multifocus_ellipse
Extending the classical pins-string-and-pencil ellipse drawing technique to more than 2 foci. The generic problem is, given a set of 2D points, make a string loop around them and the tip of a pencil and trace a convex smooth curve around the points with this pencil while keeping the loop taught.
For 3 non-collinear foci the resulting curve looks like this:
It is in fact a smooth combination of 6 elliptical fragments, each built on just two foci out of three:
Animation of a running pencil in a string loop:
For 4 non-collinear foci the resulting curve looks like this:
It is a smooth combination of 8 elliptical fragments, each built on two foci out of four:
The following drawing shows the effect of different amount of slack in the loop, ranging from "almost a polygon" to "almost a circle":
