Advanced Graphics

Universiteit Utrecht - Information and Computing Sciences

academic year 2020/21 – 2nd block

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Format & Organization

Lecture Slides


Literature & Links

Newsback to navigation

Recent news

Nov 2:

  • 2020/2021 version of the website ready for publication.
  • All announcements will be made in Teams.

Older posts used to be available here, but this year everything happens in Teams.

Format and Organizationback to navigation


The master course Advanced Graphics addresses advanced topics in 3D computer graphics. The focus of the course is Physically-based rendering of 3D scenes. The course has two main focus areas: Rendering Algorithms and Making Rendering More Efficient. Efficiency will be sought through Acceleration Structure Construction and Traversal and Variance Reduction (rather than low level optimization).

The course starts with a recap of Whitted-style ray tracing. We then explore various acceleration structures that help to run the ray tracing algorithm in real-time on commodity hardware. We will see that a well-built Bounding Volume Hierarchy provides both flexibility and speed, for static and dynamic scenes.

The second part of the course introduces the path tracing algorithm, and related light transport theory. We investigate various methods to improve the efficiency of the algorithm using probability theory. We will see that efficient path tracing can yield interactive frame rates.

In the third part of the course we use GPGPU to run ray tracing and path tracing on the GPU. We will explore recent research in high performance stochastic rendering.

This year we will also explore recent hardware developments, and related to that, various ray tracing APIs and state-of-the-art filtering technology aimed at interactive rendering.

Course objectives

At the end of this course you will have detailed knowledge about the following topics:
  • physical light transport, and how to simulate this behavior in a computer program;
  • modern ray tracing based rendering algorithms;
  • high level optimizations of the ray tracing algorithm;
  • Monte Carlo integration and variance reduction;
  • GPU-specific optimizations of ray tracing algorithms.

You will have practical experience in the following topics:

  • implementation of Whitted-style ray tracing and path tracing;
  • implementation of acceleration structure construction and traversal.

You will have a reasonable grasp of several related topics:

  • distributed ray tracing;
  • bidirectional methods, including photon mapping;
  • filtering of the noisy output of a path tracer;
  • RTX, OptiX, Embree and RadeonRays;
  • SIMD and ray packet traversal.


  • Osiris: the official (centrally managed) schedule.
  • uniform course information.
  • Join the Discord for support and collaboration.


Lecturer: Jacco Bikker (


  • Two ONLINE lectures per week: Tuesday 11:00 - 12:45, Thursday 13:15 - 15:00.
  • Two ONLINE lecturer supervised lab per week: Tuesday 9:00 - 10:45, Thursday 15:15 - 17:00.

You are kindly requested to enable your camera during the lectures.


This course has a practical project track. During this course, you will either develop an interactive renderer, or your own render core for Lighthouse 2. You may work on the project alone, or with one other student. The practical project has three milestones. The second and third milestones build on the previous one: the outcome is a full ray tracer or render core, which makes a great addition to your portfolio.

Final Exam

There will be one exam at the end of the block (i.e., no mid-term exam). A retake exam or retake assignment can be used to compensate some deficits (see grading section for details).


  • Basic knowledge in linear algebra, calculus and probability theory, as required for the masters program. See "Elementary maths for GMT".
  • Fundamentals in algorithms and data structures.
  • Bachelor level knowledge in computer graphics is strongly recommended. Without prior graphics knowledge, you will need substantial additional time (and probably some talent).
  • Good programming skills; C# and C++ will both work, but for optimal performance and certain low level aspects, C++ is recommended. Plan for additional time if you plan to familiarize yourself with C++ during the course.
  • Good to have, but not absolutely required: basic experience with graphics programming (e.g. OpenGL / DirectX). Note that we will not use an API for the assignments; we'll build our own.


Ray Tracing

Whitted-style Ray Tracing

  • Recap
  • Beer's Law, Fresnel

Acceleration Structures

  • Octree, kD-tree, BSP
  • Bounding Volume Hierarchy
  • Efficient Construction & Traversal

Dynamic Scenes

  • The Top-Level BVH


  • Ray Packet Traversal
Path Tracing

Light Transport

  • The Rendering Equation

Monte-Carlo Algorithms

  • Distributed Ray Tracing
  • Path Tracing

Variance Reduction

  • Stratification
  • Importance Sampling
  • Next Event Estimation


  • Multi-branching BVHs

GPU implementations

  • Streaming Algorithms
  • Wavefront Path Tracing

Variance reduction

  • Multiple Importance Sampling
  • Resampled Importance Sampling
  • Bi-directional Path Tracing
  • Photon Mapping

Image Postprocessing

  • Bias
  • Filtering Techniques

Scheduleback to navigation

BLOCK 2 Schedule

Week Date Lecture / Exams Working College Practical #1 Practical #2 Practical #3
46 Tue Nov 10
Lecture 1:
Thu Nov 12
Lecture 2:
Whitted Ray Tracing
47 Tue Nov 17
Lecture 3:
Acceleration Structures
Working College
Tue 9:00-10:45

Assignment 1
Basic framework or Lighthouse 2 core

Thu Nov 19
Lecture 4:
Light Transport
Working College
Thu 15:15-17:00
48 Tue Nov 24
Lecture 5:
The Perfect BVH
Working College
Tue 9:00-10:45
Thu Nov 26
Lecture 6:
Path Tracing
Working College
Thu 15:15-17:00
49 Tue Dec 1
Lecture 7:
GPU Ray Tracing (1)
Working College
Tue 9:00-10:45
Wednesday Dec 2, 17:00

Assignment 2:

