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Filled Polar plots

• To: mathgroup at smc.vnet.net
• Subject: [mg85089] Filled Polar plots
• From: Yaroslav Bulatov <yaroslavvb at gmail.com>
• Date: Mon, 28 Jan 2008 03:25:13 -0500 (EST)

What is the recommended way of creating filled polar plots? (assuming
it forms a closed non-intersecting curve)

I'm looking to create something like the image on http://en.wikipedia.org/wiki/Superformula,
but PolarPlot doesn't seem to have Filling options

formula[m_, n1_, n2_, n3_] =
  Function[{x}, (Cos[(m x)/4]^n2 + Sin[(m x)/4]^n3)^(-1/n1)];
vals = {{3, 5, 18, 18}, {2, 1, 4, 8}, {3, 3, 14, 2}, {7, 2, 8, 4}};
Table[PolarPlot[(formula @@ v)[x], {x, -Pi, Pi}, PlotRange -> All,
   Axes -> None], {v, vals}] // GraphicsColumn

• Follow-Ups:
  • RE: Filled Polar plots
    • From: "Jaccard Florian" <Florian.Jaccard@he-arc.ch>
  • Re: Filled Polar plots
    • From: "Julio de la Yncera" <ynceraj@gmail.com>