I am currently implementing a Path tracer, and I want to implement the Multiple importance sampling which use two distributions (Light and BRDF) at each bounce to evaluate direct lighting

我目前正在实现一个路径跟踪器，我想实现多重重要性采样，它在每次反弹时使用两个分布(Light和BRDF)来评估直接照明

This is my MIS implementation (implement in recursive funtion):

这是我的管理信息系统实现(以递归函数实现)：

   vec3 TraceMISRecur(const Ray& WorldRay, int MaxDepth, std::vector<Object*>& World, Object* Lights) {
        if (MaxDepth == 0) return vec3::Zero();
        // direct integral, use light dis and brdf dis to approx
        HitRecord Record;
        bool Flag = HitClosest(WorldRay, Record, World);
        if (!Flag) return vec3::Zero();
        vec3 L_direct = vec3::Zero(), L_indirect = vec3::Zero();
        
        vec3 LightSample;
        float PdfOnLight;
        vec3 LightColor;
        vec3 LightNormal;
        SampleLights(LightSample, PdfOnLight, LightColor, LightNormal, Lights);

        vec3 SurfacePosition = Record.HitPoint;
        vec3 Dir = LightSample - SurfacePosition;
        float Distance = Dir.norm();
        Dir.stableNormalize();
        bool HitOtherObject = HitAny(Ray(SurfacePosition, Dir), World);
        HitOtherObject |= LightNormal.dot(-Dir.stableNormalized()) < 0;
        HitOtherObject |= Dir.dot(Record.Normal) < 0;
        if (!HitOtherObject) {
            float GFactor = GeometryFactor(SurfacePosition, LightSample, LightNormal);
            float LightpdfOnHemisphere = PdfOnLight / GFactor;
            vec3 BRDF = Record.Mat->BRDF(-WorldRay.B, Dir, Record);
            float MatPdf = Record.Mat->PDF(-WorldRay.B, Dir, Record);
            vec3 Le = LightColor;
            float MISWeight = BalanceHuristic(LightpdfOnHemisphere, MatPdf);
            L_direct += MISWeight * BRDF.cwiseProduct(Le) * Dir.dot(Record.Normal) / LightpdfOnHemisphere;
        }

        vec3 Wi = Record.Mat->Sample(-WorldRay.B, Record);
        float MatPdf = Record.Mat->PDF(-WorldRay.B, Wi, Record);
        vec3 BRDF = Record.Mat->BRDF(-WorldRay.B, Wi, Record);
        HitRecord LightRecord;
        bool HitLight = Lights->IntersectClosest(Ray(Record.HitPoint, Wi), LightRecord);

        if (HitLight) {
            float GFactor = GeometryFactor(SurfacePosition, LightRecord.HitPoint, LightRecord.Normal);
            int LightIndex = LightRecord.PrimitiveIndex;
            float LightArea = Lights->Primitives[LightIndex]->GetArea();
            float LightpdfOnHemisphere = 1. / Lights->Primitives.size() / LightArea / GFactor;
            vec3 Le = LightRecord.Mat->BRDF();
            float MISWeight = BalanceHuristic(MatPdf, LightpdfOnHemisphere);
            L_direct += MISWeight * BRDF.cwiseProduct(Le) * Wi.dot(Record.Normal) / MatPdf;
        }

        // indirect
        L_indirect = BRDF.cwiseProduct(TraceMISRecur(Ray(Record.HitPoint, Wi), MaxDepth - 1, World, Lights)) * Wi.dot(Record.Normal) / MatPdf;
        return L_direct + L_indirect;
    }

This is my Brute force implementation (which I think can produce ground truth image):

这是我的蛮力实现(我认为它可以产生真实的图像)：

    vec3 Trace(Ray &WorldRay, int MaxDepth, std::vector<Object*> &World) {
        vec3 Background = vec3::Zero();
        vec3 Throughput = vec3::Ones();
        vec3 OutputRadiance = vec3::Zero();
        HitRecord Record;
        for (int i = 0; i < MaxDepth; i++) {
            HitRecord Record;
            bool Flag = HitClosest(WorldRay, Record, World);
            if (!Flag) {
                // currently, the env light not included in MIS
                OutputRadiance += Throughput.cwiseProduct(Background);
                return OutputRadiance;
            }
            int MaterialType = Record.Mat->MaterialType();
            bool IsBackFace = Record.IsBackFace;
            vec3 Wi = Record.Mat->Sample(WorldRay.B, Record);
            float pdf = Record.Mat->PDF(WorldRay.B, Wi, Record);
            vec3 BRDF = Record.Mat->BRDF(WorldRay.B, Wi, Record);
            if (MaterialType == EMISSION) {
                if (IsBackFace) return vec3::Zero();
                OutputRadiance += Throughput.cwiseProduct(BRDF);
                return OutputRadiance;
            }
            Throughput = Throughput.cwiseProduct(BRDF) * Wi.dot(Record.Normal) / pdf;
            WorldRay = Ray(Record.HitPoint, Wi);
        }
        return vec3::Zero();
    }

But when I compare the result of MIS to brute force, the MIS result is brigher, here is the comparision:

但当我将管理信息系统的结果与蛮力进行比较时，管理信息系统的结果更有说服力，下面是比较：

The MIS result (small light):

管理信息系统结果(小灯)：

The brute force result (small light):

暴力效果(小光)：

The MIS result (larger light):

管理信息系统结果(较大的灯光)：

The brute force result (larger light):

暴力的结果(更大的光)：

I think there is something wrong with my MIS implementation, but I can't find it, Could you give me some hint? thanks.

我想我的管理信息系统的实施有问题，但我找不到，你能给我一些提示吗？谢谢。