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Parametric Plot


A parametric plot displays the image traced by parametric equations as their parameter varies over a specified interval. A plane parametric plot has the form

 r(t)=(x(t),y(t)) for a<=t<=b,

while three component functions define a space curve. Unlike the graph of a single-valued function y=f(x), a parametric plot may double back, have vertical tangents, or pass through the same point for different parameter values.

ParametricPlot

The cycloid parametrized by x(t)=t-sint and y(t)=1-cost is illustrated above.

The Wolfram Language function ParametricPlot[{fx, fy}, {t, tmin, tmax}] plots a plane parametrized curve, and its three-component form plots a space curve.


See also

Parametric Equations, Plane Curve, Space Curve

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References

Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 1998.

Cite this as:

Weisstein, Eric W. "Parametric Plot." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ParametricPlot.html

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