---

layout: default title: (Task 4) Path Tracing permalink: /pathtracer/path_tracing parent: "A3: Pathtracer" usemathjax: true

---

(Task 4) Path Tracing

Up to this point, your renderer has only computed object visibility using ray tracing. Now, we will simulate the complicated paths that light can take throughout the scene, bouncing off many surfaces before eventually reaching the camera. Simulating this multi-bounce light is referred to as global illumination, and it is critical for producing realistic images, especially when specular surfaces are present. Note that all functions in bsdf.cpp are in local space to the surface with respect to the ray intersection point, while functions in pathtracer.cpp are generally in world space.

---

Step 1: Pathtracer::trace

Pathtracer::trace is the function responsible for coordinating the path tracing procedure. We've given you code to intersect a ray with the scene and collect information about the surface intersection necessary for computing the lighting at that point. You should read this function and remove the early-out that colors surfaces based on their normal direction.

Step 2: BSDF_Lambertian

Implement BSDF_Lambertian::scatter, BSDF_Lambertian::evaluate, and BSDF_Lambertian::pdf. Note that their interfaces are defined in rays/bsdf.h. Task 5 will further discuss sampling BSDFs, so reading ahead may help your understanding.

• BSDF_Lambertian::albedo is the ratio of incoming light to reflected light, also known as the base color of the Lambertian material. Note that this quantity is automatically divided by pi.

• BSDF_Lambertian::scatter returns a Scatter object, with direction and attenuation components. You can access the material's sampler object to randomly sample a direction from a cosine-weighted hemisphere distribution and, you can compute the attenuation component via BSDF_Lambertian::evaluate.

• BSDF_Lambertian::evaluate computes the ratio of incoming to outgoing radiance given a pair of directions. Traditionally, BSDFs are specified as the ratio of incoming radiance to outgoing irradiance, which necessitates the extra cos(theta) factor in the rendering equation. In Scotty3D, however, we expect the BSDF to operate only on radiance, so you must scale the evaluation accordingly.

• BSDF_Lambertian::pdf computes the PDF for sampling some incoming direction given some outgoing direction. However, the Lambertian BSDF in particular does not depend on the outgoing direction. Since we sampled the incoming direction from a cosine-weighted hemisphere distribution, what is its PDF?

Note: a variety of sampling functions are provided in student/samplers.cpp. The Lambertian BSDF includes a cosine-weighted hemisphere sampler Samplers::Hemisphere::Cosine sampler (see rays/bsdf.h).

Step 3: Pathtracer::sample_indirect_lighting

In this function, you will estimate light that bounced off at least one other surface before reaching our shading point. This is called indirect lighting.

• (1) Randomly sample a new ray direction from the BSDF distribution using BSDF::scatter().

• (2) Create a new world-space ray and call Pathtracer::trace() to get incoming light. You should modify Ray::dist_bounds so that the ray does not intersect at time = 0. Remember to set the new depth value.

• (3) Compute Monte Carlo estimate of incoming indirect light scaled by BSDF attenuation.

Step 4: Pathtracer::sample_direct_lighting

Finally, you will estimate light that hit our shading point after being emitted from a light source without any bounces in between. For now, you should use the same sampling procedure as Pathtracer::sample_indirect_lighting, except for using the direct component of incoming light. Note that since we are only interested in light emitted from the first intersection, we can trace a ray with depth = 0.

Note: separately sampling direct lighting might seem silly, as we could have just gotten both direct and indirect lighting from tracing a single BSDF sample. However, separating the components will allow us to improve our direct light sampling algorithm in task 6.

---

Reference Results

After correctly implementing task 4, your renderer should be able to make a beautifully lit picture of the Cornell Box with Lambertian spheres (cbox_lambertian.dae). Below is a render using 1024 samples per pixel (spp):

Note the time-quality tradeoff here. This image was rendered with a sample rate of 1024 camera rays per pixel and a max ray depth of 8. This will produce a relatively high quality result, but will take quite some time to render. Rendering a fully converged image may take a even longer, so start testing your path tracer early!

Thankfully, runtime will scale (roughly) linearly with the number of samples. Below are the results and runtime of rendering the Lambertian cornell box at 720p on a Ryzen 5950x (max ray depth 8):

---

Extra Credit

• Instead of setting a maximum ray depth, implement un-biased russian roulette for path termination. Though russian roulette will increase variance, use of a good heuristic (such as overall path throughput) should improve performance enough to show better convergence in an equal-time comparison. Refer to Physically Based Rendering chapter 13.7.

• (Advanced) Implement homogeneous volumetric scattering. Refer to Physically Based Rendering chapters 11 and 15.