After completing the Parabola Generator, I realized the
Ellipse and Hyperbola could be generated with modifications to
the same device. These modifications change the basic
parameters that describe conic sections - the distance from
the directrix to the vertex (vD) and the distance from the
vertex to the focus (vF).
The eccentricity of a conic section is determined by dividing
vF by vD.
- A value < 1 describes an ellipse.
- A value = 1 describes a parabola.
- A value > 1 describes a hyperbola.
The parabola generator was the easiest to construct because vD
= vF. This relationship allowed me to use one compass to open
the parallelogram and strike arcs, after moving the compass to
the focus. To draw ellipses and hyperbolas, the compass
setting used to open the parallelogram is different from the
setting used to strike the arcs. Instead of changing the
compass setting after opening the parallelogram, I decided to
use two compasses for the ellipse and hyperbola generators.
To make the animations easier to draw, I used multiples of vD
and vF for the compasses settings.
More Conic Section definitions are on the Hyperbola page.