Closed curve

A closed curve is a curve with no endpoints.

A closed curve flows continuously with no breaks or gaps. It forms a shape with a region or regions that have area. A closed curved can be made of curves and line segments. When drawing a closed curve, the starting point and ending point are the same point. A closed curve is the opposite of an open curve, which has two or more endpoints. The following are a few examples of open curves.

Types of closed curves

There are two types of closed curves.

Simple closed curves

A simple closed curve is a closed curve that does not intersect anywhere except at its beginning point and end point.

Each figure above is a simple curve. None of these simple curves cross over themselves.

Non-simple closed curves

A non-simple closed curve is a closed curve that intersects itself at more than just its beginning point and endpoint. A non-simple closed curve creates two or more distinct regions.

Each of the three non-simple curves above overlaps at least one time.