This module builds on Mathematics for Application Development 1 to give CGAD students the mathematical building blocks required for 3-D graphics programming.
The aim of this module is to provide the student with: the necessary mathematical tools for programming 3-D object characterisations in computer graphics.
By the end of this module the student should be able to:
1. Formulate and use transformation matrices (2-D & 3-D) for standard transformations and projections.
2. Determine equations for lines and planes in 3-D, using them to compute distances, projections and intersections.
3. Perform collision detection calculations of rays with boxes and spheres.
4. Apply Newtonian concepts involving momentum, impulse and energy to formulate and solve resulting models.
5. Use vector resolution methods for force systems, relative motion and centres of gravity.
1 Viewing Transformations:
2-D viewing transformation matrices, scaling factors, aspect ratios, windows, normalised device screen, viewports.
2 Lines and Planes:
Vector (using parameters) and Cartesian equations of 3-D lines and planes. Distances from points to lines and planes. Projection of line onto a plane, intersection of lines and planes.
3 Matrix Transformations:
3-D matrix transformations of scaling, rotation, reflection and translation (homogeneous coordinates). Composite transformation by matrix multiplication.
4 Projection Matrices:
Standard orthogonal and perspective matrix transformations.
5 Ray Tracing:
Collision detection methods of rays with boxes and spheres.
6 Newtonian Concepts:
Newton’s laws of motion. Momentum and impulse, collision of bodies (1-dimensional, elastic and inelastic). Kinetic and potential energy, elastic strings. Work and Power.
7 Centre of Gravity:
Centre of gravity of composite body. Use of principle of moments to solve centre of gravity problems. Continuous lamina centres of gravity.
Statement on Teaching, Learning and Assessment
Learning will be achieved through lectures and tutorial sessions, with hand-out material being given to students in class and posted on Blackboard. Interactive discussion with staff will be encouraged during classes and tutorial sessions will focus on students’ active enquiry into topics covered in the lectures. Each week there will be two one hour lectures followed by two one hour tutorial sessions. In week 6 there will be a formative, multiple-choice, online test, which will act as a diagnostic of student progress, and will link with structured feedback week (week 7). Students will be encouraged to engage with learning technologies that support their subject development, via web references and using specialist mathematics packages (e.g. Derive and Calmat).
Teaching and Learning Work Loads
|Supervised Practical Activity||18|
|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.
We make every effort to ensure that the information on our website is accurate but it is possible that some changes may occur prior to the academic year of entry. The modules listed in this catalogue are offered subject to availability during academic year 2017/18 , and may be subject to change for future years.