什么是重要性抽样？

import random
import math

N = 200000
TwoPi = 2.0 * math.pi

sum = 0.0

for i in range(N):
    x = random.uniform(0, TwoPi)

    fx = math.exp(-x) * math.sin(x)
    pdf = 1 / (TwoPi - 0.0)

    sum += fx / pdf

I = (1 / N) * sum
print(I)

void RenderPixel(uint x, uint y, UniformSampler *sampler) {
    Ray ray = m_scene->Camera.CalculateRayFromPixel(x, y, sampler);

    float3 color(0.0f);
    float3 throughput(1.0f);

    // Bounce the ray around the scene
    for (uint bounces = 0; bounces < 10; ++bounces) {
        m_scene->Intersect(ray);

        // The ray missed. Return the background color
        if (ray.geomID == RTC_INVALID_GEOMETRY_ID) {
            color += throughput * float3(0.846f, 0.933f, 0.949f);
            break;
        }

        // We hit an object

        // Fetch the material
        Material *material = m_scene->GetMaterial(ray.geomID);
        // The object might be emissive. If so, it will have a corresponding light
        // Otherwise, GetLight will return nullptr
        Light *light = m_scene->GetLight(ray.geomID);

        // If we hit a light, add the emmisive light
        if (light != nullptr) {
            color += throughput * light->Le();
        }

        float3 normal = normalize(ray.Ng);
        float3 wo = normalize(-ray.dir);
        float3 surfacePos = ray.org + ray.dir * ray.tfar;

        // Get the new ray direction
        // Choose the direction based on the material
        float3 wi = material->Sample(wo, normal, sampler);
        float pdf = material->Pdf(wi, normal);

        // Accumulate the brdf attenuation
        throughput = throughput * material->Eval(wi, wo, normal) / pdf;


        // Shoot a new ray

        // Set the origin at the intersection point
        ray.org = surfacePos;

        // Reset the other ray properties
        ray.dir = wi;
        ray.tnear = 0.001f;
        ray.tfar = embree::inf;
        ray.geomID = RTC_INVALID_GEOMETRY_ID;
        ray.primID = RTC_INVALID_GEOMETRY_ID;
        ray.instID = RTC_INVALID_GEOMETRY_ID;
        ray.mask = 0xFFFFFFFF;
        ray.time = 0.0f;
    }

    m_scene->Camera.FrameBuffer.SplatPixel(x, y, color);
}

// Get the new ray direction
// Choose the direction based on the material
float3 wi = material->Sample(wo, normal, sampler);
float pdf = material->Pdf(wi, normal);

void LambertBRDF::Sample(float3 outputDirection, float3 normal, UniformSampler *sampler) {
    float rand = sampler->NextFloat();
    float r = std::sqrtf(rand);
    float theta = sampler->NextFloat() * 2.0f * M_PI;

    float x = r * std::cosf(theta);
    float y = r * std::sinf(theta);

    // Project z up to the unit hemisphere
    float z = std::sqrtf(1.0f - x * x - y * y);

    return normalize(TransformToWorld(x, y, z, normal));
}

float3a TransformToWorld(float x, float y, float z, float3a &normal) {
    // Find an axis that is not parallel to normal
    float3a majorAxis;
    if (abs(normal.x) < 0.57735026919f /* 1 / sqrt(3) */) {
        majorAxis = float3a(1, 0, 0);
    } else if (abs(normal.y) < 0.57735026919f /* 1 / sqrt(3) */) {
        majorAxis = float3a(0, 1, 0);
    } else {
        majorAxis = float3a(0, 0, 1);
    }

    // Use majorAxis to create a coordinate system relative to world space
    float3a u = normalize(cross(normal, majorAxis));
    float3a v = cross(normal, u);
    float3a w = normal;


    // Transform from local coordinates to world coordinates
    return u * x +
           v * y +
           w * z;
}

float LambertBRDF::Pdf(float3 inputDirection, float3 normal) {
    return dot(inputDirection, normal) * M_1_PI;
}

// Accumulate the brdf attenuation
throughput = throughput * material->Eval(wi, wo, normal) / pdf;