GGX BRDF ImplementationGGX BRDF 实现

Microfacet Theory — The Cook-Torrance Model微表面理论 — Cook-Torrance 模型

NeoX uses the standard Cook-Torrance microfacet specular BRDF, the same family used by UE5, Frostbite, and most modern PBR engines. The specular term is:

NeoX 使用标准的 Cook-Torrance 微表面镜面 BRDF，与 UE5、Frostbite 和大多数现代 PBR 引擎同族。高光项为：

D: GGX Normal Distribution FunctionD: GGX 法线分布函数

The D_GGX function (Trowbridge-Reitz distribution) determines what fraction of microfacets are oriented to reflect light toward the viewer. Higher roughness = wider distribution = blurrier highlights.

D_GGX 函数（Trowbridge-Reitz 分布）决定有多少微表面朝向将光线反射到观察者的方向。粗糙度越高 = 分布越宽 = 高光越模糊。

// [Walter et al. 2007, "Microfacet models for refraction through rough surfaces"]
float D_GGX(float a2, float NoH) {
  NoH = min(0.999, NoH);                      // prevent singularity at NoH=1
  float d = (NoH * a2 - NoH) * NoH + 1;       // 2 mad
  return a2 / (PI * d * d);                    // 4 mul, 1 rcp
}

// Optimized version with pre-squared roughness (used in isotropy.hlsl)
float GGXTerm_ApproxWithPrecomputedVar(float NdotH, float roughness_pow2) {
  float a = roughness_pow2 * roughness_pow2;   // a = roughness^4
  NdotH = min(0.9999, NdotH);
  float d = (NdotH * a - NdotH) * NdotH + 1.0;
  return a * rcp(max(PI * d * d, FLT_MIN));
}

F: Schlick Fresnel ApproximationF: Schlick 菲涅尔近似

The Fresnel term determines how much light is reflected vs transmitted at different viewing angles. At grazing angles, all surfaces become highly reflective.

菲涅尔项决定在不同观察角度下有多少光被反射而非透射。在掠射角度，所有表面都会变得高度反射。

float3 F_Schlick(float3 SpecularColor, float VoH) {
  float Fc = Pow5(1 - VoH);                    // (1-cosθ)^5
  // 2% minimum: anything below is physically impossible (shadowing)
  return saturate(50.0 * SpecularColor.g) * Fc
       + (1 - Fc) * SpecularColor;
}

G: Smith Joint GGX VisibilityG: Smith 联合 GGX 可见性

The geometry/visibility term accounts for microfacets blocking each other (masking and shadowing). NeoX implements the height-correlated Smith approximation:

几何/可见性项考虑微表面相互遮挡（遮蔽和阴影）。NeoX 实现了高度相关 Smith 近似：

// New engine: lambdaV/L computation vectorized into float2
float SmithJointGGXVisibilityTerm(float NdotL, float NdotV, float roughness_pow2) {
  float a = roughness_pow2;
  float2 lambdaVL = float2(NdotL, NdotV) * (float2(NdotV, NdotL) * (1 - a) + a);
  // NOTE: FLT_MIN changed to FLT_MIN_SAFE in new engine for more robust guard
  return 0.5 * rcp(max(lambdaVL.x + lambdaVL.y, FLT_MIN_SAFE));
}

// Alternative: Schlick approximation (used for anisotropy)
float Vis_Schlick(float Roughness_pow2, float NoV, float NoL) {
  float k = Roughness_pow2 * 0.5;
  float Vis_SchlickV = NoV * (1 - k) + k;
  float Vis_SchlickL = NoL * (1 - k) + k;
  return 0.25 / (Vis_SchlickV * Vis_SchlickL);
}

Anisotropic GGX各向异性 GGX

For brushed metal and hair, NeoX supports anisotropic specular via D_GGXaniso (Disney's Burley 2012 formulation):

