Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 NegativePedalCurve

Source Notebook

Compute the negative pedal curve

Contributed by: Wolfram Staff (original content by Eric W. Weisstein)

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

computes the negative pedal curve with respect to the point {a,b} of the curve c in parameter t.

Details and Options

The negative pedal of a curve with respect to the point {a,b} is the curve whose pedal is obtained by the reverse of the procedure that generates the pedal curve.
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.

Examples

Basic Examples (2) 

Define a cardioid:

In[1]:=
cardiod = Entity["PlaneCurve", "Cardioid"][ EntityProperty["PlaneCurve", "ParametricEquations"]][1]
Out[1]=

Plot the cardioid along with its negative pedal curve:

In[2]:=
ParametricPlot[ Evaluate[{cardiod[t], ResourceFunction["NegativePedalCurve"][{0, 0}, cardiod[t], t]}], {t, 0.01, 2 \[Pi]}, Axes -> None]
Out[2]=

Scope (2) 

Define an ellipse:

In[3]:=
ellipse = Entity["PlaneCurve", "Ellipse"][ EntityProperty["PlaneCurve", "ParametricEquations"]][2, 1]
Out[3]=

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

In[4]:=
Manipulate[ ParametricPlot[ Evaluate[{ellipse[t], ResourceFunction["NegativePedalCurve"][p, ellipse[t], t]}], {t, 0, 2 \[Pi]}, Axes -> None, PlotRange -> 3], {{p, {0, 0}}, {-5, -5}, {5, 5}}]
Out[4]=

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.

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