SCQF Level: 08
Module Code: MAT201
Credit Value: 20
Term: Term 1
School: School of Arts, Media and Games
This module expands on the concepts of Applied Mathematics 1, on applied mathematics relevant to the Computer Games Technology programme.
The aim of this module is to provide the student with: an appreciation of the advanced ideas and techniques in applied mathematics relevant to Computer Games Technology.
By the end of this module the student should be able to:
1. Use calculus methods to describe/approximate surfaces and to solve optimisation problems.
2. Use the ideas of homogeneous coordinate matrix transformations and quaternions for 3D rotations in computer graphics applications.
3. Use the rays and beams in the modelling of reflection, refraction and collision detection with regular shapes.
4. Solve problems in 1D involving variable acceleration and resistance.
5. Solve problems in 2D, including circular and simple harmonic motion; and elastic collisions.
First and second order partial differentiation. Extrema of two variable functions.
2 Matrix and Quaternion Transformations
3D matrix transformations: translation, scaling, rotation and reflection. Parallel and perspective projections. Complex numbers. Quaternions and their application to rotations about an axis.
3 Vector Curves and Surfaces
Vector geometry of curves and surfaces in space. Tangent planes and normals.
4 Ray Tracing
Intersection of rays with 3D surfaces. Tracing reflected and refracted rays of light in 3D using vectors.
Variable velocity and acceleration. Straight−line dynamics with variable forces (e.g. dependent on speed). Circular motion, simple harmonic motion. Oblique impact of objects in 2D.
Statement on Teaching, Learning and Assessment
The module will be delivered by a mixture of lectures and tutorials. There will be a formative test during structured feedback week. The learning outcomes will be assessed by an end of semester exam.
Teaching and Learning Work Loads
|Supervised Practical Activity||0|
|Unsupervised Practical Activity||0|
Credit Value – The total value of SCQF credits for the module. 20 credits are the equivalent of 10 ECTS credits. A full-time student should normally register for 60 SCQF credits per semester.