Fill a parametric plot without seam?

Questions
1

I’m trying to fill a parametric plot, but I get this ugly seam for some values of a. Observe the following code:

f[t_, r_, a_] := {r*Cos[2 Pi*t]*Sin[Pi*t + 2*Pi*a], 
   r*Sin[4 Pi*t - 2*Pi*a]*Cos[2*Pi*t + 2*Pi*a]};
ff[a_] := 
  ParametricPlot[f[t, r, a], {t, -1, 1}, {r, 0.5, 1}, 
   PlotRange -> {{-1.2, 1.2}, {-1.2, 1.2}}, Axes -> False, 
   Frame -> False, PlotPoints -> 60];
Export["Out" <> ToString[0.1] <> ".png", ff[0.1], 
  ImageSize -> 3900];

Here’s the output when a=0.1:
enter image description here
As you can see, there’s this ugly seam that appears, and it only appears for certain values of a (not all)! I don’t know what’s causing it, but given that I’m trying to export it as an animation, this seam is not acceptable. The problem is that I don’t know how to get rid of it.

How can I change my code to prevent the seam from appearing?

2

Hi John,

The “ugly seam” is actually the boundary of the plotted function. The values of a for which the boundary is not as apparent is where the boundary narrows to a point. Specific boundaries could be removed by post processing the plot’s symbolic expression. All boundaries can be removed by specifying BoundaryStyle -> None.

3

Crossposted here.