OcclusionStrength);
#endif

处理自发光的纹理。这里纹理都是在gamma颜色空间中，要先转变成线性空间。gamma的来龙去脉也是个专题。

文档：ThreeJS 不可忽略的事情 - Gamma色彩空...

链接：http://note.youdao.com/noteshare?id=f5ab02acba1260bb2e0be26c56a9d281&sub=77FA63C5D6C24A2D8202B1D623519666

#ifdef HAS_EMISSIVEMAP
  vec3 emissive = SRGBtoLINEAR(texture2D(u_EmissiveSampler, pbr_vUV)).rgb * u_EmissiveFactor;
  color += emissive;
#endif

最后就是由线性空间转变成gamma空间。

return vec4(pow(color,vec3(1.0/2.2)), baseColor.a);

PBR核心

看起来也很简单是不，那是因为大部分代码都封装在calculateFinalColor函数中了。

接下来看一下PBR真正的核心：

vec3 calculateFinalColor(PBRInfo pbrInputs, vec3 lightColor) {
  // Calculate the shading terms for the microfacet specular shading model
  vec3 F = specularReflection(pbrInputs);
  float G = geometricOcclusion(pbrInputs);
  float D = microfacetDistribution(pbrInputs);

  // Calculation of analytical lighting contribution
  vec3 diffuseContrib = (1.0 - F) * diffuse(pbrInputs);
  vec3 specContrib = F * G * D / (4.0 * pbrInputs.NdotL * pbrInputs.NdotV);
  // Obtain final intensity as reflectance (BRDF) scaled by the energy of the light (cosine law)
  return pbrInputs.NdotL * lightColor * (diffuseContrib + specContrib);
}

再回到最初这个公式：

现在根据代码来重新解释下面几个部分。

•  L(P,V)是经过P点反射（diffuse或specular）后进入视点V的光；就是return的返回值
•  L(P,-V)是从-V方向射入P点的光，可以认为代码中的lightColor
•  R是对应的BRDF（双向反射分布函数）函数，可以认为是代码中的（diffuseContrib + specContrib）部分
•  N*V' 是代码中的pbrInputs.NdotL

这里的BRDF是根据下面公式来的。

diffuse采用的是Lambert模型：

，C是漫反射光的颜色Color，这里认为该点微观上是一个平面，漫反射以一个半圆180°均匀反射，所以除以π；至于这里的代码是考虑了菲涅尔效果，进行了一个调整，为啥这么搞我也不是很清楚。

// Basic Lambertian diffuse
// Implementation from Lambert's Photometria https://archive.org/details/lambertsphotome00lambgoog
// See also [1], Equation 1
vec3 diffuse(PBRInfo pbrInputs)
{
  return pbrInputs.diffuseColor / M_PI;
}

而后就是Specular部分，这个里面有FGD三个因素，分别是考虑菲涅尔反射、L光源能够到达V视角的概率、表面粗糙度。

(F)resnel reflectance；菲涅尔反射

既然是Fresnel，不难理解，该函数主要是用来计算不同介质之间光的折射，简化后的Schlick公式可以取得近似值，公式如下，在中心点时l和h为零度角，cos=1.为F(0)，为该材质的base reflectivity，在45°时，还基本不变，但接近90°时，则反射率则迅速提升到1，符合之前Fresnel的变化曲线

// The following equation models the Fresnel reflectance term of the spec equation (aka F())
// Implementation of fresnel from [4], Equation 15
vec3 specularReflection(PBRInfo pbrInputs)
{
  return pbrInputs.reflectance0 +
    (pbrInputs.reflectance90 - pbrInputs.reflectance0) *
    pow(clamp(1.0 - pbrInputs.VdotH, 0.0, 1.0), 5.0);
}

(G)eometric term

表示从L光源能够到达V视角的概率，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（如下图所示），这里glTF采用的是GGX，而Cesium则是Schlick模型：（不过luma的代码好像做了一些优化，具体没细研究）

最后考虑到能量守恒，需要在diffuse和specular之间添加参数，控制两者的比例，这里也有多种方式，比如前面提到的Disney给出的公式(glTF和Cesium中都采用该公式)，也有论文里提到的diffuse Fresnel term：

// This calculates the specular geometric attenuation (aka G()),
// where rougher material will reflect less light back to the viewer.
// This implementation is based on [1] Equation 4, and we adopt their modifications to
// alphaRoughness as input as originally proposed in [2].
float geometricOcclusion(PBRInfo pbrInputs)
{
  float NdotL = pbrInputs.NdotL;
  float NdotV = pbrInputs.NdotV;
  float r = pbrInputs.alphaRoughness;

  float attenuationL = 2.0 * NdotL / (NdotL + sqrt(r * r + (1.0 - r * r) * (NdotL * NdotL)));
  float attenuationV = 2.0 * NdotV / (NdotV + sqrt(r * r + (1.0 - r * r) * (NdotV * NdotV)));
  return attenuationL * attenuationV;
}

