For Part 4, your task is to render images with full global illumination, including a probabilistic estimate of infinite bounces of light.

Your job will be to implement the functions called est_radiance_global_illumination, zero_bounce_radiance, one_bounce_radiance, and at_least_one_bounce_radiance (which is recursive) in pathtracer.cpp.

  • The function est_radiance_global_illumination is called to get an estimate of the total radiance with global illumination arriving at a point from a particular direction (e.g. on the image plane and going towards the image's center of projection).
  • The function zero_bounce_radiance should return light that results from no bounces of light, which is simply the light emitted by the given point and outgoing direction. This will be zero (black) unless the current point lies on a light.
  • The function one_bounce_radiance is just the direct illumination that you implemented in Part 3. You can just call your direct lighting function that uses importance sampling of the lights.
  • The function at_least_one_bounce_radiance is the main implementation work for this Part 4. At a high level, it should call the one_bounce_radiance function, and then recursively call itself to estimate the higher bounces. This recursive call should take one random sample from the BSDF at the hit point, trace a ray in that sample direction, and recursively call itself on the new hit point.

Make sure you take a look at the pseudocode on slides 61-63 from lecture 17.

We provide with the same setup code as in the direct lighting function:

Matrix3x3 o2w;
make_coord_space(o2w, isect.n);
Matrix3x3 w2o = o2w.T();

Vector3D hit_p = r.o + r.d * isect.t;
Vector3D w_out = w2o * (-r.d);

As in part 3, w2o transforms world space vectors into a local coordinate frame where the normal is (0,0,1)(0,0,1), the unit vector in the zz direction. Thus w_out is the outgoing radiance direction in this local frame.

You need to implement the following steps:

  1. For zero_bounce_radiance, use the BSDF's get_emission() function to determine if light is emitted from the intersection point.

  2. For one_bounce_radiance, call a direct illumination function depending on the direct_hemisphere_sample program paramater.

  3. For at_least_one_bounce_radiance: Take a sample from the surface BSDF at the intersection point using isect.bsdf->sample_f(). This function requests the outgoing radiance direction w_out and returns the BSDF value as a Spectrum as well as 2 values by pointer. The values returned by pointer are

    • the probabilistically sampled w_in unit vector giving the incoming radiance direction (note that unlike the direction returned by sample_L, this w_in vector is in the object coordinate frame!) and
    • a pdf float giving the probability density function evaluated at the return w_in direction.

  4. Use Russian roulette to decide whether to randomly terminate the ray. In theory, the probability of not terminating can be arbitrary. But in order to see the Russian roulette's effect more clearly, we recommend to use something like 0.6 or 0.7. You can use the coin_flip method from random_util.h to generate randomness.

  5. Check other conditions of terminating a ray. Specifically, if indirect illumination is turned on (max_ray_depth>1), we always trace at least one indirect bounce regardless of the Russian roulette. Also, for the ray depth cutoff to work, you should initialize your camera rays' depths as max_ray_depth in raytrace_pixel, then decrease their depths by 1 at every bounce, until the depths drop to 1.

  6. If not terminating, create a ray that starts from EPS_D away from the hit point and travels in the direction of o2w * w_in (the incoming radiance direction converted to world coordinates). And remember to decrease its depth by 1.

  7. Use at_least_one_bounce_radiance to recursively trace this ray, getting an approximation for its incoming radiance.

  8. Convert this incoming radiance into an outgoing radiance estimator by scaling by the BSDF and a cosine factor and dividing by the BSDF pdf and one minus the Russian roulette termination probability.

You still can only render diffuse BSDFs until completing Part 5, however, you should now see some nice color bleeding in Lambertian scenes. You should be able to correctly render images such as

./pathtracer -t 8 -s 64 -l 16 -m 5 -r 480 360 -f spheres.png ../dae/sky/CBspheres_lambertian.dae

Remember you will be running experiments for the write-up -- since the renders will be taking some time, it's a good idea to start rendering now!

Writeup

Don't forget to read this article for writeup instructions!