**Note:** This class loosely follows up on Photorealistic Graphics (NPGR004) and is aimed mostly at students with a deeper interest in realistic rendering methods.

## Course information 2021/2022

Lectures: | Wednesdays, 9:00 – 10:30, room S1 | Contact: Alexander Wilkie |

Practicals: | Tuesdays, 12:20 – 13:50, room SW2 | Contact: Tomáš Iser, Lucia Tódová |

Lecture and practicals content and assignments for 2021/2022 will be updated throughout the semester.

**Lecture** content

**Note:** You can download the Zoom recordings from the lectures in SIS in the lecture details (you need to be logged in!)

Lecture topic |
Slides & notes |
Auxiliary materials |

Organization, Intro | Lecture: pdf | pptx / pdf | pptx | |

Radiometry | Lecture: pdf | pptx | Petr Olšák – dOmega (in Czech) Petr Olšák – Radiometric units (in Czech) Wikipedie – Radiometric units |

Light reflection, BRDF | Lecture: pdf | pptx | Scratchpixel – Mathematics of shading Scratchpixel – Introduction to shading Scratchpixel – The Phong model, Reflection models and BRDF Fabrizio Duroni – How to calculate reflection vector |

Monte Carlo methods, Direct illumination calculation | Lecture: pdf | pptx | |

Monte Carlo methods II, Image-based lighting | Lecture: pdf | pptx | |

Combined estimators & Multiple Importance Sampling | Lecture: pdf | pptx | |

Rendering equation and its solution | Lecture: pdf | pptx | |

Path tracing | Lecture: pdf | pptx | |

Quasi-Monte Carlo methods | Lecture: pdf | pptx | My favorite samples – SIGGRAPH Course 2019 Rand() considered harmful Constructing quasi-random blue noise sequences(blue noise vs. low-discrepancy, extra supplementary material) Unreasonable effectiveness of quasirandom sequences(extra supplementary material) |

Volumetric light transport and participating media rendering | Lecture: pdf | pptx Monte Carlo methods for physically based volume rendering”, SIGGRAPH 2018 course |
Steve Marschner: “Multiple Scattering” Note that the pseudocode in the above material is buggy: In the Kajiya-style path tracing, homogeneous volume, version 1.0, in the function directScatteredEst(x, ω) a multiplication by sigma_s/sigma_t (i.e. scattering albedo) is missing. Steve Marschner: “Volumetric path tracing” Patrick Harrington: Henyey-Greenstein phase function – CDF inversion, Rayleigh scattering phase function Walter Lewin: For the Love of Physics: Catchy demonstration of Mie and Rayleigh scattering |

Bidirectional path tracing | Lecture: pdf | pptx | |

Photon mapping | Lecture: pdf | pptx | |

Approximate global illumination computation | Lecture: pdf | pptx |

**Practicals** schedule

5.10. | Intro, Assignment 0 (→ slides in .pdf) | 23.11. | Math exercises |

12.10. | Math exercises (→ .mp4 video recording in SIS) | 30.11. | Evaluating assignment 2, Assignment 3 |

19.10. | Evaluating assignment 0 | 7.12. | Voluntary consultation |

26.10. | Assignment 1 | 14.12. | Evaluating assignment 3, Assignment 4 |

2.11. | Voluntary consultation |
21.12. | Voluntary consultation |

9.11. | Evaluating assignment 1, Assignment 2 | 28.12. |
Christmas |

16.11. | Voluntary consultation |
4.1. | Final evaluation |

**Practicals** assigments

#### 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.

### Assigment 1: Direct illumination calculation through explicit light source sampling (5 pts)

The goal of the first assignment is to start building infrastructure for global illumination calculation, specifically to implement the evaluation of the BRDF and the classes representing various light sources. These components will be tested on the problem of calculating direct illumination due to point and area light sources using a Monte Carlo estimator based on explicit light source sampling. You will be required to show that your solution converges to this reference solution. (The difference image should only consist of uniform noise. Even better, use color-coded positive/negative differences in HDRImageTools.)

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 |

#### Points:

Altogether you can get up to 5 points for this assignment, they are redistributed for its individual parts. 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 | 3 points |

### Assignment 2: Direct illumination estimator based on randomized direction sampling (8 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 8 points for this assignment.

Uniform hemisphere sampling | 4 points |

BRDF importance sampling | 4 points |

### Assignment 3: Combined estimator for direct illumination (10 points)

Use Multiple Importance Sampling with the balance heuristic for direct illumination calculation. Combine estimators implemented in Assignments 1 and 2 (i.e. explicit sampling of positions on the light source and BRDF importance sampling). Show that the solution is more robust than either of the two estimators in the mixture. Show that the solution converges to the same reference results as in Assignments 1 and 2.

#### Points

You may receive up to 10 points for this assignment.

### Assignment 4: Path tracer with a combined estimator for direct illumination calculation (22 points)

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

**Path tracing (15 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 (7 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.

#### Points

You may receive up to 22 points for this assignment.

Path tracing | 15 points |

MIS for direct illumination calculation in a path tracer | 7 points |

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

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 |

## Archive

Course information for the previous academic years: