21. PROBLEMS WITH LOCUS PROBLEMS

As you trace a locus, often you see interesting features of Sketchpad, and sometimes these features are features of the geometry itself.

Here we have a picture of the crossed parallelogram. When Sketchpad traces a locus, it connects points in the order they are plotted. If you move the point D controlling the figure quickly, back and forth, you will be connecting the locus points G out of left-right order, and there will be not be a clean locus.

When you animate D and trace G, you notice that the dots on the trace are more spread out to the right and more together on the left. (Sketchpad will not now let the dots stay after the animation stops.) If you watch carefully, D moves at a constant rate, but point G moves more slowly as D gets to the left of center.

To see this another way, we have constructed the locus G as D moves along. More points are being plotted more closely as G moves slower.

We first plotted the locus at 200 points, and notice that the left side of the curve extend further to the horizontal axis than the right.

Below is the same locus plot with only 20 sample locus points. You can see how the points were plotted closer together toward the left. In fact, the plot doesn't even start until quite far to the left.