3D MATHEMATICS FOR SIMULATION AND VISUALISATION

 SHE Level 2 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code M2I625705 Module Leader Leonard Scott School School of Computing, Engineering and Built Environment Subject Computing Trimester A (September start)

Pre-Requisite Knowledge

Mathematics for Computer Games or equivalent.

Summary of Content

This module continues and enhances the foundation of mathematics for games technology. The module will cover the mathematical techniques needed by professionals in the simulation and visualization industries for the understanding and application of routines used in industry standard physics engines and graphics libraries.

Syllabus

1 Trigonometry: review of sine, cosine, tangent and inter-relationships; application to 3D geometry. 2 3D Coordinate systems: cartesian; spherical; cylindrical; quaternions; homogeneous coordinate systems; relative coordinate systems; yaw, pitch and roll. 3 3D Geometry: vectors as models of position, velocity, acceleration and force; symmetry; parametric representations of curves and surfaces; polyhedrons; light sources; triangulations. 4 3D Transformations: translations, rotations, reflections, inversions and scaling. 5 Projections: perspective; axonometric. 6 Kinematics: position, velocity and acceleration of a moving particle; rigid body motion. 7 Classical mechanics of particles: force; Newton's laws; equations of motion; potential and kinetic energy. 8 Mechanics of rigid body motion: introduction to multiple integration; inertia, angular momentum, torque; Euler's theorem on rigid body motion. 9 Numerical methods: Euler method and backwards Euler Methods; Runge-Kutta methods; stability; convergence. 10 Further forces: equations of aerodynamic and hydrodynamic lift; viscosity; elasticity. 11Collisions: conservation of energy and momentum; coefficient of restitution. 12 Differential equations: differentiation and partial differentiation; solving first and second order constant coefficient differential equations.

Learning Outcomes

On successufl completion of this module, students should be able to:1 Solve games related problems in 3D geometry.2 Apply Newton's laws to modelling the motion of objects subject to a range of forces.3 Demonstrate and apply standard projections of 3D space onto a surface.4 Represent and manipulate objects with respect to different coordinate systems.5 Compare and contrast numerical algorithms.

Teaching / Learning Strategy

The University 'Strategy for Learning' documentation has informed the learning and teaching strategy for this module. The module material will be introduced through lectures, while practical exercises, based on the lecture material, will be given to students for their laboratory sessions. Tutorials will be used to help explain and elaborate on both the lecture material and the laboratory exercises. The course material will be introduced through lectures, while practical exercises, based on the lecture material, will be given to students in tutorials. Tutorials will be used to help explain and elaborate on both the lecture material and the laboratory exercises.

- Bourg, D. (2002) Physics for Games Developers. O'Reilly. ISBN-13: 978-0596000066. -Lengyel, E. (2003) Mathematics for 3D Game Programming and Computer Graphics. 2nd Edition. Charles River Media. ISBN-13: 978-1435458864. -Plastock, R. et al (2000) Schaum's outline of Computer graphics. 2nd Edition. Schaum Outline Series. ISBN-13: 978-0071357814. -Van Verth, J.M & Bishop L.M. (2015) Essential Mathematics for Games and Interactive Applications. 3rd Edition. CRC Press. ISBN-13: 978-1482250923.

Transferrable Skills

D1 Specialist knowledge and application D2 Critical thinking and problem solving D3 Critical analysis D4 Communication skills, written, oral and listening D5 Numeracy D7 Computer literacy D8 Self confidence, self discipline & self reliance (independent working) D9 Awareness of strengths and weaknesses

Module Structure

Activity Total Hours
Lectures (FT) 36.00
Independent Learning (FT) 120.00
Assessment (FT) 20.00
Tutorials (FT) 24.00

Assessment Methods

Component Duration Weighting Threshold Description
Coursework 1 n/a 30.00 35% Practically Based Assignment
Exam (Exams Office) 2.00 70.00 35% Written Examination