Exploring 3D space with a computer – Part 3: building models from plans
Adrian Oldknow
In the first part of this guide we saw how a variety of basic tools could be used to build up a 3D model. In the second part we used these tools, together with other transformations, such as a rotation, to explore the symmetry of 3D objects and to work with basic 3D shapes such as cubes and other solids. Here we will use these skills to demonstrate how 3D models and 2D plans are linked.
I guess pretty well all of us will have played with coloured cubes at some time in our life - such as 1 x 1 x 1 Lego bricks or `centicubes' etc. So we will start by making an object out of cubic bricks in Cabri 3D. When you open a `New' page in Cabri 3D you get a shaded `ground plane' and a set of three small vectors. If you right-click on the plane you can change its `Surface style' to `Empty'. If you left-click on the `origin' point you can type in a label for it, such as ` O '. Similarly you can label each of the ends of the three small vectors. Our base cube will have its bottom face in the ground plane, and have O as its centre. If its edges are to be parallel to the base vectors we can define one vertex of the cube as the sum of the vectors OX and OY . The `Vector sum' operation is on the menu for the 5 th icon: 
. First click on the vector OX , then the vector OY and finally the origin point O to create the vector OW in the ground plane. 
Now we can create our prototype cube with a face in the ground plane, centred on O and with W as a vertex. Then we can `Mask' the unit vectors and their labels etc. Finally we can select the `Surface style' e.g. `solid' and colour e.g. magenta. Then, with the `Cube' icon selected once more, we can start to `glue' more cubes together.
So make yourself a nice brick model! You can download the file 
Cube stack.cg3 here. or you can manipulate the embedded file below. The ground plane has been masked, as has the original magenta unit cube!
Now we will see how we can get Cabri 3D to show us different kinds of 2D images drawn from this model - rather than the perspective views we have used up to this point.