对于拉丝金属和头发，NeoX 通过 D_GGXaniso 支持各向异性高光（Disney Burley 2012 公式）：

// [Burley 2012, "Physically-Based Shading at Disney"]
float D_GGXaniso(float RoughnessX, float RoughnessY,
                 float NoH, float3 H, float3 X, float3 Y) {
  float mx = RoughnessX * RoughnessX;
  float my = RoughnessY * RoughnessY;
  float XoH = dot(X, H);
  float YoH = dot(Y, H);
  float d = XoH*XoH / (mx*mx) + YoH*YoH / (my*my) + NoH*NoH;
  return 1 / (mx * my * d * d);
}

Environment BRDF — Split-Sum Approximation环境 BRDF — 分离求和近似

For IBL (Image-Based Lighting), evaluating the full integral is too expensive. NeoX uses the EnvBRDFApprox from Lazarov 2013 (same as UE4's original implementation). In the new engine the LUT math is extracted into a separate EnvBRDFLUTApprox helper:

对于 IBL（基于图像的光照），计算完整积分太昂贵。NeoX 使用来自 Lazarov 2013 的 EnvBRDFApprox（与 UE4 原始实现相同）。新引擎将 LUT 数学提取到独立的 EnvBRDFLUTApprox 辅助函数中：

// New engine: LUT math extracted into reusable helper
float2 EnvBRDFLUTApprox(float Roughness, float NoV) {
  const float4 c0 = { -1, -0.0275, -0.572, 0.022 };
  const float4 c1 = {  1,  0.0425,  1.04, -0.04 };
  float4 r = Roughness * c0 + c1;
  float a004 = min(r.x * r.x, exp2(-9.28 * NoV)) * r.x + r.y;
  return float2(-1.04, 1.04) * a004 + r.zw;
}

// [Lazarov 2013] Main function now wraps the LUT helper
float3 EnvBRDFApprox(float3 SpecularColor, float Roughness, float NoV) {
  float2 AB = EnvBRDFLUTApprox(Roughness, NoV);
  return SpecularColor * AB.x + AB.y;
}

Full Specular Assembly — How It All Connects完整高光组装 — 如何组合

In the isotropy.hlsl shading model, the final specular term is assembled from D, G, and the Fresnel applied outside:

在 isotropy.hlsl 着色模型中，最终高光项由 D、G 和外部应用的菲涅尔组装：

// From isotropy.hlsl -- LightingSpecular()
float3 LightingSpecular(...) {
  return max(0.0,
    SmithJointGGXVisibilityTerm(n_dot_l, n_dot_v_abs, roughness_pow2)  // G term
    * GGXTerm_ApproxWithPrecomputedVar(n_dot_h, roughness_pow2)        // D term
    * n_dot_l                                                          // N.L
  );
}

// Called from DirectLighting():
light_specular = LightingSpecular(...) * data_rw.fresnel * data_rw.atten;
//                                       ^ F_Schlick      ^ shadow*light

New Functions: D_Quadratic & Cloth Sheen BRDF新增函数：D_Quadratic 与布料 Sheen BRDF

The new engine adds a cheaper quadratic NDF approximation and a Sheen BRDF LUT polynomial specifically for the new sheen.hlsl and cloth.hlsl shading models:

新引擎增加了一个更廉价的二次 NDF 近似和一个专门用于新 sheen.hlsl 和 cloth.hlsl 着色模型的 Sheen BRDF LUT 多项式：

// NEW: D_Quadratic — cheap quadratic NDF, cheaper than full GGX
// Used for low-quality approximations or special effects
float D_Quadratic(float a, float NoH) {
  float t = (1 - a * a);
  return lerp(1.0, a, t);  // linearly blends flat vs peaked distribution
}

// NEW: EnvClothSheenLUT3rd — polynomial LUT approximation for cloth sheen IBL
// Replaces a texture LUT lookup with a rational polynomial approximation
float EnvClothSheenLUT3rd(float R, float NoV) {
  // a, b, c, Offset = constants baked from the sheen DFG integral
  return a * R / (b * R + c * NoV + NoV * R) + Offset;
}