Jaroslav Křivánek

Computer Graphics III - Physically based rendering (NPGR010) – winter semester 2019/2020

Schedule:	Lecture - Wed 14:00-15:30 S4 | Labs - Wed 15:40-17:10 SW1 (Malá Strana)
Lecturer:	Jaroslav Křivánek, e-mail: jaroslav.krivanek at mff.cuni.cz
Organization:	2/2 C + Ex  link to SIS

The class loosely follows up on Computer Graphics II (NPGR004) and it is aimed mostly at students with a deeper interest in realistic rendering methods. The course covers methods for physically-based realistic rendering used for special effects in movie production, computer animation, architectural and product visualizations etc. Specifically, we start off by briefly covering some of the math and physics behind light transport. We then give a detailed treatment of the industry-standard Monte Carlo methods for light transport simulation, such as path tracing, photon mapping etc. We also cover some of the more advanced techniques such as bidirectional path tracing.

• Course organization and credit requirements: pdf | pptx.
• Final examination information and questions: pdf.
• Students' notes for lectures given in 2012 (in Czech and Slovak): zip.
• Google doc with acquired points

Assignment due dates

Interesting articles on rendering in practice

• fxguide - The State of Rendering
• fxguide - The Art of Rendering
• fxguide - Disney's new Production Renderer `Hyperion' - Yes, Disney!
• fxguide - Manuka: Weta Digital's new Renderer
• fxguide - RenderMan/RIS and The Start of Next 25 Years

Lecture and labs program

Assignments

Using other peoples' work and presenting it as yours is an infringement of the code of conduct and is held as a reason for failing the class immediately.

Assignment 1: Direct illumination calculation through explicit light source sampling (4 pts)

Isotropic point light Diffuse surfaces	Isotropic point light Glossy surfaces	Large area light Diffuse surfaces	Large area light Glossy surfaces
Small area light Diffuse surfaces	Small area light Glossy surfaces	Const. environment map Diffuse surfaces	Const. environment map Glossy surfaces

References:

• HDRImageTools: A tool for viewing and comparing HDR images.
• Reference images: Your code should produce the same images (except for uniform noise).
• PG3Render.zip: Skeleton of the renderer. Implement your renderer into the PathTracer class. The classes AreaLight, PointLight and BackgroundLight is where you should put the functionality of the respective light sources. The Material class is where you should put the BRDF implementation.

Points

Altogether you can get up to 4 points for this assignment. The following table gives a breakdown of the points for the individual parts of the assignment. I recommend working in this very order, always first testing only the diffuse BRDF component and only then moving to the glossy version.

Area light source	2 points
Environment map with a constant emission:	2 points
Image-based environment map (for directions see PBRT, Section 14.6.5.):	3 extra points
Implementation of any anisotropic BRDF model (e.g. anisotropic Ward, anisotropic Ashikmin-Shirley):	2 extra points
Extra assignment of your own choice:	max 3 extra points

Assignment 2: Direct illumination estimator based on randomized direction sampling (4 points)

The goal is to implement an estimator of direct illumination based on randomized sampling of directions. To get this done, you will need to implement a) sampling of random directions from a uniform distribution on a hemisphere, and b) sampling of random directions proportional to the BRDF (importance sampling). You will then use this functionality to implement the estimator itself. Note that the estimator only works for area light sources and environment maps but not for point lights (the latter cannot be hit by a ray with a randomly chosen direction). Show that an estimator based on BRDF importance sampling is more efficient than an estimator based on uniform hemisphere sampling. Show that the solution converges to the same reference results as in Assignment 1.

Points

You may receive up to 4 points for this assignment.

Uniform hemisphere sampling:	2 points
BRDF importance sampling:	2 points
Possible extra assignment:	max 3 extra points

Assignment 3: Combined estimator for direct illumination (6 points)

Points

You may receive up to 6 points for this assignment.

Possible extra assignment:

max 3 extra points

Assignment 4: Path tracer with a combined estimator for direct illumination calculation (12 points)

In this assignment, you will build on the infrastructure from the previous assignments to implement the following methods:

• Path tracing (8 points). Implement a path tracer with direct illumination calculation based on a) implicit "collecting" of emitted radiance on the path vertices, and b) explitict light source sampling (next event estimation). Use Russian roulette for path termination with the survival probability based on the the surface reflectance. Show that both methods converge to the same solution and compare their efficiency. I suggest starting off by implementing the implicit "collecting" of emitted radiance and testing it in the large area source scene where it should perform fairly well. Once this works, you may move on to the explicit light source sampling. Reference images with global illumination are shown below.
• The use of MIS for direct illumination calculation in the path tracer (4 points). A condition for receiving credit for this part of the assignment is an efficient implementation: each secondary ray in the path tracer should be used both as a sample of indirect illumination and as a sample of the "implicit" direct illumination calculation strategy.

