curve groupings

Some more general groupings of curves are the following:

A closed curve is a curve with no endpoints, so it encloses an area.
A curve that is not closed, is an open curve.

A simple curve is a curve that does not cross itself.
A nonsimple curve does cross itself.

A Jordan curve is a curve which is topologically equivalent to a circle.
Such a curve with a direction is called a contour.

A simple closed curve with no points of inflection is called an egg curve.