Nori Implement Write-up

Nori assignments implement write up.

Nori, a educational oriented path tracing renderer. In this project, will implement with path tracing, accelerate structure and many features with pbrt.

Part 1. Accelerate with Octree.

1.1 Baseline

Without octree, it will take over 7 hours on rendering one frame with single object(My cpu: AMD 7800X3D).

Without octree:

slow

1.2 Sort distance

It will 100 times faster than before.

With octree:

fast

Result screenshot:

Part 2.

Part 2.1 Monte Carlo Sampling

Tent sample

c++
/**
 * @brief 反函数，p(z)
 *
 * @param z
 * @return float
 */
float tent(float z) {
    if (z >= 0.0f && z < 0.5f) {
        return std::sqrt(2 * z) - 1.0f;
    } else if (z >= 0.5f && z <= 1.0f) {
        return 1.0f - std::sqrt(2 - 2 * z);
    }
    return 0.0f;
}

Point2f Warp::squareToTent(const Point2f& sample) {
    return sample.unaryExpr([](auto elem) { return tent(elem); });
}

/**
 * @brief tent PDF(概率密度函数)
 *
 * @param t
 * @return float
 */
inline float tentPDF(float t) {
    auto absf = std::abs(t);
    return absf <= 1.0f ? (1.0f - absf) : 0.0f;
}

float Warp::squareToTentPdf(const Point2f& p) {
    return tentPDF(p.x()) * tentPDF(p.y());
}

tent

Disk

c++
Point2f Warp::squareToUniformDisk(const Point2f& sample) {
    auto r   = std::sqrt(sample.x());
    auto phi = 2.0f * M_PI * sample.y();
    return {r * std::cos(phi), r * std::sin(phi)};
}

float Warp::squareToUniformDiskPdf(const Point2f& p) {
    return (p.squaredNorm() <= 1.0f) ? INV_PI : 0.0f;
}