How to fill a closed parametric curve?

Question

I have a curve in parametric form:

ParametricPlot[{(1 - Cos[2 \[Pi] s]) Sin[2 \[Pi] s], 
  Cos[2 \[Pi] s] (Sin[2 \[Pi] s] + 1)}, {s, 0, 1}, Axes -> False, 
 PlotStyle -> Black]

This gives:

Is there a way to fill it with black?

Answer 1

You can post-process ParametricPlot output to change Line to FilledCurve:

ParametricPlot[{(1 - Cos[2 π s]) Sin[2 π s], 
   Cos[2 π s] (Sin[2 π s] + 1)}, {s, 0, 1}, Axes -> False, 
  PlotStyle -> Black] /. l_Line :> FilledCurve[l]

Use the replacement rule

l_Line :> {Opacity[1.], FilledCurve[l]}

to get

We get the same result if we use a rule that replaces Lines with Polygons:

Line[x_] :> {Opacity[1], Polygon[Append[x, First @ x]]}