Acceleration structures

Thu Dec 3
Lecture 8:
Variance Reduction
Working College
Thu 15:15-17:00
50 Tue Dec 8
Lecture 9:
GPU Ray Tracing (2)
Working College
Tue 9:00-10:45
Thu Dec 10
Lecture 10:
Big Picture
Working College
Thu 15:15-17:00
Tue Dec 15
Lecture 11:
Working College
Tue 9:00-10:45

Assignment 3:


Thu Dec 17
Working College
Thu 15:15-17:00
Fri Dec 18, 17:00h
Christmas, New Year, Block 1 Retake Week

2 Tue Jan 12
Lecture 12:
Filtering (1)

Thu Jan 14
Lecture 13:
Working College
Thu 15:15-17:00
Tue Jan 19
Lecture 14:
Working College
Tue 9:00-10:45
Thu Jan 21
Lecture 15:
Bits and Pieces
Working College
Thu 15:15-17:00
Tue Jan 26
Lecture 16:
Exam Practice



Block 2 Exam
  Thu Jan 28, 15:15 in THEATRON
Wed Feb 3, 17:00h


Downloadsback to navigation


Will be made available in Teams.


The 2018/2019 exam, with answers.
The 2017/2018 exam, with answers.
The 2016/2017 exam, with answers.
The 2015/2016 exam, with answers.

More will be made available in Teams.


Generic C/C++ template:
Generic C# template:
GPGPU / OpenCL / C++ template:
GPGPU / OpenCL / C# template:
GPGPU / CUDA / C++ template:


LH2 can be found on GitHub.

Practical Assignmentsback to navigation

The course includes a software project that should be worked on in pairs. It is allowed to work on this alone, but be aware that the scope of the project is tuned for duos.

There are three milestones for this project:

  1.  Basics: during the first phase of the project, you will design and implement a Whitted-style ray tracer, either built on your own framework, or as a render core for the Lighthouse 2 renderer.
  2.  Interactivity: based on the theory, you will transform the Whitted-style ray tracer into an interactive renderer. The renderer is extended with basic animation support.
  3.  For the final version of your project, you will be adding global illumination to the renderer. The default approach for this is a path tracer; however other options exist as well. You are free to chose your specific focus in this phase of the project, e.g. GPU rendering or advanced variance reduction.

The final grade for the software project is calculated as follows:

practical grade = (P1 + P2 + 2 * P3) / 4

(1) Ray Tracer


  • Setup a basic ray tracing framework for rendering a depth map for a hard-coded scene consisting of spheres and planes
  • Implement a complete Whitted-style ray tracer with reflection and optionally refraction (Fresnel) and absorption (Beer)

Click to download the formal Assignment 1 description.

(2) Interactive Ray Tracer


  • Add a bounding volume hierarchy
  • Optional: add a top-level BVH
  • Optional: add ray packet traversal
  • Other optional challenges available.

Assignment details will be published on Teams.

(3) Global Illumination

Tasks (tentative):

  • Implement recent research in the field of graphics
  • Build a GPU ray tracer or path tracer.
  • Implement a real-time ray tracer for animated scenes.
  • Other challenges are available.

Assignment details will be published on Teams.

Gradingback to navigation


In order to pass the course, you must meet these requirements:

Practical grade P = (P1 + P2 + 2 * P3) / 4
Exam grade E
Final grade F = (2 * P + E) / 3


P >= 4.5
E >= 4.5
F >= 5.5.


There will be an opportunity for a retake exam or a retake assignment. In order to qualify, a grade of at least 4.0 is required in both areas (final exam, practicals). The retake exam or assignment replaces the matching exam or assignment.

IMPORTANT: you can only take the retake exam if you have both a high-enough but non-passing grade (i.e., at least 4.0 and less than 5.5).

Transfers from the previous lecture

If you are retaking this course it may be possible to transfer partial grades to this academic year. This is only possible for practical assignment grades; if you are retaking Advanced Graphics, you must retake the exam. Contact me for details.

Literature & Linksback to navigation


  • T. Whitted. An Improved Illumination Model for Shaded Display. Commun. ACM, 23(6):343–349, 1980.
  • Interactive Rendering with Coherent Ray Tracing, Wald et al., 2001.
  • Large Ray Packets for Real-time Whitted Ray Tracing, Overbeck et al., 2008.
  • Fast Agglomerative Clustering for Rendering, Walter et al., 2008.
  • Heuristics for Ray Tracing using Space Subdivision, MacDonald & Booth, 1990.
  • Distributed Ray Tracing, Cook et al., 1984.
  • The Rendering Equation, Kajiya, 1986.
  • Importance Sampling for Production Rendering, pages 5-38.
  • Ray tracing on programmable graphics hardware. Purcell et al., 2002.
  • Interactive k-d tree GPU raytracing. Horn et al., 2007.
  • Understanding the Efficiency of Ray Tracing on GPUs. Aila & Laine, 2009.
  • Getting Rid of Packets - Efficient SIMD Single-Ray Traversal using Multi-branching BVHs. Wald et al., 2008.
  • Megakernels Considered Harmfull: Wavefront Path Tracing on GPUs. Laine et al., 2013.
  • Theory for Off-Specular Reflection from Roughened Surfaces. Torrance & Sparrow, 1967.

Recommended literature

Physically Based Rendering - From Theory to Implementation, Third Edition, Pharr & Humphreys. Morgan Kaufmann, 2016. ISBN-10: 9780128006450. Also available for free online:


Additional materials will be posted here in due time.

News Archiveback to navigation

Old posts

Not this year; the page is static and all the action is on Teams.