Resource for a library of closed curves.

Question

I am working on a computation project and I need a bunch of closed curves to test my programs on. Does anybody know of a resource or library of such curves somewhere preferably online. I would like to not have to come up with a bunch by hand especially since I want to avoid any bias that may appear in constructing them myself. Any help is greatly appreciated.

Answer 1

The following provides a way to get a somewhat unbiased set of many closed curves, but takes a bit of work by hand. Start from some table of integrals (say "Pierce's Short Table of Integrals"). Go to one of the chapters and for each formula that is not generic for unspecified $f(x)$, look at either the integrand or the result. Then plot that result as a polar plot, and observe when (if) the curve closes. There you have one sample curve.

For example, integral $3$ in chapter $1$ is $\int \frac{dx}x = \log x$. Plotting $r = \log \theta$ gives a curve that comes in from the left, crosses the origin from below, loops around and crosses itself at about $\theta = 0.2913$. So take $r = \log \theta, \theta \in [0.2913, 0.2913+\pi]$ as your first example closed curve.

In may cases the curve will not close; then just move on to the next one.

Answer 2

This is really a good site for what you are looking for.