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I attempted to plot a parametric plot using the following code:

q := Sqrt[((2 + \[Delta])*(4 + \[Delta]))/
      ((-2 - \[Delta]/2)^(4/(2 + \[Delta])^2)*
       (4 + \[Delta]*(6 + \[Delta])))]*
    ((1 - Cos[\[Theta]])^((\[Delta]*(4*M + \[Delta]))/
       (2*(2*M + \[Delta])^2))/(1 + Cos[\[Theta]])^(1/2))*
    (-3*M - \[Delta] + M*Cos[\[Theta]])^((2*M^2)/
      (2*M + \[Delta])^2) //. {M -> 1, \[Delta] -> 1}

R := ((2*M*Sin[\[Theta]])/Sqrt[(M + \[Delta] - M*Cos[\[Theta]])/
       (3*M + \[Delta] - M*Cos[\[Theta]])])*
    ((1 + q^2)/(2*q)) //. {\[Delta] -> 1, M -> 1}

Chop[ParametricPlot[{{R*((2*q)/(1 + q^2)), R*((1 - q^2)/(1 + q^2))}, {(-R)*((2*q)/(1 + q^2)), R*((1 - q^2)/(1 + q^2))}}, {\[Theta], 0, Pi}, PlotStyle -> {{Black}}, 
Axes -> None, PlotRange -> All, Exclusions -> None, Mesh -> False]]

However, I obtained such a graph:

enter image description here

where gaps can be seen although the plot should be continuous throughout. In my code, I have also tried several remedies proposed in earlier posts albeit none worked. How do I resolve this issue?

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  • $\begingroup$ Apparently if I change the delta value from 1 to for e.g. 1.001, the graph will be completely continuous though I have no idea why that solves the issue. $\endgroup$
    – user74137
    Commented Mar 7, 2021 at 15:30
  • 2
    $\begingroup$ Use Chop (or Re) inside (not outside) ParametricPlot to ,,clear'' spurious several $MachineEpsilon imaginary parts. $\endgroup$ Commented Mar 7, 2021 at 15:33
  • $\begingroup$ Just Simplify the functions: ParametricPlot[Evaluate[{{R*((2*q)/(1 + q^2)), R*((1 - q^2)/(1 + q^2))}, {(-R)*((2*q)/(1 + q^2)), R*((1 - q^2)/(1 + q^2))}} // Simplify], {\[Theta], 0, Pi}, PlotStyle -> Black, Axes -> None, PlotRange -> All, Exclusions -> None, Mesh -> False] $\endgroup$
    – Bob Hanlon
    Commented Mar 8, 2021 at 1:39

1 Answer 1

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This seems to do the job:

ParametricPlot[{{R*((2*q)/(1 + q^2)), 
   R*((1 - q^2)/(1 + q^2))}, {(-R)*((2*q)/(1 + q^2)), 
   R*((1 - q^2)/(1 + q^2))}}, {\[Theta], 0, Pi}, 
 PlotStyle -> {{Black}}, Axes -> None, PlotRange -> All, 
 Exclusions -> None, Mesh -> False, PlotPoints -> 10, 
 WorkingPrecision -> 20]

So does the other two suggestions by Andrzej Odrzywolek.

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