Mathematics for Computer Games 2
Aims of Module
- To provide the necessary mathematics for the production of 3-d games software.
- To extend the studentís knowledge of dynamics to include rigid body dynamics in 3-d.
The student will be able
- To solve differential equations using simple numerical methods and to solve second order ordinary differential equations with constant coefficients, using analytical techniques.
- To solve simple problems in rigid body dynamics (for box-like objects only).
- To apply numerical techniques to interpolation and the solution of equations and systems of linear equations.
- To represent 3-d objects in a 2-d domain.
- 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%)