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Real-time graphics and computational geometry 7.5 credits

Realtidsgrafik och geometriska algoritmer
Second cycle, D7045E
Course syllabus valid: Autumn 2021 Sp 1 - Present
The version indicates the term and period for which this course syllabus is valid. The most recent version of the course syllabus is shown first.

Education level
Second cycle
Grade scale
G U 3 4 5
Computer Science
Subject group (SCB)
Computer Technology
Main field of study
Computer Science and Engineering

Entry requirements

Bachelor-level knowledge in computer science and specific knowledge corresponding to D0012E Algorithms and data structures, D0003E Real-time systems and D0020E Project in computer science.

More information about English language requirements


The selection is based on 20-285 credits

Course Aim
This course treats theories, methods, and principle for programming interactive real-time computer graphics based on time-variant scenes.

After the course, the goal is that the student should know 

  1. efficient algorithms and data structures for time-variant scenes consisting of three-dimensional objects.
  2. the various steps taken to construct a rendered image of a scene.
  3. the fundamental transforms and algorithms applied in the construction of the previous item.
  4. ways to improve and optimize the rendering process.
  5. how real-time computer graphics is programmed using modern low-level API:s like OpenGL.
  6. how graphics cards function and are built. 

After the course, the goal is that the student should be able to 

  1. write programs that generate interactive real-time computer graphics for time-variant scenes using low-level API:s like OpenGL.
  2. create, analyze, and evaluate algorithms and data structures for building and representing scenes with three-dimensional objects so functional requirements are fulfilled.
  3. create, analyze, and evaluate programmable solutions to the problems concerning the production of real-time computer graphics based on scenes with three-dimensional objects.
  4. formulate and implement optimization algorithms for real-time computer graphics.
  5. work together with other students and plan, carry out, and report the result of projects that results in software elements of time-variant real-time computer graphics both in writing and orally.

The course focuses on theory, methods and principles for computer-based systems containing real-time graphics as well as algorithms and data structures for computer graphics and geometry.

Practical programming of interactive real-time computer graphics. Algorithms and data structures for 1) representing and constructing three-dimensional scenes with curves, surfaces, and compound objects, and 2) the rendering of real-time computer graphics (the pipeline). Geometric transforms. Rasterization. Pixels. Fundamental algorithms for computer graphics. Optimization of the rendering process. Optical surface properties. Lighting and texturing.

Each course occasion´s language and form is stated and appear on the course page on Luleå University of Technology's website.
The teaching consists of lectures on theory and some supervision at lab sessions. Laboratory work is carried out in a computer lab. Most lab work is done individually but some could also be done in groups. Homework assignments that render credit marks on the subsequent written exam may also occur during the course.

If there is a decision on special educational support, in accordance with the Guideline Student's rights and obligations at Luleå University of Technology, an adapted or alternative form of examination can be provided.
Examination consists of a final written exam and mandatory programming assignments during the course. Passing the lab assignment part of the course requires a passed grade on all individual assignments.

The final course grade is a function of the grades of the lab assignments and the grade on the final exam.

The course goals are examined as follows:

Goals 1, 2, 3, 4, 5, 6, 8, and 9: Written exam.
Goals 2, 5, 7, 10, and 11: Laboratory work.

Håkan Jonsson

Literature. Valid from Autumn 2020 Sp 2
Angle and Shreiner. Interactive computer graphics: A top-down approach. Boston, MA: Pearson. Edition 6 (C++) or edition 7-8 (WebGL/javascript).

de Berg, Cheong, van Kreveld och Overmars. Computational Geometry - Algorithms and Applications, 3rd edition, Springer (2008).

Reference: Akenine-Möller, Haines och Hoffman. Real-Time Rendering, 4th edition, CRC Press (2018).

Course offered by
Department of Computer Science, Electrical and Space Engineering

CodeDescriptionGrade scaleCrStatusFrom periodTitle
0001Laboratory workG U 3 4 54.00MandatoryA19
0002Written examG U 3 4 53.50MandatoryA19

Study guidance
Study guidance for the course is to be found in our learning platform Canvas before the course starts. Students applying for single subject courses get more information in the Welcome letter. You will find the learning platform via My LTU.

Syllabus established
by Jonny Johansson, HUL SRT 15 Feb 2019

Last revised
by Jonny Johansson, HUL SRT 17 Feb 2021