Note

This Mathematica notebook is from the WWW project A Visual Dictionary of Special Plane Curves. Copyright © 1995-2004 by Xah Lee. (http://xahlee.org/)

Piriform

Packages and Initializations

Needs["ParaPlot`"]
Needs["PlaneCurveFormulas`"]
Needs["PlaneCurveGenerator`"]

Needs["Graphics`ImplicitPlot`"]
(*MathSource Item:0200-529*)

definition

?Piriform

ParaPlot[ Evaluate[ Piriform[2][t]],  {t, 0, 2*Pi}]

plotting the family of curves

ParametricPlot[
Evaluate@
        Table[Piriform[h][t], {h, 0.3, 
            5, (5 - 0.3)/9}], 
{t, 0, Pi}, 
      AspectRatio -> Automatic, PlotRange -> All, 
      PlotStyle -> 
        Table[Hue@i, {i, 0, 1, 1/10}]
]

plotting the family with more even distribution

we use this cubic function

Table[
      0.3 + 0.037608* (h^3), {h, 0.3, 
        5, (5 - 0.3)/12}]

Piriform[#][t] & /@ 
      Table[0.3 + 0.037608* (h^3), {h, 0.3, 
          5, (5 - 0.3)/12}]

ParametricPlot[
Evaluate@(Piriform[#][t] & /@ 
            Table[0.3 + 0.037608* (h^3), {h, 0.3, 
                5, (5 - 0.3)/12}]), 
{t, 0, Pi}, 
      AspectRatio -> Automatic, PlotRange -> All, 
      PlotStyle -> 
        Table[Hue@i, {i, 0, 1, 1/12}]
]