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I have the following toroid surface:

tt = ParametricRegion[{Cos[u] (10 + 0.2 Sin[v]), 
    Sin[u] (10 + 0.2 Sin[v]), Cos[v]}, {{u, 0, 2 Pi}, {v, 0, 2 Pi}}];
ParametricPlot3D[Evaluate[tt[[1]]], {u, 0, 2 Pi}, {v, 0, 2 Pi}, 
 PlotRange -> {-11, 11}]

parametric torus

I want to build the solid region of the toroid (for the purposes of building a region difference and solving Laplace equation over that boundary)

I proceed by turning the torus

$\{Cos[u](R+r_f Sin[v]), Sin[u](R+r_f Sin[v]), Cos[v]\}$

into the implicit expression

$(\frac{\sqrt{x^2+y^2}-R}{r_f})^2 + z^2 \le 1$

ttSolid = 
 ImplicitRegion[((Sqrt[x^2 + y^2] - 10.0)/0.2)^2 + z^2 <= 1, {x, y, 
   z}]
RegionPlot3D[ttSolid]

But the implicit region doesn't look like a torus

broken implicit torus

Any idea what is the problem, and further, how to properly define a toroid region for NDSolve?

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  • 1
    $\begingroup$ Could you copy your code into the Question instead of giving an image of it, so that others can copy the code directly into Mathematica? Thanks. $\endgroup$ – bbgodfrey Jan 3 '15 at 18:08
  • $\begingroup$ It should be better now $\endgroup$ – lurscher Jan 3 '15 at 18:13
  • $\begingroup$ Did you want an elliptic section toroid? This gives a thin circular section 0.2 radius ParametricPlot3D[{Cos[u] (10 + 0.2 Sin[v]), Sin[u] (10 + 0.2 Sin[v]), 0.2 Cos[v]}, {u, 0, 2 Pi}, {v, 0, 2 Pi}] $\endgroup$ – Narasimham Feb 18 '16 at 16:37
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You have too few PlotPoints. Try

RegionPlot3D[((Sqrt[x^2 + y^2] - 10.0)/0.2)^2 + z^2 <= 1,
 {x, -10, 10}, {y, -10, 10}, {z, -10, 10}, PlotPoints -> 100]

enter image description here

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