Congratulations! By finishing this assignment, you have built a rendering core of state-of-the-art production renderers such as Corona or Arnold.

Points

You may receive up to 8 points for this assignment.

Quasi-Monte Carlo path tracing (e.g. the Halton sequence):	2 extra points
Extra assignment of your own choice:	max 3 extra points

Isotropic point light Diffuse surfaces	Isotropic point light Glossy surface	Large area light Diffuse surfaces	Large area light Glossy surface
Small area light Diffuse surfaces	Small area light Glossy surface	Const. environment map Diffuse surfaces	Const. environment map Glossy surface

Assignment 5: Volumetric path tracer (14 points)

Extend your MIS path tracer such that it supports rendering scenes with a global homogeneous and isotropic participating medium. The medium is ‘global’ in the sense that it fills the entire space. (This makes the task much simpler for you because you don’t need to deal with the complex infrastructure for tracking which medium you are currently in.) The homogeneity refers to the fact that all the optical parameters of the medium are constant in space. Isotropic medium has a constant phase function (1/4π). The medium parameters are:

• absorption coefficient σ_a = 0.1 m^-1,
• scattering coefficient σ_s = 0.2 m^-1,
• phase function p(ω) = 1/4π

The reference images that I provide are for the diffuse scene with a small area light (the -s 4 command line parameter) where the path tracer converges relatively quickly. To make the rendering faster, I use a resolution of 300x300 pixels. Still, bear in mind that rendering multiple scattering in a medium using a basic path tracer is a computationally intensive process.

To make the debugging of your code simpler, I have prepared a number of tests:

• Direct illumination, no medium (reference image: s4-nomedium-l02.hdr). Included only for reference.
• Full global illumination, no medium (reference image: s4-nomedium-l40.hdr). Included only for reference.
• Direct illumination-only, purely absorbing medium (no scattering in the medium, i.e. σ_a = 0.1, σ_s = 0, reference image: s4-mabs-l02.hdr). Making this variant work only involves adding attenuation by the transmittance for all ray segments in the path tracer.
  You may also take advantage of this variant to start testing your distance-sampling code: for any ray, you may sample the collision distance and accept the contribution only if the distance is beyond the next surface, and reject it otherwise. (Note that the medium is purely absorbing, so whenever the sampled distance is shorter than the distance to the next surface, i.e. the collision occurs in the medium, we know it is an absorption event, so we must terminate the path.) This latter variant, in fact, corresponds to a stochastic evaluation of the transmittance term, and should therefore converge to the same result (albeit with more variance).
• Full global illumination, purely-absorbing medium (reference image: s4-mabs-l40.hdr). This variant adds no extra requirements on your medium rendering infrastructure, so if the previous variant works, this one should work out of the box, too. This is added only as a way for you to double check that your code is indeed correct.
• Direct illumination-only, scattering medium (i.e. σ_a = 0.1, σ_s = 0.2, reference image: s4-mscat-l02.hdr). In this variant, we are calculating contributions from paths with two segments, so one vertex is either in the medium (single-scattering) or on a surface (direct-illumination). Making this work already requires a full-fledged volumetric path tracer, where the path length is limited to two segments.
  When you sample the collision distance, and the sampled location is closer than the next surface, you have sampled a collision event in the medium. In this case, you connect to a randomly chosen point on a light source (and of course, calculate attenuation between the source and the sampled scattering point). If, on the other hand, the sampled distance is beyond the surface, you just compute the direct illumination at the surface (again, do not forget to take into account light attenuation to the light source).
• Full global illumination, scattering medium (reference image: s4-mscat-l40.hdr). This is the final result of your work. The only difference from the previous case is that you whenever you sample a collision event (in the medium or on a surface) you continue the path (with some probability, i.e. use the Russian roulette). If you previous code was correct, this should work out of the box. Note that without MIS, the volumetric path tracer with a light source embedded in the medium has theoretical infinite variance. A practical result is that the image contains fireflies that are essentially impossible to get rid of just by increasing the computation time. This is fine, don’t worry about it.

Reference images for the volumetric path tracer

Download a zipped archive

Direct illumination No medium	Full global illumination No medium	Direct illumination-only Purely absorbing medium	Full global illumination Purely-absorbing medium
Direct illumination-only Scattering medium	Full global illumination Scattering medium