Here is the assignment handout for Homework 5.

Here is the framework for the assignment. To facilitate merging with your existing code, here is a summary of changes from the solution to the previous assignment:

New abstract class: PathTracer
New classes: BruteForcePathTracer, KajiyaPathTracer
New interfaces: Medium, PhaseFunction
New classes: BoundedMedium, HomogeneousMedium, IsotropicPhaseFunction, MediumSamplingRecord
New classes: DirectOnlyMediumRenderer, KajiyaMediumPathTracer
LambertianEmitter has a BRDF
Vector3 has bug fix
Color adds invScale method
LuminaireSamplingRecord adds shadowRay
Ray gets copy constructor
Scene has a medium and a second version of chooseVisiblePointOnLuminaire
DirectIlluminator adds directScattering method
LuminairesIlluminator.directIllumination attenuates shadow rays
MultipleIlluminator.directIllumination attenuates shadow rays
ProjSolidAngleIlluminator implements directScattering
ProjSolidAngleIlluminator.incidentRadiance includes attenuation and takes point rather than IntersectionRecord
MeshTriangle supports luminaire sampling (to enable mesh luminaire for Cornell Box)
Surface.chooseSamplePoint and Surface.pdfSamplePoint take receiver point rather than IntersectionRecord

A number of these changes would require small changes to your surface rendering code, but there no real design changes.

There are a few test scenes for this assignment, which are listed below together with the output from my implementation.

First, some numerical-answer scenes. A diffuse enclosure (of any shape) with walls that have emitted radiance L and reflectance R has a very simple answer under global illumination: the radiance everywhere is L / (1 - R). This kind of environment is called a furnace:

furnace.xml

Remember you can get a numerical answer from the renderer by setting the image size to 1 by 1.

Pure absorption in a backlit slab of homogeneous medium:

attenuate.xml

Single scattering from a slab of homogeneous medium with a distant source and camera has an analytic solution (but not for multiple scattering):

layer.xml | layer.nb

A sufficiently deep layer of non-absorbing medium, under multiple scattering, reflects all of the incident light. You'll need to let the paths get pretty long, though:

semi-infinite.xml

Here is the classic test scene, the Cornell Box:

The following images were computed at 100 samples per pixel:

From left to right: direct only (luminaire sampling); brute force path tracer (depth 5); Kajiya path tracer with luminaire sampling (depth 5).

The Cornell box, with no light source; it is just illuminated by the background.

cbox-bg.xml

The following image was computed at 100 samples per pixel:

Here the brute force algorithm works just fine.

An empty Cornell Box with a cube of scattering medium in it:

cbox-vol.xml

The following images were computed at 400 samples per pixel:

These are all with direct only, using luminaire sampling. They have different absorption and scattering coefficients, in the range 0.000–0.050, indicated in the filenames.

The Cornell Box illuminated by a shaft of light coming in through a hole in the ceiling, with and without a scattering atmosphere:

cbox-shaft-empty.xml | cbox-shaft-vol.xml

The following images were computed at 100 samples per pixel:

From left to right: direct only (luminaire sampling); brute force path tracer (depth 5); Kajiya path tracer with luminaire sampling (depth 5).
The following images were computed at 400 and 1600 samples per pixel respectively:

From left to right: direct only (luminaire sampling); Kajiya path tracer with luminaire sampling (depth 5).