Exploring 3D space with a computer – an Introduction
Adrian Oldknow
This is the first of a series of monthly features on ideas and techniques for exploring 3D space using the Cabri 3D software for PC or Mac. In order to make use of the materials you will need to have a copy of Cabri 3D installed. You can obtain a full copy from Chartwell-Yorke for £50 + VAT: http://www.chartwellyorke.com/cabri3d/cabri3d.html
Alternatively you can download the free 30-day evaluation version from the CabriLog website: http://www.cabri.com/download-cabri-3d.html .
I will be providing resources in each of two different forms. There will be files written in Cabri 3D which you can open with your copy of the software – and hence you can both manipulate and amend these files. This applies to the evaluation version even when the 30-days have expired – you can open and interact with files, but you will not be able to save or print your own work.
The working models created in Cabri 3D can be imported as objects into web-pages, MS Word documents, other MS Office applications etc. In order to manipulate these objects you just need to have a number of special files (of the type called DLL) installed on your computer. These are automatically installed as part of the process of installing Cabri 3D (whether using the purchased version or the free evaluation one). Even the 30-day trial period has expired you will be able to manipulate the embedded objects as long as the software is installed on your computer.
* Once you have Cabri installed on your system, you will be able to see and interact with all of the examples displayed on this page.
To download and use the examples within the Cabri program itself, click links dislayed as: 
filename.cg3 etc.
So what sorts of `manipulation’ are possible? The simplest type is just to `spin’ the displayed objects to see them from different viewpoints. This is done by holding down the right-hand button on the mouse and dragging it. Try it on the example below!
(You may first need to right-click in the box, select `Cabri3ActiveDoc Object’ and then `Manipulate’.) You should see a `hand’ symbol, which turns into a `4-arrow’ symbol when you hold the right-hand mouse button down.
The picture shows the usual starting display provided by Cabri 3D - which is an impression of the `ground plane' together with three `unit vectors'. I have used one of the basic tools in Cabri 3D to create a segment AB in the plane. You should be able to place the mouse somewhere on the segment AB - when you will see it turn colour and start to flash! If you hold down the left-hand mouse button the symbol changes to a `dragging hand' and you should be able to slide the segment around in the plane without changing its length or direction, just its position. You should also be able to `select-and-drag' one of the segment's endpoints, such as A , and drag the point to change the length and/or direction of the segment. If I had decided to hide the end-points A, B of the segment, then you would not be able to change its length. Thus the person creating Cabri 3D `manipulatives' for use in this way can determine just how much control to give to the user. However if you download the Cabri 3D file
trials.cg3 you will be able to open it with the Cabri 3D software, and then it is yours to do what you like with! For example you can select the segment AB and open a menu with a right-click to change the colour, size and style of the segment - also to mask (or hide) it.
The final thing you will need to do to equip yourself for this venture into 3D space with Cabri 3D is to download the English version of the manual, together with the Flash tutorials, from: http://www.cabri.com/download-cabri-3d.html#manuals .
Before we get involved with building some models we ought to consider just where the `3D-ness' of the computer lies! You will be looking at a computer screen, or monitor - or maybe an image projected onto a screen, wall or Interactive WhiteBoard (IWB). Each of these is (more-or-less) flat and so is firmly two-dimensional. However, the Cabri 3D software keeps an internal record of the 3D coordinates of each point, as well as how lines, planes etc depend on them. The software assumes you are viewing the image somewhere on a line perpendicular to the display coming out for the `origin' point on the base-plane - just as an artist does when drawing in perspective - and in the same way as a camera takes a picture. Cabri 3D then uses the mathematical rules of perspective to create a mathematically correct image on the 2D display - so you see the image much as you would do by looking at a building, say, with one eye closed. We learn as infants how to bring together the pair of 2D images we receive on the retinas of our eyes to create our own mental idea of 3D. These images are just a small rotation of each other - and so by `spinning' the Cabri 3D image a small amount we can achieve a similar effect.
So now we will explore how we can use some of the main tools from the Cabri 3D toolbar to create 3D objects around a theme. There are three main kinds of built-in object - (a) dotty things, (b) stringy things and (c) papery things.
