Example 7- Two Quadratic Splines |
Top |
In the diagram below, D and E are located at proportion t along AB and BC respectively. F is the intersection of AE and CD. G is the point proportion t along the line DE. We examine the loci of F and G as t varies from 0 to 1. Observing the parametric form of the curves we see that one is a parametric quadratic, while the other is a rational quadratic. Implicit forms are both conics (and almost, but not quite, identical). ![]() What types of conics are they? Extending the curves a little can give a clue: ![]() The upper curve looks like a parabola, the lower certainly does not. Can you show this is generally true from the algebraic equations of the curves?
|