SPI2006 Mathematical methods for interactive systems
- Course codeSPI2006
- Number of credits15
- Teaching semester2028 Spring
- Language of instruction and examinationEnglish
- CampusHamar
- Required prerequisite knowledge
Recommended prerequisite knowledge: SPI2005 Applied mathematics for Computer Graphics and simulation
This course covers mathematical foundations for computer graphics, simulation, and game development. Students learn affine spaces and homogeneous matrices, numerical methods for solving linear systems, and techniques for interpolation and approximation. The course introduces polynomials, splines, and continuity, as well as triangulations, barycentric coordinates, and 3D curves and planes including Bézier and B-splines. Additional topics include collision detection and elementary concepts from game theory, with emphasis on practical applications in interactive systems.
Learning outcome
A candidate who has completed the course has the following learning outcomes:
The candidate
- has a good mathematical foundation for advanced visualisation and simulation
- can demonstrate knowledge of interpolation, approximation, and continuity using polynomials and splines
- understand affine spaces, homogeneous matrices, and their role in geometric modelling
The candidate
- can apply homogeneous coordinates and matrices to model 2D and 3D transformations
- can solve linear systems numerically and evaluate the accuracy of solutions
- can construct and analyse curves and surfaces using Bézier and B-spline techniques
- can implement interpolation and approximation methods for data fitting and geometric design
- can use triangulation and barycentric coordinates to perform computations on meshes and surfaces
The candidate
- can work independently and in teams to apply mathematical methods to problems in graphics, simulation, and games
- can critically evaluate different mathematical approaches for accuracy, efficiency, and suitability
- can communicate mathematical models and computational methods clearly in written and oral form
- can demonstrate readiness to apply these foundations in advanced courses in computer graphics, simulation, or game technology
The students work both individual and in groups to solve given assignments. Teaching is mostly done through pre-recorded videos, presented reading material and through learning activities in class, individual or in groups.
Supervision will be conducted both at an individual level and in groups or project teams.
- 1 group assignment
- 2 individual assignments
- 80% attendance in teaching and 100% attendance in specific learning activities according to the teaching plan
| Form of assessment | Grading scale | Grouping | Duration of assessment | Support materials | Proportion | Comments |
|---|---|---|---|---|---|---|
Portfolio examination | ECTS - A-F | Individual | Hour(s) | 100 | ||
Oral examination | Passed - not passed | Individual |