Table of ParametricPlots crashes Kernel

Question

I can usually crash the Mathematica Kernel by using Table to generate a List of ParametricPlots, as follows:

 testpara[α_] :=
 ParametricPlot[
  {
   {Cos[θ], Sin[θ]},
   {2 Cos[α] + Cos[θ], 
    2 Sin[α] + Sin[θ]},
   {r, 0}
   },
  {θ, 0, 2 π},
  {r, 1, 2},
  PlotRange -> 3,
  Frame -> False
  ]

Table[testpara[α], {α, 0, 2. π - π/36, π/36.}]

The current "high" number of plots, with a step size of π/36, crashes the Kernel every time. Starting with a large step size (eg. π/6) often works well on first execution, but also crashes if I execute the cell again. The smaller the step size (leading to a larger number of plots in the List), the higher the regularity of the Kernel crashes.

• Surely a list containing 12 ParametricPlots isn't too much?
• How can I prevent this crashing behavior?

(For example, is it something I can code differently, or do I need to change available memory in Options somewhere or ...?)

Answer 1

On further look, your ParametricPlot expression is a bit odd. You have something like :

 ParametricPlot[{ f[t] , g[t] , h[r] } , {t,trange} , {r,rrange } .. ]

By supplying ParametricPlot with two independent variables it thinks you want to plot regions, yet none of your functions depends on both variables.

Try this:

 testpara[\[Alpha]_] := Show[{
       ParametricPlot[{
           {Cos[\[Theta]], Sin[\[Theta]]},
           {2 Cos[\[Alpha]] + Cos[\[Theta]],2 Sin[\[Alpha]] + Sin[\[Theta]]}
                       }, {\[Theta], 0, 2 \[Pi]},
                          PlotRange -> 3, Frame -> False],
       ParametricPlot[{{r, 0}}, {r, 1, 2}, PlotRange -> 3,
           Frame -> False, PlotStyle -> {Thick, Red}]}]
 Table[ testpara[\[Alpha]], {\[Alpha], 0, 2. \[Pi] - \[Pi]/36, [Pi]/36.}]

( Etc ... )

A more simple example in case that doesn't make sense: This apparently works just fine

 ParametricPlot[ { r, r^2  } , {r, 0, 1}, {p, 0, 1}]

but looking close,

 Cases[ Normal@% , _Polygon , Infinity] // Length

3136

that curve is rendered as thousands of tiny degenerate polygons.

Of course having the kernel just shut down is never acceptable, but it least we can sort of see why.

Answer 2

ClearAll[t, al];

set[t_, al_] := {{Cos[t], al + Sin[t]}, {2 Cos[al] + Cos[t], 2 Sin[al] + Sin[t]}, {al, t}};

ParametricPlot[set[t, al], {t, 0, 2 \[Pi]}, {al, 1, 2}, PlotRange -> All]

Table[set[1., al], {al, 0, 2. \[Pi] - \[Pi]/36, \[Pi]/36.}] // TableForm

Taking one parameter only in the Table, it works.