Module Title: Applied Maths (Elective2) English
 Credits: 10
 NFQ Level: 6
Module Delivered In 1 programme(s)
Teaching & Learning Strategies: A mix of traditional lectures and programming practicals that will enable the student to fully understand the use of mathematical methods in computer graphics and apply these ideas in their own computer code.
Module Aim: To provide the student with an understanding of the mathematics required to model the real world as applied in computer graphics.
Learning Outcomes
On successful completion of this module the learner should be able to:
LO1 carry out vector and matrix operations and apply these operations in computer graphics;
LO2 use matrices to represent and carry out transformations and rotations in 2 and 3D space;
LO3 manipulate complex numbers and quaternions and use them in graphics transformations;
LO4 apply the mathematical methods required for 3D geometry and colour manipulation in computer graphics;
LO5 represent mathematical structures in computer code;
LO6 use computer programmes to further explore the concepts of this syllabus.
Pre-requisite learning
Module Recommendations

This is prior learning (or a practical skill) that is recommended before enrolment in this module.

No recommendations listed
Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module.
No incompatible modules listed
Co-requisite Modules
No Co-requisite modules listed
Requirements
This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed.
No requirements listed

Module Content & Assessment

Indicative Content
Trigonometry:
angles, trigonometric functions and Pythagorasâ€™s theorem.
Vectors
vector properties, operations on vectors, dot products, cross products, dimensions, normalisation, geometric interpretations
Matrices
matrix properties, linear systems, matrix inverses, determinants, eigenvalues and eigenvectors, diagonalization, tensors.
Complex Numbers
the argand diagram, operations on complex numbers, conjugates, Euler's identity, 2D rotations with complex numbers, extention to quaternions, 3D rotations with quaternions.
Transforms
coordinate systems, simple translations, scaling transforms, rotational transforms, general linear transforms, homogeneous coordinates, Euler angle representation compared to quaternions and converting between the two.
3D Engine Geometry
lines in 3D space, planes in 3D space, intersections of lines with planes, the view frustum, parallel and perspective projections.
Ray Tracing
root finding, ray and surface intersections, normal vector calculation, reflection and refraction of rays
Illumination
RGB colour, light sources, diffuse lighting, specular lighting, texture mapping.
Assessment Breakdown%
Continuous Assessment20.00%
Practical30.00%
End of Module Formal Examination50.00%
Continuous Assessment
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Other CA marks will be based on the results of four or five 45 minute written tests held during the term. 1,2,3,4,5,6 20.00 n/a
 No Project
Practical
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Practical/Skills Evaluation Practical marks will be allocated for participation in and the completion of the practical exercises. 5,6 30.00 n/a
End of Module Formal Examination
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Formal Exam The terminal examination will include questions on all aspects of the course. 1,2,3,4,5,6 50.00 End-of-Semester

ITCarlow reserves the right to alter the nature and timings of assessment