修正辐照度预积分贴图计算的重要性采样算法

25-IBL-MultiInstance-Sphere/Shader/GRS_IBL_BRDF_Integration_LUT.hlsl

@@ -48,7 +48,7 @@ float2 IntegrateBRDF(float NdotV, float roughness)
 		float NdotH = max(H.z, 0.0); // N = (0.0f, 0.0f, 1.0f);
 		float VdotH = max(dot(V, H), 0.0);
 
-		if (NdotL > 0.0)
+		if ( NdotL > 0.0 )
 		{
 			float G = GeometrySmith_IBL(N, V, L, roughness);
 			float G_Vis = (G * VdotH) / (NdotH * NdotV);

25-IBL-MultiInstance-Sphere/Shader/GRS_IBL_Diffuse_Irradiance_Convolution_With_Monte_Carlo_PS.hlsl

@@ -10,72 +10,50 @@ struct ST_GRS_HLSL_PS_INPUT
     float3 m_v4WPos : POSITION;
 };
 
-float2 UniformOnDisk(float Xi)
-{
-    float theta = TWO_PI * Xi;
-    return float2(cos(theta), sin(theta));
-}
-
-float3 CosOnHalfSphere(float2 Xi)
-{
-    float   r = sqrt(Xi.x);
-    float2  pInDisk = r * UniformOnDisk(Xi.y);
-    float   z = sqrt(1 - Xi.x);
-    return float3(pInDisk, z);
-}
-
-float4 Quarternion_ZTo(float3 to)
-{
-    // from = (0, 0, 1)
-    //float cosTheta = dot(from, to);
-    //float cosHalfTheta = sqrt(max(0, (cosTheta + 1) * 0.5));
-    float cosHalfTheta = sqrt(max(0, (to.z + 1) * 0.5));
-    //float3 axisSinTheta = cross(from, to);
-    //    0    0    1
-    // to.x to.y to.z
-    //float3 axisSinTheta = float3(-to.y, to.x, 0);
-    float twoCosHalfTheta = 2 * cosHalfTheta;
-    return float4(-to.y / twoCosHalfTheta, to.x / twoCosHalfTheta, 0, cosHalfTheta);
-}
-
-float4 Quarternion_Inverse(float4 q) 
-{
-    return float4(-q.xyz, q.w);
-}
-
-float3 Quarternion_Rotate(float4 q, float3 p)
-{
-    // Quarternion_Mul(Quarternion_Mul(q, float4(p, 0)), Quarternion_Inverse(q)).xyz;
-
-    float4 qp = float4(q.w * p + cross(q.xyz, p), -dot(q.xyz, p));
-    float4 invQ = Quarternion_Inverse(q);
-    float3 qpInvQ = qp.w * invQ.xyz + invQ.w * qp.xyz + cross(qp.xyz, invQ.xyz);
-    return qpInvQ;
-}
-
-float3 CosOnHalfSphere(float2 Xi, float3 N)
-{
-    float3 p    = CosOnHalfSphere(Xi);
-    float4 rot  = Quarternion_ZTo(N);
-    return Quarternion_Rotate(rot, p);
-}
-
 float4 PSMain(ST_GRS_HLSL_PS_INPUT stPSInput) :SV_Target
 {
     float3 N = normalize(stPSInput.m_v4WPos.xyz);
 
     float3 irradiance = float3(0.0f,0.0f,0.0f);
 
-    const uint SAMPLE_NUM = GRS_INT_SAMPLES_CNT;
+    // 计算切空间
+    float3 Up = float3(0.0f, 1.0f, 0.0f);
+    float fdot = dot(Up, N);
+    if ((1.0 - fdot) > 1e-6)
+    {
+        Up = float3(1.0f, 0.0f, 0.0f);
+    }
+
+    float3 Right = normalize(cross(Up, N));
+    Up = normalize(cross(N, Right));
+    N = normalize(cross(Right, Up));
 
+
+    float theta = 0.0f;
+    float phi = 0.0f;
+    float2 Xi;
+    float3 L;
+
+    const uint SAMPLE_NUM = 4096u;
+    // 蒙特卡洛积分循环
     for (uint i = 0u; i < SAMPLE_NUM; i++)
     {
-        float2 Xi = Hammersley(i, SAMPLE_NUM);
-        float3 L = CosOnHalfSphere(Xi, N);
+        // 产生均匀分布随机数
+        Xi = Hammersley(i, SAMPLE_NUM);
+
+        // 根据 CDF 反函数计算指定分布的随机变量
+        phi = TWO_PI * Xi.x;
+        theta = asin(sqrt(Xi.y));
 
+        // 球坐标转换到笛卡尔坐标（切空间）
+        L = float3(sin(theta) * cos(phi), sin(theta) * sin(phi), cos(theta));
+        // 切空间转换到世界坐标空间
+        L = L.x * Right + L.y * Up + L.z * N;
+
+        // 采样求和统计入射辐照度
         irradiance += g_texHDREnvCubemap.Sample(g_sapLinear, L).xyz;
     }
-
+    // 取平均得到最终结果
     irradiance *= 1.0 / float(SAMPLE_NUM);
 
     return float4(irradiance,1.0f);