Exploring 3D space with a computer – an Introduction
Adrian Oldknow
Sawing through a log continued
The segment AA' is made in the ground-plane, and B as a slider on it. The green plane is the perpendicular to AA' through A, which intersects the ground plane in a line.
This line is perpendicular to AB , and we take a point C as a slider on it. The perpendicular to the green plane through C is a line parallel to AB . The red plane is the perpendicular to AA' through B , which intersects the parallel line in D . The quadrilateral (polygon) ABCD is our required rectangle. Its length and breadth are controlled by the sliders B and C . The Cabri 3D file is 
Rectangle.cg3.
In order to complete the box we will need to construct a perpendicular to the ground plane through A and use it to define a vector AE by which to translate the rectangle ABCD . The `Transformation' menu is the sixth icon.
The perpendicular to the ground-plane through A has been constructed, and a slider E created on it. The line AE has been masked and the vector AE created. The vector AE and the polygon ABCD are used with the Translation tool to create the polygon which is the upper surface of the box. The points B, C and D are also translated by AE and the segments EF, FG, GH, HE created. The `back wall' has been created using the Polygon tool, and by clicking in turn on A,C,H,E and then clicking back on A again. Check that you can slide E to raise and lower the `roof'.
The Cabri 3D file is Box.cg3. Can you open it with Cabri 3D and complete the remaining faces of the box.
Challenge: Can you build on the `Box' techniques to create a model of a building such as a barn, house or church? I used the Midpoint tool to help create my attempt at a barn.
Finally here are some mathematical solids created using the techniques of this opening guide to exploring 3D with a computer. You might like to see if you can work out how to make these or other ones yourself. Next time we will look at using the software to explore properties of the main shapes met in solid geometry. See you then.
