Exploring 3D space with a computer – an Introduction
Adrian Oldknow
Now we shall see what happens when we saw through a log!
The origin O and the vertical vector OZ have been used to define a line, on which the point Z' has been created. The line OZ has been masked and the vector OZ' defined.
A slider S has been created on OZ' . The point A has been created in the plane, and along with vector OZ' is used to define the circle with OZ' as axis passing though A . This circle and the vector OZ' are used to define the cylinder. The points P and Q are created to lie on the surface of the cylinder. Finally a plane is created through the points P, Q and S . The green curve is created as the intersection of the cylinder with the plane PQS . So the points P and Q model points on the `log' through which the `saw' will pass, and S controls the angle at which the saw cut will be made. See the effect of dragging P, Q and/or S . Use A to control the radius of the `log' and Z' its length. The Cabri 3D file is 
Logslice.cg3.
To complete the techniques of this first section we shall see how to create perpendiculars and parallels, and then use translations to build up some models of common objects like pyramids and boxes. We shall start with a making a rectangle in the ground plane using the Perpendicular tool from the menu for the fifth icon.
The origin O and the vertical vector OZ have been used to define a line, on which the point Z' has been created. The line OZ has been masked and the vector OZ' defined. A slider S has been created on OZ' . The point A has been created in the plane, and along with vector OZ' is used to define the circle with OZ' as axis passing though A . This circle and the vector OZ' are used to define the cylinder. The points P and Q are created to lie on the surface of the cylinder. Finally a plane is created through the points P, Q and S . The green curve is created as the intersection of the cylinder with the plane PQS . So the points P and Q model points on the `log' through which the `saw' will pass, and S controls the angle at which the saw cut will be made. See the effect of dragging P, Q and/or S . Use A to control the radius of the `log' and Z' its length. The Cabri 3D file is Logslice.cg3.
To complete the techniques of this first section we shall see how to create perpendiculars and parallels, and then use translations to build up some models of common objects like pyramids and boxes. We shall start with a making a rectangle in the ground plane using the Perpendicular tool from the menu for the fifth icon.
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.