Normal (d)istribution term

该函数用来描述材质的roughness，在能量守恒下，控制物体在反射与折射间的分配，glTF中采用的是Trowbridge-Reitz GGX公式，其中α是唯一参数，而h可以通过粗糙度α和法线n求解：

（又是一堆公式，以后遇到直接拿来用，不在公式上花费时间）

// The following equation(s) model the distribution of microfacet normals across
// the area being drawn (aka D())
// Implementation from "Average Irregularity Representation of a Roughened Surface
// for Ray Reflection" by T. S. Trowbridge, and K. P. Reitz
// Follows the distribution function recommended in the SIGGRAPH 2013 course notes
// from EPIC Games [1], Equation 3.
float microfacetDistribution(PBRInfo pbrInputs)
{
  float roughnessSq = pbrInputs.alphaRoughness * pbrInputs.alphaRoughness;
  float f = (pbrInputs.NdotH * roughnessSq - pbrInputs.NdotH) * pbrInputs.NdotH + 1.0;
  return roughnessSq / (M_PI * f * f);
}

IBL

现在环境光、点光源、平行光的计算基本说清楚了。还有一种是来自四面八方的光照计算。

对于来自四面八方的光，就有一个求和的过程，这里，对该积分做了如下两步近似求解

因为如上的近似推导，证明我们可以通过EnvironmentMap和BRDF lookup table两张纹理，对Sum求和的过程预处理，减少real time下的计算量。（这里是直接拷贝大牛的文章，根据我的理解就是IBLContrib部分可以简化成两个部分，环境贴图和一个根据BRDF公式计算出来的一个纹理（LUT，lookup table），这个纹理里面存储了对四面八方的光的specular部分进行参数调节的两个变量）

Environment Map和BRDF lookup table。前者根据不同的Roughness，计算对应光源的平均像素值。后者根据Roughness和视角计算出对应颜色的调整系数（scale和bias）。虽然两部分的计算量比较大，但都可以预处理，通常Cube Texture都是固定的，我们可以预先获取对应的Environment Map，根据Roughness构建MipMap；后者只跟Roughness和视角V的cos有关，一旦确定了BRDF模型，计算公式是固定的，也可以预先生成U(Roughness) V(cosV)对应的 Texture：

Cook-TorranceModel对应的LUT

这样，我们可以获取环境光的计算公式如下：

finalColor += PrefilteredColor * ( SpecularColor* EnvBRDF.x + EnvBRDF.y );

（这里理论和代码不是完全一致，这里的EnvironmentMap分为了两个，u_DiffuseEnvSampler和u_SpecularEnvSampler，当然这两个都是需要提前准备的）

// Calculation of the lighting contribution from an optional Image Based Light source.
// Precomputed Environment Maps are required uniform inputs and are computed as outlined in [1].
// See our README.md on Environment Maps [3] for additional discussion.
#ifdef USE_IBL
vec3 getIBLContribution(PBRInfo pbrInputs, vec3 n, vec3 reflection)
{
  float mipCount = 9.0; // resolution of 512x512
  float lod = (pbrInputs.perceptualRoughness * mipCount);
  // retrieve a scale and bias to F0. See [1], Figure 3
  vec3 brdf = SRGBtoLINEAR(texture2D(u_brdfLUT,
    vec2(pbrInputs.NdotV, 1.0 - pbrInputs.perceptualRoughness))).rgb;
  vec3 diffuseLight = SRGBtoLINEAR(textureCube(u_DiffuseEnvSampler, n)).rgb;

#ifdef USE_TEX_LOD
  vec3 specularLight = SRGBtoLINEAR(textureCubeLodEXT(u_SpecularEnvSampler, reflection, lod)).rgb;
#else
  vec3 specularLight = SRGBtoLINEAR(textureCube(u_SpecularEnvSampler, reflection)).rgb;
#endif

  vec3 diffuse = diffuseLight * pbrInputs.diffuseColor;
  vec3 specular = specularLight * (pbrInputs.specularColor * brdf.x + brdf.y);

  // For presentation, this allows us to disable IBL terms
  diffuse *= u_ScaleIBLAmbient.x;
  specular *= u_ScaleIBLAmbient.y;

  return diffuse + specular;
}
#endif

渲染部分基本讲完了，这里面还涉及几个辅助函数用来设置一些向量乘积变量。

void PBRInfo_setAmbientLight(inout PBRInfo pbrInputs) {
  pbrInputs.NdotL = 1.0;
  pbrInputs.NdotH = 0.0;
  pbrInputs.LdotH = 0.0;
  pbrInputs.VdotH = 1.0;
}

void PBRInfo_setDirectionalLight(inout PBRInfo pbrInputs, vec3 lightDirection) {
  vec3 n = pbrInputs.n;
  vec3 v = pbrInputs.v;
  vec3 l = normalize(lightDirection);             // Vector from surface point to light
  vec3 h = normalize(l+v);                        // Half vector between both l and v

  pbrInputs.NdotL = clamp(dot(n, l), 0.001, 1.0);
  pbrInputs.NdotH = clamp(dot(n, h), 0.0, 1.0);
  pbrInputs.LdotH = clamp(dot(l, h), 0.0, 1.0);
  pbrInputs.VdotH = clamp(dot(v, h), 0.0, 1.0);
}

void PBRInfo_setPointLight(inout PBRInfo pbrInputs, PointLight pointLight) {
  vec3 light_direction = normalize(pointLight.position - pbr_vPosition);
  PBRInfo_setDirectionalLight(pbrInputs, light_direction);
}

