02561 Computer Graphics

Course description from the DTU course catalogue.

Course Overview

Interactive computer graphics enables us to manipulate digital 3D objects. The ability to work interactively with digital objects is an important engineering skill. Our objective in this course is to enable the participants to (a) implement real-time computer graphics systems and (b) to develop graphics algorithms with applications in visualization, modelling, and animation. The course covers web graphics technology and introduces the principles of 3D graphics that one would need for working on CAD systems, game engines, computer animation, 3D multimedia, virtual reality, and scientific visualization.

We will do lectures and exercises interspersed in the first half of each teaching session and then exercises only in the second half.

You need a computer to complete the course work.

Timetable

Calender weeks: 35-41 + 43-48.

Weekly timetable:

Wednesday	8-10	lecture	Building 208, Auditorium 54
	10-12	exercises	Building 210, Rooms 168, 162, 118, 112

Hand-in deadline: Thursday 18 December 2025 at 23:59.

Textbooks and Notes

The textbook for this course is

R	Akenine-Möller, T., Haines, E., and others. Real-Time Rendering, 4th edition. A K Peters / CRC Press, 2018. [website]

In addition, we may upload papers to DTU Learn that serve sometimes as part of the curriculum, sometimes as supplementary reading material.

In the spirit of web graphics, a very useful collection of articles is available that teaches WebGPU from basic principles using interactive editable examples: WebGPU Fundamentals.

Prerequisites

We assume that you know basic geometry, trigonometry, and vector algebra, and also introductory linear algebra and the concept of multivariate functions. We further expect that you have some general experience with programming and problem solving from other courses.

Programmatically, you will work with HTML, JavaScript, and WebGPU. This entails working with buffers and data flow between server, CPU, and GPU. Mathematically, you will work with projections in space, projective geometry, transformations, and mappings. We may also explore parametric curves and surfaces. The subjects listed in this paragraph will be covered in the course.

Lab Journal

You are expected to maintain a lab journal where you present the outcome of your work. The lab journal is a webpage containing your solution for each part of each worksheet. A good way to work is to have a separate html and js file for each part of each worksheet. The lab journal must be submitted in a zip-file to DTU Learn (Assignments) before the deadline (see above).

Project

Toward the end of the course you must choose a minor project to work on. Some projects will be proposed at the lectures. A project of your own choosing is acceptable as long as it has a reasonable connection with the course. You can choose one of the proposed projects or hand in a short project description (one paragraph) and get it approved by the course responsible. The project must be submitted to DTU Learn (Assignments) before the deadline (see above). This submission must include a project report of the following structure: Introduction, Method, Implementation, Results, Discussion, so that it is possible to understand what you developed and the intentions and ideas behind the project. Include a zip-file containing the code.

Assessment

The assessment is based on your lab journal and project report (and associated code). These must be in pdf or html format and uploaded to DTU Learn (Assignments) before the deadline (see above). There is no oral examination in this course. Your work is assessed in its entirety and you will be graded using the 7-step scale.

As a rough guideline, the project is usually 40% to 50% of the grade because it is carried out more independently. The exercises are then roughly 50% to 60% of the grade. You need more than 50% to pass. This means that it is very difficult to pass the course if you do not hand in a project together with a project report, and it is not possible to pass if you do not hand in any solutions for any of the worksheets. On the other hand, if you do 75% of the exercise worksheets and work your way through the project and write a decent project report for this work, you will probably pass with a decent grade. The word "probably" in this context means "depending on the correctness of your solutions".

Individualization

In case you work in a group, it is important that proper credit is assigned to your collaborator(s) and that your final hand-in is individualized.

As an example, you can work on exercises and project in a group of two and each write your own lab journal and project report. These must then clearly state who you collaborated with.

It is allowed to write lab journal and project report in a group of two (or perhaps three), but then you must clearly state the main responsible for each part of the lab journal and the project. In the project report, you can share main responsibility for introduction and discussion. Having assigned main responsibility of a part to one person in the group does not mean that the other person did not contribute to this part. A statement saying that all group members contributed equally is inadequate.

Feedback

Use your current status with respect to solving the worksheets and completing your project as an indicator of your performance. Ask instructors during exercise sessions to get an indication of the correctness of your solutions or the level of ambition of your project work.

Preliminary Weekly Schedule

Week	Subject	Curriculum	Exercises
1 3/9	Introduction, graphics pipeline, primitives, attributes, color.	R: Chapters 1-2	Worksheet 1
2 10/9	Animation, interaction, event-driven input, position input.	A: Chapter 3	Worksheets 1-2
3 17/9	Interactive programs, time-stamped animation.	[R: Chapter 3]	Worksheets 2
4 24/9	Synthetic camera models, transformation matrices, viewing and perspective.	R: Chapter 4	Worksheet 3
5 1/10	Hidden-surface removal, lighting and shading.	R: Chapter 5	Worksheet 4
6 8/10	Indexed face set, load and display 3D models, local vs. online webpage.	R: Chapter 16 GL: pp. 414-430	Worksheet 5
7 22/10	Buffers and images, texture mapping, multitexturing.	R: Sections 6.1-6.5	Worksheet 6
8 29/10	Environment mapping, reflection mapping, bump mapping.	R: Sections 10.2-10.5 R: Sections 6.7-6.8	Worksheet 7
9 5/11	Projection shadows, blending, z-buffer and depth sorting.	R: Sections 7-7.1 R: Sections 6.6	Worksheet 8
10 12/11	Off-screen buffers, multiple shaders, shadow mapping.	R: Sections 7.2-7.10	Worksheet 9
11 19/11	Quaternion rotation, virtual trackball, project proposals.	[R: Section 4.3] A: Section 4.13 GL: pp. 357-360	Worksheet 10
12 26/11	Curves and surfaces.	R: Chapter 17 (supplement)	Project work
13 3/12	Volume rendering.	R: Chapter 14	Project work