问基于重要性抽样的BRDF集成

EN

float f(Vec3f sampleDir) { return sampleDir.z; }
float pdf(Vec3f sampleDir) { return sampleDir.z; } // cosine function is also its PDF

void uniformIntegrationCos()
{
    double sum = 0.0;
    const int N = 1000;
    for (int i = 0; i < N; ++i)
    {
        Vec3f sampleDir = randomHemisphere(i, N); // fibonacci hemisphere spiral

        float value = f(sampleDir);
        float weight = sampleDir.z; // NdotL == pdf(sample)
        sum += value * weight / PI / N; // divide by PI to normalize cosine-weighted PDF

    }
    const float HEMISPHERE_SOLID_ANGLE = 2.f * PI; // integration area
    sum *= HEMISPHERE_SOLID_ANGLE;

    std::cout << "Sum = " << sum << std::endl;
}

void importanceIntegrationCos()
{
    double sum = 0.0;
    const int N = 1000;
    for (int i = 0; i < N; ++i)
    {
        // generate sample direction using inversed CDF of cosine BRDF
        Vec2f r = randomHammersley(i, N);
        float phi = 2.f * PI * r.x;
        float sinTheta = sqrt(r.y);
        float cosTheta = sqrtf(1.f - sinTheta * sinTheta);

        Vec3f sampleDir;
        sampleDir.x = cos(phi) * sinTheta;
        sampleDir.y = sin(phi) * sinTheta;
        sampleDir.z = cosTheta;

        float value = f(sampleDir);
        sum += value / N; // BRDF is divided by it's PDF, so no NdotL weight and no PDF normalization by dividing by PI
    }

    //const float HEMISPHERE_SOLID_ANGLE = 2.f * PI; // integration area
    //sum *= HEMISPHERE_SOLID_ANGLE; // Not needed, why ???

    std::cout << "Sum = " << sum << std::endl;
}

void main()
{
    uniformIntegrationCos();
    importanceIntegrationCos();
}