Exploring 3D space with a computer – an Introduction
Adrian Oldknow
Stringy things
Clicking the arrow at the bottom right of the third icon opens up a menu of lines and curves. As these have length but not breadth or width, they are technically called one-dimensional - and we can think of them as thin strings. But to represent them on the screen they are show as tubes, whose radius, colour and style can be changed.
The first four `straight' choices will be familiar if you have used a computer to work in 2D geometry with software like Cabri II Plus or The Geometer's Sketchpad. A circle can be defined in several ways. Technically in 3D a circle is defined by an axis (line) and a point P not on the line - so it is the locus of all points Q in the plane perpendicular to the axis through P which are the same distance from the axis as P is. So a circle does not just have a centre, but an axis instead. However Cabri 3D makes life easier for us by letting us define the plane in which the circle is to lie. A conic (such as an ellipse or hyperbola) is defined by 5 points which it passes through - but these have all to be in the same plane! We cannot create an intersection curve until we have some papery things. The next figure shows a variety of stringy things - again in different colours, styles etc.
Can you identify which of the stringy things are segments, lines, rays, vectors, circles and conics? Can you drag points to change their shapes and positions? Can you spin the picture to get a clearer 3D impression? If you download the Cabri 3D file
Strings.cg3 then you will be able to create more stringy objects of your own, as well as hide or delete the ones above.
Challenge:
Can you make a model of bicycle, like the racing bike below, using just points, segments and circles.? Which bits cause the most difficulty?
Of course the bicycle has bits which jut out of the plane - like the handlebars and pedals. To make these will need to find how to create a perpendicular to a given plane.
