(Task 4) Shadow Rays

In this task you will modify Pathtracer::trace_ray to implement accurate shadows.

Currently Pathtracer::trace_ray computes the following:

It computes the intersection of ray r with the scene.
It computes the amount of light arriving at the hit point hit.position (the irradiance at the hit point) by integrating radiance from all scene light sources.
It computes the radiance reflected from the hit point in the direction of -r. (The amount of reflected light is based on the BSDF of the surface at the hit point.)

Shadows occur when another scene object blocks light emitted from scene light sources towards the hit point. Fortunately, determining whether or not a ray of light from a light source to the hit point is occluded by another object is easy given a working ray tracer (which you have at this point!). You simply want to know whether a ray originating from the hit point (hit.position), and traveling towards the light source (direction to light) hits any scene geometry before reaching the light.

Your job is to implement the logic needed to compute whether hit point is in shadow with respect to the current light source sample. Below are a few notes:

Get yourself oriented in the starter code by taking a look at Pathtracer::trace_ray in src/student/pathtracer.cpp. Notice that the code, after finding a hit, loops over all light source accumulating radiance. (look for the comment // loop over all the lights and accumulate radiance). For each light the lambda function sample_light() is invoked, and in that function the key line is the line that adds radiance into the variable radiance_out. This code is the code where the refection equation is being evaluated.
In the starter code, notice that when the code calls light.sample(hit.position), it returns the caller a Light_sample sample. (You might want to take a look at rays/light.h for the definition of struct Light_sample and class light.) A Light_sample contains the fields radiance, pdf, direction, and distance. In particular, sample.direction is the direction from the surface hit point to the point on the light source being sampled, and sample.distance is the distance from the hit point to the light sample. Given this information, all you need to do is determine if there is any scene geometry closer than that sample point.
A common ray tracing pitfall is for the “shadow ray” shot into the scene accidentally hits the same object as r did. (The surface is erroneously determined to be occluded because the shadow ray is determined to hit the surface itself!). We recommend that you make sure the origin of the shadow ray is offset from the surface to avoid these erroneous “self-intersections”. For example, consider setting the ray’s dist_bounds appropriately to avoid hits with very small t values, or adjust the origin of the shadow ray to be hit.position + epsilon * sample.direction instead of simply hit.position. EPS_F is defined in for this purpose (see lib/mathlib.h).
Another common pitfall is forgetting that the surface is not in shadow if the shadow ray hits scene geometry after reaching the light. (Also note that Ray has a member called time_bound…)
You will find it useful to debug your shadow code using the DirectionalLight since it produces hard shadows that are easy to reason about.
When you get started on Task 4, comment out the line Spectrum radiance_out = Spectrum(0.25f); and initialize the radiance_out to be the correct value. Hint: is there supposed to have any light before we even start considering each light sample?

At this point you should be able to render very striking images with shadows.

Sample results:

At this point, you can add all kinds of lights using “New Light” in Layout mode, except for Sphere Light and Environment Map which you have the option to implement later (Note that you can still fill in Sphere::Uniform::sample in Samplers.cpp now to view the result of a mesh under Sphere Light). Here are some examples:

A sphere and a cube with hemishphere lighting

shadow_hemisphere