Advanced Graphics

Universiteit Utrecht - Information and Computing Sciences

academic year 2017/18 – 2nd period

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ADVGR on Slack

Format & Organization


Lecture Slides


Literature & Links

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Recent news

Feb 5:

Feb 2:

Jan 30:

  • P3 grades now available.
  • Some images from P3 (click for larger version):

Older posts still available

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.

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;
  • GPGPU-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;
  • SIMD and ray packet traversal.


  • Osiris: the official (centrally managed) schedule.
  • uniform course information.
  • Check here for a list of students for this course. 
  • Join the Slack channel for support and collaboration.


Lecturer: Jacco Bikker (


  • Two lectures per week: Tuesday 09:00 - 10:45, Thursday 13:15 - 15:00.
  • One lecturer supervised lab per week: Thursday 15:15 - 17:00.
  • Rooms: BBG-001 (all Tuesday lectures), BBG-205 (first lecture), BBG-165 (all subsequent Thursday lectures plus LAB).


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

Final Exam

For this course, 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: basic experience with graphics programming (e.g. OpenGL / DirectX).


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 14
NO LECTURE        
Thu Nov 16
Lecture 1:
47 Tue Nov 21
Lecture 2:
Acceleration Structures

Assignment 1
Basic framework

Thu Nov 23
Lecture 3:
The Perfect BVH
Working College #1
Thu 15:15-17:00
48 Tue Nov 28
Lecture 4:
Real-time Ray Tracing
Thu Nov 30
Lecture 5:
SIMD (optional)
Working College #2
Thu 15:15-17:00
49 Tue Dec 5
Lecture 6:
Light Transport
Wednesday Dec 6, 23:59

Assignment 2:

Acceleration structures

Thu Dec 7
Lecture 7:
Path Tracing
Working College #3
Thu 15:15-17:00
50 Tue Dec 12
Lecture 8:
(cancelled due to snow)
Thu Dec 14
Lecture 9:
Variance Reduction
Working College #4
Thu 15:15-17:00
Tue Dec 19
Lecture 10:

Assignment 3:


Thu Dec 21
Lecture 11:
GPGPU Recap (optional)
Working College #5
Thu 15:15-17:00
Thu Dec 28, 23:59h
Christmas, New Year, Block 1 Retake Week

2 Tue Jan 9
Lecture 12:
GPU Path Tracing (1)

Thu Jan 11
Lecture 13:
GPU Path Tracing (2)
Working College #6
Thu 15:15-17:00
Tue Jan 16
Lecture 14:

Thu Jan 18
Lecture 15:
Guest lecture
Working College #7
Thu 15:15-17:00
Tue Jan 23
Lecture 16:
Grand Recap
Thu Jan 25
Extended Lab
Preparation for Final Assignment Deadline
Block 2 Exam Week
Exam: Thu Feb 1, 17:00 in EDUC-MEGARON
Mon Jan 29, 23:59h


Downloadsback to navigation


Lecture 1: Introduction & Whitted
Lecture 2: Acceleration Structures
Lecture 3: The Perfect BVH
Lecture 4: Real-time Ray Tracing
Lecture 5: SIMD Recap
Lecture 6: Light Transport
Lecture 7: Path Tracing
Lecture 8: Variance Reduction
Lecture 9: Various
Lecture 10: GPGPU recap
Lecture 11: GPU Raytracing (1)
Lecture 12: GPU Raytracing (2)
Lecture 13: BRDFs
Lecture 14: Grand Recap


SIMD Tutorial
GPGPU Tutorial (to be released)
Probability Theory

FILES - C++ framework for rapid graphics prototyping - C# framework for graphics prototyping - Cross-platform version of the template, by Mathijs and Kevin - C++ framework for CUDA application development - C++ framework for OpenCL application development    (UPDATED)

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 framework with most of the low level functionality for the subsequent milestones. This includes scene management, ray generation, primitive intersection and simulation of optics.
  2.  Interactivity: based on the theory, you will transform the framework into an interactive renderer. The framework 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 here to download Assignment 1 details.

(2) Interactive Ray Tracer


  • Add a bounding volume hierarchy
  • Add a scene graph
  • Add a top-level BVH
  • Add ray packet traversal

Click here to download Assignment 2 details.

(3) Global Illumination

Tasks (tentative):

  • Convert the Whitted-style ray tracer to a uni-directional path tracer
  • Add support for the MBVH
  • Add various variance reduction techniques

Click here to download Assignment 3 details.

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, Second Edition - From Theory to Implementation, Pharr & Humphreys. Morgan Kaufmann, 2010. ISBN-10: 0123750792.


Additional materials will be posted here in due time.

News Archiveback to navigation

Old posts

Jan 23:

Jan 16:

Jan 11:

Jan 9:

Jan 8:

  • GPGPU Recap slides are now available.

Dec 30:

Dec 29:

  • Assignment 2 grades can be downloaded here.
  • Assignment 3 description now available.

Dec 20:

Dec 19:

  • Slides for lecture 9 ("Various") now available.

Dec 15:

Dec 13:

Dec 8:

Dec 7:

Nov 30:

Nov 28:

Nov 23:

Nov 21:

Nov 17:

Nov 16:

  • Slides for lecture 1 can be downloaded here.

Nov 14:

  • Join the #ag channel on!
  • Get the ebook for this course for free (legally) here.

Nov 6:

Oct 25:

Initial version of the 2017/2018 website.