SPI2006 Mathematical methods for interactive systems

    • Course code
      SPI2006
    • Number of credits
      15
    • Teaching semester
      2028 Spring
    • Language of instruction and examination
      English
    • Campus
      Hamar
Course content

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

Upon passing the course, students have achieved the following learning outcomes:

Knowledge

The student

  • 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
Skills

The student

  • 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
General competence

The student

  • is able to work independently and in teams to apply mathematical methods to problems in graphics, simulation, and games
  • is able to critically evaluate different mathematical approaches for accuracy, efficiency, and suitability
  • is able to communicate mathematical models and computational methods clearly in written and oral form
  • is able to demonstrate readiness to apply these foundations in advanced courses in computer graphics, simulation, or game technology
Working and teaching methods

The students work both individually and in groups to solve given assignments that connect theory to practice. Teaching is primarily conducted through in-class lectures combined with presented reading material, ensuring that key mathematical concepts are introduced and discussed interactively. Learning takes place mainly through classroom activities, both individual and group-based, where students apply theoretical knowledge to practical problems from graphics and games.

Each topic is supported by study materials such as texts, lectures, and online tutorials, along with minor assignments to be completed through self-study either individually or in groups prior to class. In-class learning activities include problem-solving assignments, group discussions, critique, pitches, and workshops, all designed to reinforce understanding of mathematical tools in real applications.

Supervision is provided both individually and in groups or project teams, ensuring that each student has access to the teaching resources and guidance needed in collaborative projects and productions where “problem-based learning” is applied.

Compulsory activities
  • 1 group assignment
  • 2-3 individual assignment
  • attendance in all organised activities
Examination
Form of assessmentGrading scaleGroupingDuration of assessmentSupport materialsProportionComments
Written examination with supervision
ECTS - A-F
Individual
6 Hour(s)
100
Faculty
Faculty for Film, TV and Games
Department
Department of Game Development - The Game School
Area of study
Matematisk-naturvitenskapelige fag/informatikk
Programme of study
Bachelor in Game Technology
Course level
Foundation courses, level I (100-LN)