Game Mathematics and Algorithms (5 cr)

Evaluation scale

H-5

Content scheduling

7 weeks in September – October

- Cartesian coordinate system
- Vectors and Matrices
- Different metrics to define distances
- Projection and Raycast
- UV coordinate system and textures
- Image processing algorithms
- Vector displacement map vs. heightmap displacement
- Optimisation in rendering: LOD, MipMap Quadtree

Objective

After completing the module, the student will be able to:
- Describe a 2D Cartesian coordinate space and how to locate points using that space and extend these ideas into 3D
- Calculate vectors and use them in games
- Describe some basic concepts of image and video processing and compression
- Calculate matrices and use them in games
- Learn about linear transformations (such as translations, scaling, skewing, and rotations) and multilinear transformations (including rotations about an arbitrary axis)
- Calculate algorithmic (Kolmogorov) complexity and understand how this is related to game performance

Content

- Cartesian Coordinate Systems
- Vectors
- Multiple Coordinate Spaces
- Matrices & Linear Transforms
- Polar Coordinate Systems
- Rotation
- Geometric Primitives
- Algorithmic complexity

Materials

Materials shared on lectures and in labworks

Teaching methods

Teacher-directed classroom activities, group work and independent work.
Weekly task and learning repots.

The use of AI to support learning is allowed

Pedagogic approaches and sustainable development

Students learn the basic concepts involved in creating visual interactive 3D content and transfer mathematical concepts into code.

Student workload

Classroom activities: Classroom activities participation 7 weeks 6h/week ( 2 h theory, 4 h labwork), Total 42 h
Homework: Working on homework 7 weeks 12 h /week, total
Learning report: Writing personal learning report 1h /week, total 7 h

Evaluation methods and criteria

- Participation to contact lessons are mandatory
- Weekly assignments are divided to three levels.
- Students will gain point from every successfully completed task level -> course maximum points 3 * 7 = 21
- Every week at least level 1 assignment need to be returned.-> course minimum points 1 * 7 = 7
- Grade will be derived linearly from gained points:
- 7 points -> grade 1
- 17 points -> grade 5
- Weekly learning report mandatory
- Purely made reports can lower the grade
- Nicely made reports can raise the grade

Failed (0)

Course will fail if:
- if not attended at least 50% of the contact lessons
- Not delivered at least one weekly task for every week

Assessment criteria, satisfactory (1-2)

Participated on lectures and delivered at least one task and learning report every week

Assessment criteria, good (3-4)

Participated on lectures, delivered learning report every week and most of the tasks in course.

Assessment criteria, excellent (5)

Participated on lectures, delivered learning report every week and all most all of the tasks in course.

Further information

All additional information in Course Itslearning pages