What Are Curved Line Segments?

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Lines are two-dimensional objects defined by two or more distinct points. In mathematics, there are two types of lines: straight lines and curved lines. While a straight line segment will always have a slope that is constant, the slope of a curved line segment will be different at each point along the line.

Closed Curves

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A closed curve is a mathematical term that refers to a shape with no endpoints. A closed curve can be simple, meaning that the curve never crosses over itself. Examples of simple closed curves include circles, ovals and polygons. A non-simple or complex closed curve is a curve in which segments of the curve cross over each other such as in a figure eight. Although the term curve is used, a closed curve does not need to contain any curved lines. It can contain curved lines, straight lines or a combination of both. A simple or a non-simple closed curve does not need to be a regular or uniform shape; a flower outline, an irregular blob outline or an arrow outline are all examples of closed curves.

Open Curves

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As its name would suggest, an open curve is any curve where the endpoints don't meet. The letter U is an example of an open curve. As with closed curves, open curves can be composed of either straight or curved lines or a combination of both. Open curves can be irregular or regular shapes. Also like closed curves, an open curve is considered simple if its segments never cross.

Bezier Curves

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A Bezier curve is a type of open curve used in many computer drawing and design programs. This classical curve is named for Pierre Bezier who introduced the curves for use with computer-assisted design software. Although a Bezier curve is a line segment, it is defined by not two, but four separate points. Although it can't be seen, these four points form a quadrilateral shape that contains the curve. Moving any of these points will change the shape of the Bezier curve.

Parabolas

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A parabola is another type of simple open curve. One way to picture a parabola is as an ellipse with one focus in infinity. It is a uniform curve in which the two sides expand outward from the focus infinitely. The parabola is a type of curve that lends itself to shapes like satellite dishes and suspension bridges.