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

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definition

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.

notes

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.

 

 

 

  • 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.

 

 

 

 

 

  • 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.

 




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.

 






Simple closed curve:

 

 

 

 

Simple open curve:

A closed curve that is not simple:     

                                 
 An Open curve that is not simple:

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