Mathematics for Computer Games 2

More maths

Aims of Module

1. To provide the necessary mathematics for the production of 3-d games software.
2. To extend the student’s knowledge of dynamics to include rigid body dynamics in 3-d.

Learning Outcomes

The student will be able

1. To solve differential equations using simple numerical methods and to solve second order ordinary differential equations with constant coefficients, using analytical techniques.
2. To solve simple problems in rigid body dynamics (for box-like objects only).
3. To apply numerical techniques to interpolation and the solution of equations and systems of linear equations.
4. To represent 3-d objects in a 2-d domain.

Outline Syllabus

• Differential equations: second order with constant coefficients and their use in modelling impact.(10%)
• Rigid Body Dynamics: centre of mass, inertia matrices, Principle of Angular Momentum, Euler equations, case studies. (55%)
• Numerical Techniques: interpolation, splines and Bezier curves, solution of non-linear equations by Newton-Raphson, solution of systems of linear equations, simple numerical solution of o.d.e.s by Euler with an awareness of instability.(20%)
• Introduction to 3-d representations: rotations translations, perspective, quaternions.(15%)