Different Types of Curves - Closed Curve, Open Curve, Simple Curve.

Closed Curves: Figures in which initial and endpoints coincide with each other are called closed figures.

Region: The interior of a curve together with its boundary is called its region.

Open Curves: A curve has two endpoints, and when it does not enclose the area within itself it is known as an open curve.

Simple Curves: Simple curve are those curves which changes direction but does not cross itself while changing direction.

Non-simple curve: If a curve does cross itself, then it is called a Non-simple curve.

Different Types of Curves:

1. Closed Curve:

• Figures in which initial and endpoints coincide with each other are called closed figures.

• A closed curve is formed by joining the endpoints of an open curve together.

• A closed curve has no endpoints and encloses an area (or a region). 
  Examples, Circles, ellipses are form of closed curves.

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• In a closed curve, there are three parts. 
  (i) interior (‘inside’) of the curve 
  (ii) boundary (‘on’) of the curve and 
  (iii) exterior (‘outside’) of the curve.

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• The interior of a curve together with its boundary is called its “region”.

2. Open Curve:

• A curve has two endpoints, and when it does not enclose the area within itself it is known as an open curve.

• An open curve does not enclose an area within itself and it has two endpoints.

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3. Simple Curve:

• A curve changes its direction but does not cross itself while changing direction. This type of curve is known as a simple curve.

• A simple curve may be open or closed.

• If a curve does cross itself, then it is called a Non-simple curve.

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Simple closed curve:

Simple open curve:

A closed curve that is not simple:     

                                 
 An Open curve that is not simple: