curve categorization

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 curve can have one or more inflection points: that is a point where the second derivative d²y/dx² = 0 and this derivative changes sign at opposite sides.

A Jordan curve is a curve which is topologically equivalent to a circle.
When such a curve has a direction it is called a contour.