This book brings together a number of different mathematical approaches which are used by computer programmers to create and manipulate images. Many of these were originally developed to define shapes used in the manufacture of objects as diverse as drinking glasses, shoes, aircraft wings and car bodies as part of a process called CADCAM (Computer Aided Design and Computer Aided Manufacture). More recently many of these techniques have found their way into producing “virtual reality”, initially for simulating views in motion, such as in training pilots to use flight controls to land in a simulator. Now many are used in the entertainment industry to create cartoons, animations, special effects and video games. Most of us are quite unaware just how much mathematics is being used when, for example, you play even the simplest video game – let alone when you “bowl” a ball down a simulated bowling alley on a Nintendo Wii.
The mathematics spans quite a range, from the use of simple constructions, circular arcs, transformation geometry, coordinates and vectors to functions, calculus, matrices, parametric and polar equations etc.., and so covers material from KS3, GCSE, AS, A2, FM, S1-S3 and Senior. One way of using the materials is to enhance normal lesson content when a particular topic e.g. vectors is being covered – in order to stimulate some more engagement with the topic by seeing an application. Another is to offer individuals, clubs etc.. enrichment activities outside normal lessons e.g. to stretch high attaining students. The materials provide full details of the mathematics involved, as well as references for further reading. However the mathematical details can be skipped by those who just want to use the files to make their own designs.
Most of the geometric (and analytic) techniques used are ones which may be familiar to experienced users of dynamic geometry software, such as Cabri II Plus and the Geometer’s Sketchpad. However we will not assume that most readers of this booklet, whether students or teachers, have that experience, so we also give full details of the software techniques used. Again these can be skipped by those who are already familiar with them. While the emphasis in this book is on the development and use of TI-Nspire files to create computer graphics, students should also be encouraged to try practical activities such as drawing and making objects, pacing out a locus etc..