还有将gamma颜色空间转成线性空间的函数

vec4 SRGBtoLINEAR(vec4 srgbIn)
{
#ifdef MANUAL_SRGB
#ifdef SRGB_FAST_APPROXIMATION
  vec3 linOut = pow(srgbIn.xyz,vec3(2.2));
#else //SRGB_FAST_APPROXIMATION
  vec3 bLess = step(vec3(0.04045),srgbIn.xyz);
  vec3 linOut = mix( srgbIn.xyz/vec3(12.92), pow((srgbIn.xyz+vec3(0.055))/vec3(1.055),vec3(2.4)), bLess );
#endif //SRGB_FAST_APPROXIMATION
  return vec4(linOut,srgbIn.w);;
#else //MANUAL_SRGB
  return srgbIn;
#endif //MANUAL_SRGB
}

以及获取法向量的函数，关于法向量纹理，里面涉及切向量空间，又是另外一个专题，不展开了。

// Find the normal for this fragment, pulling either from a predefined normal map
// or from the interpolated mesh normal and tangent attributes.
vec3 getNormal()
{
  // Retrieve the tangent space matrix
#ifndef HAS_TANGENTS
  vec3 pos_dx = dFdx(pbr_vPosition);
  vec3 pos_dy = dFdy(pbr_vPosition);
  vec3 tex_dx = dFdx(vec3(pbr_vUV, 0.0));
  vec3 tex_dy = dFdy(vec3(pbr_vUV, 0.0));
  vec3 t = (tex_dy.t * pos_dx - tex_dx.t * pos_dy) / (tex_dx.s * tex_dy.t - tex_dy.s * tex_dx.t);

#ifdef HAS_NORMALS
  vec3 ng = normalize(pbr_vNormal);
#else
  vec3 ng = cross(pos_dx, pos_dy);
#endif

  t = normalize(t - ng * dot(ng, t));
  vec3 b = normalize(cross(ng, t));
  mat3 tbn = mat3(t, b, ng);
#else // HAS_TANGENTS
  mat3 tbn = pbr_vTBN;
#endif

#ifdef HAS_NORMALMAP
  vec3 n = texture2D(u_NormalSampler, pbr_vUV).rgb;
  n = normalize(tbn * ((2.0 * n - 1.0) * vec3(u_NormalScale, u_NormalScale, 1.0)));
#else
  // The tbn matrix is linearly interpolated, so we need to re-normalize
  vec3 n = normalize(tbn[2].xyz);
#endif

  return n;
}

以及PBRInfo信息：

// Encapsulate the various inputs used by the various functions in the shading equation
// We store values in this struct to simplify the integration of alternative implementations
// of the shading terms, outlined in the Readme.MD Appendix.
struct PBRInfo
{
  float NdotL;                  // cos angle between normal and light direction
  float NdotV;                  // cos angle between normal and view direction
  float NdotH;                  // cos angle between normal and half vector
  float LdotH;                  // cos angle between light direction and half vector
  float VdotH;                  // cos angle between view direction and half vector
  float perceptualRoughness;    // roughness value, as authored by the model creator (input to shader)
  float metalness;              // metallic value at the surface
  vec3 reflectance0;            // full reflectance color (normal incidence angle)
  vec3 reflectance90;           // reflectance color at grazing angle
  float alphaRoughness;         // roughness mapped to a more linear change in the roughness (proposed by [2])
  vec3 diffuseColor;            // color contribution from diffuse lighting
  vec3 specularColor;           // color contribution from specular lighting
  vec3 n;                       // normal at surface point
  vec3 v;                       // vector from surface point to camera
};

部分图和文字借用了一些大佬的文章，侵权请联系我，必删！

参考文章

https://mp.weixin.qq.com/s?__biz=MzA5MDcyOTE5Nw==&mid=2650545802&idx=1&sn=282eec1403c901cbf406141ec668a96a&scene=19#wechat_redirect

https://blog.csdn.net/qjh5606/article/details/89948573

https://mp.weixin.qq.com/s?__biz=MzA5MDcyOTE5Nw==&mid=2650545891&idx=1&sn=938f1e2d37864bf0cff5ec9e308fdae0&scene=19#wechat_redirect

https://zhuanlan.zhihu.com/p/58692781?utm_source=wechat_session

https://zhuanlan.zhihu.com/p/58641686

https://zhuanlan.zhihu.com/c_1084126907469135872

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