Mathematics for Application Development 2 | Abertay University

Mathematics for Application Development 2

Description

This module builds on Mathematics for Application Development 1 to give CGAD students the mathematical building blocks required for 3-D graphics programming.

Aims

The aim of this module is to provide the student with: the necessary mathematical tools for programming 3-D object characterisations in computer graphics.

Learning Outcomes

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.

Indicative Content

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

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

Total 200
Lecture 18
Tutorial/Seminar 0
Supervised Practical Activity 18
Unsupervised Practical Activity 0
Assessment 80
Independent 84



Guidance notes

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.


Disclaimer

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 2018/19 , and may be subject to change for future years.