Function Repository Resource:

ContrapedalCurve

Compute the contrapedal curve

Contributed by: Alfred Gray

ResourceFunction["ContrapedalCurve"][{a,b},c,t]

gives the contrapedal curve of the plane curve c with respect to the point {a,b} and parameter t.

Details and Options

The contrapedal curve is the analog of the pedal curve but computed using the normal instead of the tangent.

The pedal of a given curve c from a fixed point p is the locus of the foot of the perpendicular from p to the tangent to c.

The contrapedal curve (or normal pedal curve) is the pedal curve of the evolute of a curve c.

Examples

Basic Examples (3)

Define a cardioid:

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Compute the contrapedal of the cardioid:

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Plot the cardioid along with its contrapedal:

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$ParametricPlot[ Evaluate[{cardiod[t], ResourceFunction["ContrapedalCurve"][{0, 0}, cardiod[t], t]}], {t, 0.1, 2 \[Pi]}, Axes -> None]$

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Basic Examples (3)

Define an ellipse:

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Compute the contrapedal of the ellipse:

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Interactively plot the ellipse along with its contrapedal curve, varying the base point:

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$Manipulate[ ParametricPlot[ Evaluate[{ellipse[t], ResourceFunction["ContrapedalCurve"][p, ellipse[t], t]}], {t, 0, 2 \[Pi]}, Axes -> None, PlotRange -> 3], {{p, {0, 0}}, {-5, -5}, {5, 5}}]$

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Publisher

Enrique Zeleny

Version History

1.0.0 – 26 February 2020

Source Metadata

Citation:
- Gray, A., Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 1997.

Related Resources

License Information

This work is licensed under a Creative Commons Attribution 4.0 International License